A Hybrid Multiattribute Decision Making Model for ...repo.uum.edu.my/14894/1/801308.pdf ·...

Research ArticleA Hybrid Multiattribute Decision Making Model forEvaluating Studentsrsquo Satisfaction towards Hostels

Anath Rau Krishnan1 Engku Muhammad Nazri Engku Abu Bakar2

and Maznah Mat Kasim2

1Labuan Faculty of International Finance Universiti Malaysia Sabah 87000 Labuan Sabah Malaysia2Department of Decision Science School of Quantitative Sciences Universiti Utara Malaysia 06010 Sintok Kedah Malaysia

Correspondence should be addressed to Anath Rau Krishnan anath 85yahoocom

Received 18 October 2014 Accepted 13 April 2015

Academic Editor Mahyar A Amouzegar

Copyright copy 2015 Anath Rau Krishnan et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

This paper proposes a new hybrid multiattribute decision making (MADM) model which deals with the interactions that usuallyexist between hostel attributes in the process of measuring the studentsrsquo satisfaction towards a set of hostels and identifyingthe optimal strategies for enhancing their satisfaction The model uses systematic random stratified sampling approach for datacollection purpose as students dwelling in hostels are ldquonaturallyrdquo clustered by block and gender factor analysis for extracting largeset of hostel attributes into fewer independent factors 120582-measure for characterizing the interactions shared by the attributes withineach factor Choquet integral for aggregating the interactive performance scores within each factor Mikhailovrsquos fuzzy analyticalhierarchy process (MFAHP) for determining the weights of independent factors and simple weighted average (SWA) operator tomeasure the overall satisfaction score of each hostel A real evaluation involving fourteen Universiti Utara Malaysia (UUM) hostelswas carried out in order to demonstrate the modelrsquos feasibility The same evaluation was performed using an additive aggregationmodel in order to illustrate the effects of ignoring the interactions shared by attributes in hostel satisfaction analysis

1 Introduction

These days mushrooming number of universities forces eachof them to try all the possible means to survive or winin the competitive marketplace In the attempt to reflectthemselves as the best place for pursuing tertiary educationcertain universities are unceasingly putting effort in offeringaccommodations or hostels with satisfying quality as pleasinghostel condition always appears as one of the criteria for somestudents in choosing a university [1] Apart as a strategy toattract large number of students providing satisfying hostellife is also a key to encourage the students to bemore engagedwith the education environment [2] and thus could drivethem for better academic performance [3 4] Besides thestudents who are satisfied with their hostels express highersense of attachment and tend to further their studies in thesame intuition In nutshell it is essential for the universitiesto timely identify and implement appropriate strategies in

fulfilling the studentsrsquo actual needs and enhance the studentsrsquosatisfaction towards their hostels

Unfortunately identifying the optimal strategies is nota simple task as the degree of students satisfaction towardsthe hostels is normally influenced by multiple attributesFollowing are some of the hostel attributes highlighted in paststudies number of roommates [5] floor level [6] recreationarea drain condition and distance to clinic [7] thermalcomfort indoor air quality and furniture quality [8] hostelmaintenance laundry [9] internet facilities [10] fees roomsafety and room size [11] study room ATMmachine [12]

Besides the review on past literature discloses that thereis only minimal number of quantitative approaches thathave been presented to this date in determining the optimalstrategies for boosting the satisfaction towards a hostel Mostof the past studies (eg [11]) only employed factor analysis todiscover the factors that influence the studentsrsquo satisfactionbut the tool alone failed to offer other types of essential

Hindawi Publishing CorporationAdvances in Decision SciencesVolume 2015 Article ID 801308 14 pageshttpdxdoiorg1011552015801308

2 Advances in Decision Sciences

information for the hostel administration (eg type ofinteractions between attributes and weights of the factors) indeciding efficient strategies In addition in several studies theoverall satisfaction score of each hostel under evaluation wassimply computed by using the common arithmetic aggregatorwhich presumes independency among attributes Howeverin reality most of the attributes used for an assessment areinteracted to each other [13] The hostel attributes hold thesame characteristic as well

Hence it is can be concluded that there is a need for aquantitative model which mainly deals with or considers theinteractions between attributes in the process of evaluatingthe performance of a set of hostels based on studentsrsquosatisfaction in order to implement more practical strategiesin enhancing their satisfaction

This paper is organized as follows Firstly the needs forenhancing studentsrsquo satisfaction towards a hostel and theexisting problems relating to hostel evaluation are elucidatedSecondly a review on past literature focusing on the usage ofChoquet integral and its associated 120582-measure is presentedThirdly the proposed hybrid MADM model is introducedFourthly the workability of the proposed model is demon-strated by conducting a real analysis involving fourteenUniversity Utara Malaysia (UUM) hostels The contributionsof the paper and the potential future research are summarizedin the final section

2 Aggregation Phase in MADM

MADMrefers to a process of selecting ranking or classifyinga set of alternatives based on varied usually conflictingattributes [14] Applying multiple attribute utility theory(MAUT) techniques appears as a well-accepted standardquantitative means for modeling MADM problems [15]There are only three basic phases in implementing any of theMAUT techniques [16] In the first phase all the pertinentattributes for evaluating the alternatives under considerationare identified The core components of a typical MAUTmodel are comprised of a set of 119898 alternatives denoted by119860 = 119886

1 1198862 119886

119898 and a set of 119899 attributes represented

by 119862 = 1198881 1198882 119888

119899 In the following phase the weights

of attributes and performance score of each alternative withrespect to each attribute are derivedwhere some judgments orpreference values from the experts or respondents are usuallyrequired for this purpose [17] In the final phase a specificfunction namely aggregation operator is used to composethe set of weights and performance scores of each alternativeinto a single global score [18] Based on these global scoresthe alternatives can be then ranked up classified or selectedwhere an alternative with highest global score signifies themost preferred alternative for the evaluation problem

21 Aggregation Based on Choquet Integral Normally addi-tive operators such as SWA which assume independencybetween attributes [19] are simply employed for the aggre-gation purpose Unfortunately this assumption is completelyirrelevant to real scenario where in many cases the attributeshold interactive characteristics [13 20] Therefore aggrega-tion should not be always performed via additive aggregators

as they failed to model the interactions between attributes[21 22] However with the aid of Choquet integral operator[23] the interactions between attributes can be capturedduring aggregation [24 25] The usage of Choquet integralrequires a prior identification of monotone measure weights119892 These weights represent not only the importance of eachattribute but also the importance of all possible combinationsor subsets of attributes [26ndash28] As a result for a MADMproblem comprising 119899 number of attributes 2119899 number ofweights needs to be identified prior to employing Choquetintegral [29 30]

120582-measure which was introduced by Sugeno [31] appearsas one of the broadly used monotone measures due to itsease of usage mathematical soundness and modest degreeof freedom characteristics [32] Let 119862 = (119888

1 1198882 119888

119899) be a

finite set A set function 119892120582(sdot) defined on the set of the subsets

of 119862 119875(119862) is called a 120582-measure if it meets the followingconditions

(a) 119892120582 119875(119862) rarr [0 1] and 119892

120582(0) = 0 119892

120582(119862) = 1

(boundary condition)

(b) forall119860 119861 isin 119875(119862) if 119860 sube 119861 then implies 119892120582(119860) le 119892

120582(119861)

(monotonic condition)

(c) 119892120582(119860 cup 119861) = 119892

120582(119860) + 119892

120582(119861) + 120582119892

120582(119860)119892120582(119861) for all

119860 119861 isin 119875(119862) where 119860 cap 119861 = 0 and 120582 isin [minus1 +infin]

According to [33 34] consider the following

(a) If 120582 lt 0 then it implies that the attributes are shar-ing subadditive (redundancy) effects This means asignificant increase in the performance of the targetcan be achieved by only enhancing some attributes in119862 which have higher individual weights

(b) If 120582 gt 0 then it interprets that the attributes are shar-ing superadditive (synergy support) effects Thismeans a significant increase in the performance of thetarget can be achieved by simultaneously enhancingall the attributes in 119862 regardless of their individualweights

(c) If 120582 = 0 then it indicates that the attributes are non-interactive

As 119862 = 119888119895= 1198881 1198882 119888

119899 is finite the entire 120582-measure

weights can be identified using

1198921205821198881 1198882 119888

119899 =

1

120582

10038161003816100381610038161003816100381610038161003816100381610038161003816

119899

prod

119895=1

(1 + 120582119892119895) minus 1

10038161003816100381610038161003816100381610038161003816100381610038161003816

for minus 1 lt 120582 lt +infin

(1)

where 119892119895= 119892120582(119888119895) 119895 = 1 119899 denotes the individual weights

of attributes Ifsum119899119895=1

119892119895= 1 120582 = 0 whereas ifsum119899

119895=1119892119895

= 1 thevalue of 120582 can be identified by solving

1 + 120582 =

119899

prod

119895=1

(1 + 120582119892119895) (2)

Advances in Decision Sciences 3

The identified 120582-measure weights and the available per-formance scores can be then swapped into Choquet integralmodel to compute the global score of each alternative Let 119892

120582

be a monotone measure on 119862 = (1198881 1198882 119888

119899) and let 119883 =

(1199091 1199092 119909

119899) be the performance score of an alternative

with respect to each attribute in 119862 Suppose 1199091ge 1199092ge

sdot sdot sdot ge 119909119899 Then 119879

119899= (1198881 1198882 119888

119899) and the aggregated

score using Choquet integral can be determined using thefollowing equation [35]

Choquet119892120582(1199091 1199092 119909

119899)

= 119909119899sdot 119892120582(119879119899) + [119909

119899minus1minus 119909119899] sdot 119892120582(119879119899minus1

) + sdot sdot sdot

+ [1199091minus 1199092] sdot 119892120582(1198791)

= 119909119899sdot 119892120582(1198881 1198882 119888

119899) + [119909

119899minus1minus 119909119899]

sdot 119892120582(1198881 1198882 119888

119899minus1) + sdot sdot sdot + [119909

1minus 1199092] sdot 119892120582(1198881)

(3)

where119879119899relies on the performance score with respect to each

attribute For better understanding assume that the scoresof a student 119909 in three subjects (attributes) Mathematics(119909119872) Physics (119909

119875) Literature (119909

119871) are 75 80 and 50

respectively Since 119909119875

ge 119909119872

ge 119909119871 119879119899= (119875119872 119871) and

the aggregated score of the student using Choquet integralChoquet

119892120582(119909119872 119909119875 119909119871) = 119909

119871sdot 119892120582(119875119872 119871) + (119909

119872minus 119909119871) sdot

119892120582(119875119872) + (119909

119875minus 119909119872) sdot 119892120582(119875)

3 Methodology

The steps for executing the proposed hybrid model can besummarized as follows

31 Identification of Attributes In the first stage a set ofrelevant attributes to assess the hostels under considerationare identified Omitting any important attributes could leadto misleading decision

32 Data Collection Using Systematic Random StratifiedSampling Approach In the second stage a questionnaire isdesigned based on the predetermined attributes as an instru-ment to collect the required data for the evaluation Throughthe questionnaire the selected students (respondents) arerequested to express their satisfaction on each attribute withrespect to their hostels and also to state their general viewson the importance each attribute in determining a studentrsquossatisfaction based on a preset Likert scale Systematic ran-dom stratified sampling approach can be utilized in selectingthe respondents for the survey purpose According to [12]this sampling approach has been applied in many hostelevaluation studies as the students are usually or ldquonaturallyrdquogrouped into groups that is by block and gender

33 Deriving Decision Matrix (Hostels versus Attributes) Inthe third stage the decision matrix of the evaluation problemwhich shows the performance score of each hostel withrespect to each attribute is derived The performance scoreof a hostel 119894 with respect to an attribute 119895 can be identified byaveraging the satisfaction scores given by the students fromhostel 119894

34 Factor Analyzing the Data on the Importance of AttributesIn the fourth stage the large dataset on the importance ofattributes is used to perform factor analysis in order to extractthe large set of attributes into fewer independent factors

35 Constructing Simpler Hierarchal Evaluation System Byadhering to the result of factor analysis the complex hostelevaluation problem is decomposed into a simpler hierarchicalstructure which depicts the goal of the evaluation the factorswhich independently contributes to the actualization of thegoal and the interacted attributes within each factor togetherwith the hostelsrsquo performance scores extracted from thederived decision matrix in order to conduct the analysis inan organized means with better understanding

36 Identification of Monotone Measure Weights Since theattributes within each factor are being interactive Choquetintegral can be then employed in order to aggregate the per-formance scores within each factor However before applyingChoquet integral the 120582-measure weights need to be identi-fied The identification process can be simplified as follows

Firstly the experts are required to express the individualimportance or contribution of each attribute towards itscorresponding factor in linguistic terms Based on theseterms one of the eight fuzzy conversion scales as suggestedby Chen and Hwang [36] is selected in order to quantifythe linguistic terms into their respective fuzzy numbersFurther details on the principle of selecting the best scalecan be found in [36] Then the corresponding crisp valuesfor each of these fuzzy values are identified using a fuzzyscoring method as suggested in [36] Subsequently the finalindividual importance 119868

119895119901of an attribute 119895 corresponding to

factor 119901 can be determined using

119868119895119901=1

119911

119911

sum

119890=1

119868119895119890119901 (4)

Suppose119864119890= 1198641 1198642 119864

119911 represents the experts involved

in the analysis then based on (4) 119868119895119890119901

denotes the crispimportance of attribute 119895 with respect to factor 119901 that isderived from expert 119890 and 119911 implies the total number ofexperts involved These final values actually represent theindividual weights of attributes 119892

119895= 119892120582(119888119895) 119895 = 1 2 119899

Equations (2) and (1) can be then applied in order to findthe interaction parameter 120582 and 120582-measure weights of eachfactor

37 Choquet Integral for Aggregating Interactive Scores Withthe available 120582-measure weights Choquet integral model (3)can be then used to aggregate the interactive performancescores within each factor As a result by end of this stepeach hostel will have an aggregated score with respect to eachfactor (in other words each hostel will have a set of factorscores) and thus a newdecisionmatrix (hostels versus factors)can be developed for further analysis

38 Using MFAHP for Allocating Weights on IndependentFactors MFAHP [37] is used to identify the weights of inde-pendent factors due to its ability to capture the uncertainty


Table 1 Fuzzy AHP scale

Linguistic terms Corresponding TFNs DescriptionsEqually important 1 = (1 1 2) Two factors contribute equallySlightly important 3 = (2 3 4) One factor is slightly favoured over anotherStrongly important 5 = (4 5 6) One factor is strongly favoured over anotherVery strongly important 7 = (6 7 8) One factor is very strongly favoured over anotherExtremely important 9 = (8 9 9) One factor is most favoured over anotherThe intermediate values 2 = (1 2 3) 4 = (3 4 5) 6 = (5 6 7) 8 = (7 8 9) Used to compromise between two judgments

that usually embedded in humanrsquos judgments and to derivethe weights of the factors and consistency value of pairwisecomparison matrix simultaneously by simply solving thenonlinear optimizationmodel suggested in [37]With respectto the proposed model MFAHP can be executed as follows

Firstly after achieving consensus via Delphi method theexperts are required to linguistically express the mutuallyagreed judgments on the relative importance of the factorsthrough a single pairwisematrix (for sake of simplicity) basedon Saatyrsquos fuzzy AHP scale as shown in Table 1 It has tobe mentioned here that in order to avoid using reciprocaljudgment (values between 9

minus1 and 1minus1) which could lead

to rank reversal problem MFAHP only requires the expertsto offer assessment whenever factor 119891

119886is equally or more

important than 119891119887 If they consider that 119891

119886is less important

than119891119887then the assessment should be done oppositely where

119891119887is compared to 119891

119887 It can be noticed that the reciprocal

judgments are not offered in Table 1 as they are not requiredfor using MFAHP

Secondly the linguistic terms in the assessed pairwisematrix are quantified into their corresponding triangularfuzzy numbers (TFNs) Finally the suggested nonlinearoptimizationmodel (5) can be constructed based on the fuzzypairwise matrix and solved with the aid of EXCEL Solver toderive the consistency value of the matrix and the weights ofthe factors

Maximize 120583

Subject to (119898119886119887minus 119897119886119887) 120583119908119887minus 119908119886+ 119897119886119887119908119887le 0

(119906119886119887minus 119898119886119887) 120583119908119887+ 119908119886minus 119906119886119887119908119887le 0

119902

sum

119901=1

119908119901= 1 119908

119901gt 0 119901 = 1 119902

(5)

With regard to the proposedmodel 119897119886119887 119906119886119887 and 119906

119886119887represent

the lower upper and most probable values correspondingto the fuzzy judgment given by the experts when com-paring factor 119891

119886to 119891119887 Meanwhile 119908

119901denotes the weight

of factor 119891119901and 120583 represents the consistency index of the

pairwise comparison Positive 120583 value indicates that the fuzzypairwise comparison matrix is being consistent If the valueis negative then it implies that the comparisonmatrix is beinginconsistent and reevaluation on the pairwise comparison isrequired

39 SWA Operator for Aggregating Independent Factor ScoresWith the identified weights of factors the independent factorscores can be then aggregated using SWA operator (6)in order to compute the overall satisfaction score of eachhostel

119902

sum

119901=1

(119908119901119910119901) (6)

where 119908119901implies the weight of factor 119901 and 119910

119901represents

the score of a hostel with respect to factor 119901 The hostels canbe then ranked in a descending order based on their overallscores The result or information derived through the modelcan be utilized by each hostel administration to develop theoptimal strategies for enhancing the studentsrsquo satisfactiontowards their respective hostels

4 Real Application

Universiti Utara Malaysia (UUM) offers accommodationfor nearly 22000 students through its fifteen hostels whichare named after multinational companies MAS TNBTradewinds Proton Petronas EON SimeDarbyMISC TMPerwaja Bank Muamalat YAB Bank Rakyat SME andMaybank The accommodation is provided for all the under-graduate students ranging from first to final semester and thepostgraduate students are allowed to stay upon the approvalof the authorized unit In the attempt to test the feasibility ofthe proposedmodel this paper has focused on evaluating andsuggesting the strategies to improve the studentsrsquo satisfactiontowards fourteenUUMhostelsMaybank hostel which is spe-cially designed for married students was excluded from theevaluation to minimize biasness as it has different standardof facilities management and service

41 Hostel Attributes for Evaluation Through the participa-tion of five panels of experts who are familiar with UUMrsquoshostels management in a series of brainstorming sessions 22attributes as listed in Table 2 were finalized for the evaluationpurpose

42 Data Collection The questionnaire designed for thedata collection process was divided into two main sectionsfirst section to let the respondents to specify their level ofsatisfaction on each attribute with respect to their own hosteland second section to let the respondents to indicate their


Table 2 List of hostel attributes

Number Attributes Descriptions1 Hostelrsquos exterior Attractive landscape and exterior design

2 Distance to university facilities Distance to university facilities such as library post office book store bank minimarket and sports complex

3 Bus Frequent and prompt bus service hospitable driver4 Room population The room is not too crowded5 Security system Effectiveness of security guard and availability of CCTV surveillance

6 Safety Availability and condition of fire extinguishers smoke detectors and handrails forstairs

7 Room size Room is spacious8 Fees Fees per semester is reasonable value for money

9 Cafeteria Fresh hygienic variety of food with reasonable price cleanliness of cafeteria and soforth

10 Maintenance service The defect facilities and equipment in room are fixed promptly after the complaintis madeeffectiveness of service

11 Cleaning service The cleanliness level of toilets corridors exterior of building are well maintained12 Physical condition of room Ventilation lighting furniture and painting13 Wi-Fi accessibility Good Wi-Fi connection accessible everywhere within the hostel

14 Computer lab facility Organized computers are in good condition availability of printing service and soforth

15 Study room facility Quite clean encouraging environment to study and so forth16 Accessibility to ATM Easy to get to the nearest ATM17 TV facility Quality of TV number of TVs available availability of ASTRO channel packages

18 Laundry facility Laundry room and washing machines in good condition suitable and enough spaceto dry up laundry and so forth

19 Sports facility Variety of sports facilities within hostel good condition of futsalnetball courtothersports facilities within hostel

20 Management Satisfaction with principal fellows and administrative staff services

21 Washrooms and toilets Well-equipped privacy is secured sufficient numbers of toilets spacious andcomfortable toilets

22 Students representative committee (SRC) SRC really conscious about studentsrsquo problems and needs organizing valuable andinteresting programs for students throughout the semester

general views on the importance of each hostel attributefor a student Prior to conducting the actual survey thequestionnaire was pretested with a small group of studentsand based on their feedbacks some alterations were madeon the questionnaire especially some puzzling terms werereplaced with straightforward words The actual data collec-tion process was then conducted using the revised version ofthe questionnaire

The respondents from each hostel were selected usinga systematic random stratified sampling approach the stu-dents living in each hostel were naturally clustered by blockand gender The respondents from each ldquoclusterrdquo or blockwere then selected by using a systematic random samplingapproach where the students residing in every forth room inthe block were chosen for the survey purpose after randomlyselecting the first room at the first floor

As a cautionary measure during survey the actual pur-pose of the survey which was to evaluate the satisfactiontowards 14 residential halls was kept confidential as they

could offer biased judgment due to the sense of attachmentfactor Therefore the respondents were simply informed thatthe purpose of the survey was just to analyze and enhance thecurrent condition of the particular hostel Besides prior tooffering the questionnaire a screening question was asked tothe respondents to ensure they are really staying in the hosteland not there for visiting or other reasons We assisted therespondents throughout the answering process and assuredthat the questionnaires were fulfilled completely The surveywas scheduled and conducted after 5 pm as most of thestudents would be free from classes or any other campusactivities after this point of timeThe survey took almost threeweeks to be accomplished with the help of two male andfemale postgraduate students

43 Decision Matrix (Hostels versus Attributes) By averagingthe scores given by the students from each hostel with respectto each attribute the decision matrix as shown in Table 3 wasderived


Table 3 Hostels versus attributes

Exterior Distance Bus Population Security Safety Size Fees Cafeteria Maintenance CleaningBR1 5549 4703 3773 7043 4673 5685 6255 4830 3045 4890 5475SME 5415 4575 4620 7230 5303 6255 6923 5340 5497 6098 5445SD2 5573 5865 4763 6570 4110 5618 5610 4822 3000 4560 4350EON 5475 5640 4928 6690 4095 5100 5587 5115 4995 5092 5227MT3 5175 5535 5978 4800 3998 4710 3855 4163 4912 4845 4703YAB 5018 4785 5325 5873 3915 4673 5250 4800 4350 4372 5310PR4 4793 5888 3675 6555 3735 4950 5483 4658 4500 4613 3885MAS 5280 4965 4718 6915 4493 5213 6540 4912 3893 4642 3975PS5 5663 6930 4305 6615 4673 5460 5490 4830 4800 4838 4860TNB 5078 5790 4140 6473 4583 5445 5873 5415 4793 5423 4433TS6 4590 6015 4237 6068 3420 4687 5205 4230 3795 4395 4793PJ7 5258 5940 5670 7297 3818 5933 5955 5108 6262 5213 5820MISC 5565 4935 5385 6923 3427 4860 5820 5055 5047 4815 5325TM 4905 5040 5587 7425 3922 4957 5925 4815 2970 4875 5430

Physical Wi-Fi Lab Study room ATM TV Laundry Sports Management Washroom SRCBR1 5783 3112 5775 4838 6180 4020 3915 5303 5243 5175 4192SME 6885 3495 5767 5295 5288 3060 3945 5573 5430 5632 4687SD2 5985 4620 5775 3795 4133 3150 2985 4350 4860 4088 4755EON 5902 5670 5947 4448 4763 3975 4455 5295 5722 4785 5258MT3 4845 3720 5835 3930 6120 3975 4343 4890 4898 4912 4703YAB 5452 4410 4343 4433 5168 3368 4597 5168 5344 4950 5520PR4 6233 4695 5722 4673 4230 3848 4613 4095 4275 3195 3713MAS 5677 5685 6248 4358 3015 2310 4065 3825 4725 4035 4313PS5 6098 5640 6675 4822 6518 5565 5670 5182 5085 5198 5205TNB 5925 5063 5745 4650 4035 2685 3495 3870 4710 3900 4335TS6 5992 4770 5317 4845 5213 5280 4845 4905 5130 4875 4763PJ7 6615 5550 6383 4440 2797 4020 4350 4440 5055 4568 4943MISC 5288 4793 6105 3472 2250 2895 3112 3945 4133 3533 5303TM 6503 5632 6622 4620 2880 3713 4425 4057 4620 4530 52801BR = Bank Rakyat 2SD = Sime Darby 3MT = Muamalat 4PR = Proton 5PS = Petronas 6TS = Tradewinds and 7PJ = Perwaja

44 Conducting Factor Analysis Before factor analyzingthe large dataset on the importance of attributes obtainedthrough the second section of the questionnaire the suitabil-ity of the data for factor analysis was verified with the aidof SPSS software The inspection on the correlation matrixrevealed the presence of many coefficients of 03 and aboveBesides the Kaiser-Meyer-Olkin (KMO) value of the datasetexceeded the recommended value 06 and Bartlettrsquos Test ofSphericity reached statistical significance as the 119901 value wasless than 005 These three circumstances indicated that thedataset was suitable for factor analysis

By performing factor analysis the large set of hostelattributes was clustered into five independent factors How-ever it has to be emphasized that the attributes within eachextracted factor are still interacted to each other The resultof factor analysis for this study can be further detailed asfollows (refer to Table 4) Extraction through principal com-ponent analysis revealed the presence of five common factorswith eigenvalues exceeding one explaining 30014 8487

5667 5522 and 5291 of the variance respectivelyThe total variance explained reached 54982 To aid in theinterpretation of these five common factors varimax rotationwas performed

Five attributes ldquocleaningrdquo ldquowashroomsrdquo ldquomaintenancerdquoldquomanagementrdquo and ldquoSRCrdquo which had higher loading at factor1 were renamed as service factor (119891

1) Meanwhile ldquoTVrdquo

ldquolaundryrdquo ldquoATMrdquo ldquosportsrdquo and ldquostudy roomrdquo which showedhigher loading at factor 2 were relabeled as ldquofacilityrdquo factor(1198912) ldquoPopulationrdquo ldquosizerdquo ldquophysicalrdquo ldquolabrdquo and ldquoWi-Firdquo which

were clustered into factor 3 were identified as conveniencefactor (119891

3) and ldquobusrdquo ldquodistancerdquo ldquocafeteriardquo ldquoexteriorrdquo and

ldquofeesrdquo were classified as value for money factor (1198914) Finally

ldquosecurityrdquo and ldquosafetyrdquo which had higher loading at factor 5were renamed as precaution factor (119891

5)

45 Hierarchical Evaluation System for Analyzing UUM Hos-tels Table 5 is hierarchical structure constructed based onthe result of factor analysis used to systematically evaluate


Table 4 Result of factor analysis

Total variance explained Rotated component matrix

Component Initial eigenvalues Attributes ComponentTotal of variance Cumulative 1 2 3 4 5

1 6603 30014 30014 Cleaning (11988811) 749

2 1867 8487 38501 Washroom (11988821) 717 379

3 1247 5667 44169 Maintenance (11988810) 612

4 1215 5522 49691 Management (11988820) 602 341

5 1164 5291 54982 SRC (11988822) 527

6 929 4222 59204 TV (11988817) 786

7 871 3961 63166 Laundry (11988818) 723

8 777 3530 66696 ATM (11988816) 665

9 768 3489 70184 Sports (11988819) 638

10 710 3225 73410 Study room (11988815) 435 346

11 649 2949 76359 Population (1198884) 673

12 594 2701 79060 Size (1198887) 647 412

13 582 2644 81704 Physical (11988812) 409 583

14 570 2591 84295 Lab (11988814) 561 412

15 515 2339 86635 Wi-Fi (11988813) 547 427

16 490 2229 88864 Bus (1198883) 307 650

17 476 2163 91027 Distance (1198882) 329 649

18 458 2082 93109 Cafeteria (1198889) 449 453

19 427 1941 95050 Exterior (1198881) 453 448

20 391 1779 96829 Fees (1198888) 355 391

21 375 1705 98535 Security (1198885) 756

22 322 1465 100000 Safety (1198886) 684

the studentsrsquo satisfaction towards the 14 hostels It has to beemphasized that Table 5 exemplifies that the attributes withineach factor are interacted to each other whereas the factorsare playing independent roles in determining the studentsrsquooverall satisfaction

46 Identification of 120582-Measure Weights Based on the judge-ments from the experts the 11-point scale as shown inTable 6 was chosen to aid the process of identifying the indi-vidual weights of attributes The Identification of aggregatedor final individual weights of the attributes within each factorbased on the judgements from the five experts is summarizedin Table 7

With the available individual weights (2) and (3) werethen used in order to obtain the interaction parameter 120582and monotone measure weights of each factor as presentedin Table 8

Through the proposedmodel by extracting the attributesinto fewer independent factors the actual number of mono-tone measure weights which need to be identified priorto applying Choquet integral was reduced from 4194304(213) weights to 132 (25 + 2

5+ 25+ 25+ 22) weights In

general the proposed model reduces the required numberof monotone measure weights from 2

119899 to sum119902

119901=12|119891119901| where

119891119901= (1198911 1198911 119891

119902) is the set of extracted factors 119902 denotes

the total number of factors and |119891119901| represents the number

of attributes within factor 119901

47 Aggregation Using Choquet Integral By aggregating theinteractive scores within each factor using the identifiedmonotone measure and Choquet integral model (3) a newdecision matrix (14 hostels versus 5 factors) as shown inTable 10 was attained

48 Identifying the Weights of Independent Hostel FactorsAfter achieving consensus through Delphi method the fiveexperts have linguistically expressed their judgments on therelative importance of the hostel factors through a singlepairwise matrix based The linguistic pairwise matrix wasthen converted into fuzzy pairwise matrix as shown inTable 9 based on fuzzy AHP scale (refer to Table 1) It can benoticed that since the ldquovalue for moneyrdquo was found to be lessimportant than ldquoprecautionrdquo factor the evaluation was donevice versa to avoid using reciprocal values

Based on the fuzzy pairwise comparison the suggestednonlinear optimizationmodel (5)was constructed and solvedwith the aid of EXCEL Solver Following result was obtainedweight of service factor 119908

1= 0374 weight of facility factor

1199082

= 0309 weight of convenience factor 1199083

= 0147weight of value for money factor 119908

4= 0065 weight of


Table5Hierarchicalsystem

fore

valuatingstu

dentsrsquosatisfactiontowards

UUM

hoste

ls

Goal

Evaluatin

gperfo

rmance

ofho

stelsbasedon

studentsrsquosatisfaction

Factors

Service

Con

venience

Precautio

nFacility

Valuefor

mon

eyAttributes

119888 11

119888 21

119888 10

119888 20

119888 22

119888 4119888 7

119888 12

119888 14

119888 13

119888 5119888 6

119888 17

119888 18

119888 16

119888 19

119888 15

119888 3119888 2

119888 9119888 1

119888 8

Bank

Rakyat

5475

5175

4890

5243

4192

7043

6255

5783

5775

3112

4673

5685

4020

3915

6180

5303

4838

3773

4703

3045

5549

4830

SME

544

55632

6098

5430

4687

7230

6923

6885

5767

3495

5303

6255

306

03945

5288

5573

5295

4620

4575

5497

5415

5340

SimeD

arby

4350

4088

4560

4860

4755

6570

5610

5985

5775

4620

4110

5618

3150

2985

4133

4350

3795

4763

5865

300

05573

4822

EON

5227

4785

5092

5722

5258

6690

5587

5902

5947

5670

4095

5100

3975

4455

4763

5295

444

84928

564

04995

5475

5115

Muamalat

4703

4912

4845

4898

4703

4800

3855

4845

5835

3720

3998

4710

3975

4343

6120

4890

3930

5978

5535

4912

5175

4163

YAB

5310

4950

4372

5344

5520

5873

5250

5452

4343

4410

3915

4673

3368

4597

5168

5168

4433

5325

4785

4350

5018

4800

Proton

3885

3195

4613

4275

3713

6555

5483

6233

5722

4695

3735

4950

3848

4613

4230

4095

4673

3675

5888

4500

4793

4658

MAS

3975

4035

464

24725

4313

6915

6540

5677

6248

5685

4493

5213

2310

4065

3015

3825

4358

4718

4965

3893

5280

4912

Petro

nas

4860

5198

4838

5085

5205

6615

5490

6098

6675

564

04673

546

05565

5670

6518

5182

4822

4305

6930

4800

5663

4830

TNB

4433

3900

5423

4710

4335

6473

5873

5925

5745

5063

4583

544

52685

3495

4035

3870

4650

4140

5790

4793

5078

5415

Tradew

inds

4793

4875

4395

5130

4763

606

85205

5992

5317

4770

3420

4687

5280

4845

5213

4905

4845

4237

6015

3795

4590

4230

Perw

aja

5820

4568

5213

5055

4943

7297

5955

6615

6383

5550

3818

5933

4020

4350

2797

444

0444

05670

5940

6262

5258

5108

MISC

5325

3533

4815

4133

5303

6923

5820

5288

6105

4793

3427

4860

2895

3112

2250

3945

3472

5385

4935

5047

5565

5055

TM5430

4530

4875

4620

5280

7425

5925

6503

6622

5632

3922

4957

3713

4425

2880

4057

4620

5587

504

02970

4905

4815


Table 6 11-point linguistic scale for expressing individual impor-tance of attributes

Linguistic terms Fuzzy numbersCorresponding crispvalues identified via

fuzzy scoringapproach

Exceptionally low (EL) (0 0 01) 0045Extremely low (ExL) (0 01 02) 0135Very low (VL) (0 01 03 05) 0255Low (L) (01 03 05) 0335Below average (BA) (03 04 05) 0410Average (A) (03 05 07) 05Above average (AA) (05 06 07) 0590High (H) (05 07 09) 0665Very high (VH) (05 07 09 1) 0745Extremely high (ExH) (08 09 1) 0865Exceptionally high (EH) (09 1 1) 0955

precaution factor 1199085= 0106 consistency index 120583 = 0634

The value of 120583 implied that the pairwise comparison matrixwas consistent

49 Aggregation Using SWAOperator The identified weightsof factors and available factor scores were precisely replacedinto SWAmodel (6) to compute the overall satisfaction scoreof each hostel The satisfaction score of each hostel and theirranking are summarized in Table 10

410 Proposed Hybrid MADM Model versus Classical SWAOperator In this section the same hostel satisfaction prob-lemwas evaluated using a classical additive aggregation oper-ator or to be precise by only employing the common SWAoperator and the obtained result was comparedwith the resultgenerated by the proposed model The motive of choosingclassical SWA was to mainly demonstrate the implicationof discounting the interactions between attributes in hostelsatisfaction analysis

As SWA assumes independency between attributes it iscrucial to assure the sum of weights of the 22 attributes isbeing additive (or equal to one) To derive the weights forSWA firstly the nonadditive individual weights of attributeswithin each factor (refer to Table 7) were normalized toensure the sum of the weights is equal to one Thesenormalized weights were just represented the contributionof attributes towards their respective factor Hence the finaladditive weight of each attribute (contribution of attributestowards overall satisfaction) was then computed by multi-plying an attributersquos normalized weight with the weight ofits respective factor Note that the weights of factors donot demand any normalization as they were already in theadditive state Table 11 recapitulates the process involved indetermining the required additive weights of attributes forapplying SWA operator

The identified additive weights and the performancescores as presented in Table 3 were then swapped into

SWA model (6) to compute the overall satisfaction scoreof each hostel Table 12 shows the disparities on the overallsatisfaction scores and ranking of the hostels resulting fromthe proposed model and conventional SWA

It can be concluded that there was a significant variationbetween the result generated through the proposed modeland classical SWA as the latter model ignores the usualinteractions that exist between hostel attributes Besidesthe additive weights used for SWA failed to express theinteractions shared by the attributes and thus could lead tothe implementation of inefficient satisfaction enhancementstrategies

411 Discussion on the Result Through the proposed modelwith the help of factor analysis it was discovered that theactual determinants of the studentsrsquo satisfaction towards thehostels are service facility convenience value for moneyand precaution aspects However it was understood that theprioritization on these determinants is as follows service(0374) ≻ facility (0309) ≻ convenience (0147) ≻ precaution(0106)≻ value formoney (0065)where≻means ldquois preferredor superior tordquo Therefore in order to enhance the studentsrsquosatisfaction a hostel can simply focus on the four crucialaspects service facility convenience and precaution aspectswhich are independent of each other

The interaction parameter 120582 = minus0956 indicates that inorder to improve a hostelrsquos performance in term of service itis enough to simultaneously enhance some of the attributeswhich have higher individual weights management andmaintenance In other words by only enhancing manage-ment and maintenance attributes a significant improvementin the aspect of service can be achievedThe experts involvedin the analysis accepted this fact by stating that a goodmanagement and maintenance team can ensure the otherattributes within the factor are being at the satisfactorylevel According to them a good management team oftenmonitors the cleanliness level of the hostel and motivatesthe studentsrsquo representative committee (SRC) to frequentlyorganize fruitful activities for the students Besides a caringmanagement and effective maintenance team timely ensurethe washrooms and toilets are being in good condition

Meanwhile 120582 = 0035 implies that in order to improvea hostelrsquos performance with respect to facility factor all theattributes within the factor need to be enhanced simulta-neously regardless of their individual weights TV laundryATM sports amenities and study roomThe similar strategyapplies for improving the precaution level of a hostel as it hasa positive interaction parameter (120582 = 0140)

The value 120582 = minus0943 shows that in order to attaindrastic improvement in convenience aspect it is sufficient tosimultaneously enhance some of the attributes which havehigher individual weights physical condition of the roomandWi-Fi accessibility According to the experts a good furniturearrangement ventilation paint colours and lighting havethe capability to form spacious and comforting in-roomenvironment even if the room is small (refers to ldquoroom sizerdquoattribute) or crowded (refers to ldquoroom populationrdquo attribute)Besides in current trend of education which largely relieson internet facility a fine Wi-Fi accessibility would enable


Table 7 Identification of individual weights of attributes within each factor

Factors CriteriaDegree of Importance Importance Aggregated

individualweights

(in linguistic terms) (in crisp values after defuzzyfying fuzzy numbers)1198641

1198642

1198643

1198644

1198645 119864

11198642

1198643

1198644

1198645

Service

Cleaning VH AA A BA A 0745 059 05 041 05 0549Washroom BA A VL A ExL 041 05 0255 05 0135 0360Maintenance H A H A H 0665 05 0665 05 0665 0599Management H EH ExH A L 0665 0955 0865 05 0335 0664

SRC ExL EL ExL ExL EL 0135 0045 0135 0135 0045 0099

Facility

TV EL VL EL ExL ExL 0045 0255 0045 0135 0135 0123Laundry VL VL VL ExL VL 0255 0255 0255 0135 0255 0231ATM ExL VL EL ExL ExL 0135 0255 0045 0135 0135 0141Sports VL BA VL L A 0255 041 0255 0335 05 0351

Study room ExL ExL VL EL ExL 0135 0135 0255 0045 0135 0141

Convenience

Population ExL L A L ExL 0135 0335 05 0335 0135 0288Size A BA BA A H 05 041 041 05 0665 0497

Physical VH H A AA BA 0745 0665 05 059 041 0582Lab ExL L VL L VL 0135 0335 0255 0335 0255 0263Wi-Fi H A A H H 0665 05 05 0665 0665 0599

Value for money

Bus ExH A AA BA A 0865 05 059 041 05 0573Distance BA BA L L A 041 041 0335 0335 05 0398Cafeteria H A A AA A 0665 05 05 059 05 0551Exterior L ExL AA AA BA 0335 0255 059 059 041 0436Fees H A VH H AA 0665 05 0745 0665 059 0633

Precaution Security H H AA A AA 0665 0665 059 05 059 0602Safety A BA L L VL 05 041 0335 0335 0255 0367

the students to access the required information from anycorners of the hostel and reduces the studentsrsquo dependencyon computer lab and also ensures them not to concern toomuch about the quality of the lab service

According to the proposed model the ranking of theresidential halls based on global satisfaction score is asfollows SME ≻ Petronas ≻ Bank Rakyat ≻ EON ≻ Perwaja ≻YAB≻Tradewinds≻TM≻TNB≻Muamalat≻ SimeDarby≻Proton ≻MAS ≻MISC

SME Petronas Bank Rakyat EON and Perwaja ruledthe top five positions as they had satisfactory scores onservice facility and convenience aspects which are themain determinants of studentsrsquo satisfaction towards a hostelPetronas has the potential to be in the top in the future ifthe hostelrsquos administration put major effort on improving itsservice level by simultaneously enhancing the managementand maintenance efficiency while retaining its performancein both facility and convenience aspects Perwaja also hasthe opportunity to be in the lead if the administrationsimultaneously improves all the attributes within facilityfactor (TV laundry ATM sports and study room) regardlessof their individual weights as they shared superadditive effect

Tradewinds which obtained the lowest precaution scorecertainly can be in top 5 positions in future if the hosteltightens its security system and adds more safety equipmentor features while maintaining its performance on servicefacility and convenience aspects

Muamalat Sime Darby Proton MAS and MISC whichare being at the bottom five positions attained poor scoresmainly on service and facility aspects thus appropriatestrategies should be planned to achieve perfection in thesetwo aspects They need to assure the management and main-tenance doing their job effectively in fulfilling the studentsrsquoneeds Besides they should offer better TV laundry ATMsports and study room facilities to their students However itwas discovered that MISC needs to take an extra effort whereit should also focus on stepping up the precaution measureswhich can be achieved by simultaneously enhancing theexisting security system and safety features

The same evaluation is also carried out by only usingthe additive SWA operator and a different set of scores andrankingwas obtainedThis shows that neglecting interactionsbetween hostel attributes could offer flawed informationwhich consequently leads to wrong decisions Therefore


Table 8 120582-measure weights for each factor

Service (120582 = minus0956) Facility (120582 = 0035) Convenience (120582 = minus0943) Value for money (120582 = minus0972)Subsets Weights Subsets Weights Subsets Weights Subsets Weights 0000 0000 0000 000011988811 0549 119888

17 0123 119888

4 0288 119888

3 0573

11988821 0360 119888

18 0231 119888

7 0497 119888

2 0398

11988811 11988821 0720 119888

17 11988818 0355 119888

4 1198887 0650 119888

3 1198882 0749

11988810 0599 119888

16 0141 119888

12 0582 119888

9 0551

11988811 11988810 0834 119888

17 11988816 0265 119888

4 11988812 0712 119888

3 1198889 0817

11988821 11988810 0753 119888

18 11988816 0373 119888

7 11988812 0806 119888

2 1198889 0736

11988811 11988821 11988810 0907 119888

17 11988818 11988816 0498 119888

4 1198887 11988812 0875 119888

3 1198882 1198889 0899

11988820 0664 119888

19 0351 119888

14 0263 119888

1 0436

11988811 11988820 0865 119888

17 11988819 0476 119888

4 11988814 0480 119888

3 1198881 0766

11988821 11988820 0795 119888

18 11988819 0585 119888

7 11988814 0637 119888

2 1198881 0665

11988811 11988821 11988820 0927 119888

17 11988818 11988819 0710 119888

4 1198887 11988814 0752 119888

3 1198882 1198881 0868

11988810 11988820 0883 119888

16 11988819 0494 119888

12 11988814 0701 119888

9 1198881 0753

11988811 11988810 11988820 0968 119888

17 11988816 11988819 0619 119888

4 11988812 11988814 0798 119888

3 1198889 1198881 0907

11988821 11988810 11988820 0939 119888

18 11988816 11988819 0729 119888

7 11988812 11988814 0869 119888

2 1198889 1198881 0860

11988811 11988821 11988810 11988820 0995 119888

17 11988818 11988816 11988819 0855 119888

4 1198887 11988812 11988814 0921 119888

3 1198882 1198889 1198881 0954

11988822 0099 119888

15 0141 119888

13 0599 119888

8 0633

11988811 11988822 0596 119888

17 11988815 0265 119888

4 11988813 0724 119888

3 1198888 0853

11988821 11988822 0425 119888

18 11988815 0373 119888

7 11988813 0815 119888

2 1198888 0786

11988811 11988821 11988822 0751 119888

17 11988818 11988815 0498 119888

4 1198887 11988813 0882 119888

3 1198882 1198888 0921

11988810 11988822 0641 119888

16 11988815 0283 119888

12 11988813 0852 119888

9 1198888 0845

11988811 11988810 11988822 0854 119888

17 11988816 11988815 0407 119888

4 11988812 11988813 0909 119888

3 1198889 1198888 0947

11988821 11988810 11988822 0781 119888

18 11988816 11988815 0516 119888

7 11988812 11988813 0950 119888

2 1198889 1198888 0916

11988811 11988821 11988810 11988822 0920 119888

17 11988818 11988816 11988815 0641 119888

4 1198887 11988812 11988813 0980 119888

3 1198882 1198889 1198888 0979

11988820 11988822 0762 119888

19 11988815 0494 119888

14 11988813 0713 119888

1 1198888 0801

11988811 11988820 11988822 0882 119888

17 11988819 11988815 0619 119888

4 11988814 11988813 0808 119888

3 1198881 1198888 0928

11988821 11988820 11988822 0819 119888

18 11988819 11988815 0729 119888

7 11988814 11988813 0876 119888

2 1198881 1198888 0889

11988811 11988821 11988820 11988822 0938 119888

17 11988818 11988819 11988815 0855 119888

4 1198887 11988814 11988813 0926 119888

3 1198882 1198881 1198888 0967

11988810 11988820 11988822 0898 119888

16 11988819 11988815 0637 119888

12 11988814 11988813 0904 119888

9 1198881 1198888 0923

11988811 11988810 11988820 11988822 0976 119888

17 11988816 11988819 11988815 0763 119888

4 11988812 11988814 11988813 0946 119888

3 1198889 1198881 1198888 0982

11988821 11988810 11988820 11988822 0949 119888

18 11988816 11988819 11988815 0873 119888

7 11988812 11988814 11988813 0977 119888

2 1198889 1198881 1198888 0964

11988811 11988821 11988810 11988820 11988822 1000 119888

17 11988818 11988816 11988819 11988815 1000 119888

4 1198887 11988812 11988814 11988813 1000 119888

3 1198882 1198889 1198881 1198888 1000

Safety (120582 = 0140)Subsets Weights 00001198885 0602

1198886 0367

1198885 1198886 1000

Table 9 Fuzzy pairwise comparison matrix between hostel factors

Service Facility Convenience Value for money PrecautionService (1 1 1) (1 2 3) (2 3 4) (4 5 6) (3 4 5)Facility mdash (1 1 1) (1 2 3) (3 4 5) (2 3 4)Convenience mdash mdash (1 1 1) (2 3 4) (1 2 3)Value for money mdash mdash mdash (1 1 1) mdashPrecaution mdash mdash mdash (1 2 3) (1 1 1)


Table 10 Overall satisfaction score of each hostel and their ranking

Factorshostels Service(1199081= 0374)

Facility(1199082= 0309)

Convenience(1199083= 0147)

Value formoney

(1199084= 0065)

Precaution(1199085= 0106) Final scores Ranking

Bank Rakyat 5337 4870 6105 4991 5044 5257 3SME 5860 4789 6679 5385 5652 5602 1Sime Darby 4751 3765 5981 5373 4663 4663 11EON 5536 4732 6086 5404 4464 5252 4Muamalat 4883 4680 4890 5629 4259 4809 10YAB 5275 4699 5409 5127 4193 4998 6Proton 4414 4285 6068 5136 4181 4644 12MAS 4627 3647 6406 5036 4757 4631 13Petronas 5091 5479 6261 5867 4962 5425 2TNB 5091 3764 5998 5437 4899 4822 9Tradewinds 5002 4972 5763 5024 3885 4993 7Perwaja 5508 4128 6626 5998 4594 5186 5MISC 5004 3304 6021 5384 3953 4546 14TM 5159 4008 6651 5247 4302 4943 8

Table 11 Identification of additive weights of attributes for SWA operator

Factors Attributes Individual weights Normalized weights Final weights

Service (0374)

Cleaning 0549 0242 0090Washroom 0360 0159 0059Maintenance 0599 0264 0099Management 0664 0292 0109

SRC 0099 0044 0016SUM 2271 1000

Facility (0309)

TV 0123 0125 0039Laundry 0231 0234 0072ATM 0141 0143 0044Sports 0351 0356 0110

Study room 0141 0143 0044SUM 0987 1000

Convenience (0147)

Population 0288 0129 0019Size 0497 0223 0033

Physical 0582 0261 0038Lab 0263 0118 0017Wi-Fi 0599 0269 0039SUM 2229 1000

Value for money (0065)

Bus 0573 0221 0014Distance 0398 0154 0010Cafeteria 0551 0213 0014Exterior 0436 0168 0011Fees 0633 0244 0016SUM 2591 1000

Precaution (0106)Security 0602 0621 0066Safety 0367 0379 0040SUM 0969 1000

SUM 1000


Table 12 Proposed model versus classical SWA operator

Hostels Proposed model Classical SWAOverall scores Ranking Overall scores Ranking

Bank Rakyat 5257 3 5024 4SME 5602 1 5369 1Sime Darby 4663 11 4473 11EON 5252 4 5098 3Muamalat 4809 10 4680 9YAB 4998 6 4825 6Proton 4644 12 4412 13MAS 4631 13 4470 12Petronas 5425 2 5290 2TNB 4822 9 4595 10Tradewinds 4993 7 4821 7Perwaja 5186 5 4983 5MISC 4546 14 4296 14TM 4943 8 4741 8

the proposed model is recommended in order to identifymore practical ranking and to develop the optimal strategiesfor enhancing studentsrsquo satisfaction towards each hostel as thehostel attributes are normally interacted to each other

5 Conclusion and Recommendation

Thispaper has finally introduced a newhybridMADMmodelwhich considers the interactions between hostel attributeswhile evaluating the studentsrsquo satisfaction towards a set ofhostels The execution of the model can be simplified intofollowing steps identifying hostel evaluation attributes datacollection using simple random stratified sampling approachconstructing the performance matrix by averaging data onsatisfaction factor analyzing the data on importance ofattributes to reduce the attributes into independent factorsexemplifying the evaluation problem via simpler hierarchi-cal system diagram identifying the interaction parameterand monotone measure within each factor aggregating theinteractive scores within each factor using Choquet integralassigningweights on each independent factors usingMFAHPand finally the overall satisfaction score of each hostel isby aggregating the independent factor scores using SWAoperator

Apart from dealing with the interactions betweenattributes the model is able to discover the main determi-nants of hostel satisfaction together with their weights andalso reduces the actual number of 120582-measure weights whichneed to be determined prior to using Choquet integral from2119899 to sum119902

119901=12|119891119901| where 119899 represents the number of attributes

119891119901= (1198911 1198911 119891

119902) represents the set of extracted factors 119902

is the total number of factors and |119891119901| denotes the number of

attributes within factor 119901The feasibility of the model was verified by carrying out

a real evaluation problem involving fourteen UUM hostelswhere some potential strategies for enhancing the studentsrsquosatisfaction towards certain hostels were proposed Thesame hostel evaluation problem was assessed by only using

the additive SWA operator which simply assumes indepen-dency between attributes and a different set of satisfactionscores and ranking of hostels were obtained Therefore itis advisable to use the proposed model for analyzing hostelsatisfaction problem in order to identifymore practical hostelrankings and to develop strategies with better efficiencyfor enhancing the studentsrsquo satisfaction towards each hostelas in reality most of the hostels attributes hold interactivecharacteristics

In future besides analyzing studentsrsquo satisfaction towardshostels the proposed model can be also applied in otherdomains where the ranking of alternatives and the enhance-ment strategies need to be identified by considering multipleinteractive attributes However the sampling approach mayvary based on the objective of the evaluation problem ortarget population

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research is supported by Ministry of Higher Educationof Malaysia under Fundamental Research Grant Scheme(FRGS) with SO Code 11877 and Universiti Utara Malaysiathrough postgraduate incentive grant

References

[1] H Oppewal Y Poria N Ravenscroft and G Speller ldquoStudentpreferences for university accommodation an application of thestated preference approachrdquo in Housing Space and Quality ofLife R G Mira D L Uzzell J E Real and J Romay Eds pp113ndash124 Ashgate Publishing Surrey UK 2005

[2] W A AstinWhat Matters in College Four Critical Years Revis-ited Jossey-Bass San Francisco Calif USA 1993


[3] R Moos and E Lee ldquoComparing residence hall and indepen-dent living settingsrdquo Research in Higher Education vol 11 no 3pp 207ndash221 1979

[4] D Amole ldquoCoping strategies for living in student residentialfacilities in Nigeriardquo Environment and Behavior vol 37 no 2pp 201ndash219 2005

[5] R M Baron D R Mandel C A Adams and L M GriffenldquoEffects of social density in university residential environ-mentsrdquo Journal of Personality and Social Psychology vol 34 no3 pp 434ndash446 1976

[6] C J Holahan and B L Wilcox ldquoResidential satisfaction andfriendship formation in high- and low-rise student housing aninteractional analysisrdquo Journal of Educational Psychology vol70 no 2 pp 237ndash241 1978

[7] N B A Bakar and N M B A Bakart ldquoStudentsrsquo satisfactiontowards the university accommodation and public amenitiesrdquoin Proceedings of the International Conference on Constructionand Building Technology Kuala Lumpur Malaysia June 2008

[8] M A Hassanain ldquoOn the performance evaluation of sustain-able student housing facilitiesrdquo Journal of Facilities Manage-ment vol 6 no 3 pp 212ndash225 2008

[9] D Amole ldquoResidential satisfaction in studentsrsquo housingrdquo Jour-nal of Environmental Psychology vol 29 no 1 pp 76ndash85 2009

[10] Y Adewunmi M Omirin F Famuyiwa and O FarinloyeldquoPost-occupancy evaluation of postgraduate hostel facilitiesrdquoFacilities vol 29 no 3 pp 149ndash168 2011

[11] F Khozaei N Ayub A S Hassan and Z Khozaei ldquoThe factorspredicting studentsrsquo satisfaction with university hostels casestudy Universiti SainsMalaysiardquoAsian Culture andHistory vol2 no 2 pp 148ndash158 2010

[12] N U Najib N A Yusof and Z Osman ldquoMeasuring satisfactionwith student housing facilitiesrdquoAmerican Journal of Engineeringand Applied Sciences vol 4 no 1 pp 52ndash60 2011

[13] J-L Marichal ldquoAn axiomatic approach of the discrete Choquetintegral as a tool to aggregate interacting criteriardquo IEEE Trans-actions on Fuzzy Systems vol 8 no 6 pp 800ndash807 2000

[14] C L Hwang and K Yoon ldquoIntroductionrdquo inMultiple AttributeDecision Making vol 186 of Lecture Notes in Economics andMathematical Systems pp 1ndash15 Springer Berlin Germany 1981

[15] S Mussi ldquoFacilitating the use of multi-attribute utility theoryin expert systems an aid for identifying the right relativeimportance weights of attributesrdquo Expert Systems vol 16 no2 pp 87ndash1102 1999

[16] E Triantaphyllou Multi-Criteria Decision Making Methodolo-gies A Comparative Study vol 44 of Applied OptimizationKluwer Academic Publishers 2000

[17] E U Choo B Schoner and W C Wedley ldquoInterpretation ofcriteria weights in multicriteria decision makingrdquo Computers ampIndustrial Engineering vol 37 no 3 pp 527ndash541 1999

[18] J-LMarichalAggregation operator formulticriteria decision aid[PhD thesis] University of Liege Liege Belgium 1999

[19] M Detyniecki Mathematical aggregation operators and theirapplication to video querying [PhD thesis] University of ParisVI Paris France 2000

[20] H Bendjenna P-J Charre and N E Zarour ldquoUsing multi-criteria analysis to prioritize stakeholdersrdquo Journal of Systemsand Information Technology vol 14 no 3 pp 264ndash280 2012

[21] D Ralescu and G Adams ldquoThe fuzzy integralrdquo Journal ofMathematical Analysis and Applications vol 75 no 2 pp 562ndash570 1980

[22] G-H Tzeng Y-P Ou Yang C-T Lin and C-B Chen ldquoHier-archical MADM with fuzzy integral for evaluating enterpriseintranet web sitesrdquo Information Sciences vol 169 no 3-4 pp409ndash426 2005

[23] G Choquet ldquoTheory of capacitiesrdquoAnnales de lrsquoInstitut Fouriervol 5 pp 131ndash295 1953

[24] M Grabisch ldquoFuzzy integral in multicriteria decision makingrdquoFuzzy Sets and Systems vol 69 no 3 pp 279ndash298 1995

[25] M Grabisch ldquoFuzzy integral as a flexible and interpretabletool of aggregationrdquo in Aggregation and Fusion of ImperfectInformation B Bouchon-Meunier Ed vol 12 of Stud FuzzinessSoft Comput pp 51ndash72 Physica Heidelberg Germany 1998

[26] M Grabisch andM Roubens ldquoApplication of the Choquet inte-gral in multicriteria decision makingrdquo in Fuzzy Measures andIntegrals Theory and Applications M Grabisch T Murofushiand M Sugeno Eds pp 415ndash434 Physica Berlin Germany2000

[27] S Angilella S Greco F Lamantia and BMatarazzo ldquoAssessingnon-additive utility for multicriteria decision aidrdquo EuropeanJournal of Operational Research vol 158 no 3 pp 734ndash7442004

[28] G Beliakov and S James ldquoCitation-based journal ranks the useof fuzzy measuresrdquo Fuzzy Sets and Systems vol 167 no 1 pp101ndash119 2011

[29] I Kojadinovic ldquoEstimation of the weights of interacting criteriafrom the set of profiles by means of information-theoreticfunctionalsrdquo European Journal of Operational Research vol 155no 3 pp 741ndash751 2004

[30] P Meyer and M Roubens ldquoOn the use of the Choquet integralwith fuzzy numbers inmultiple criteria decision supportrdquo FuzzySets and Systems vol 157 no 7 pp 927ndash938 2006

[31] M Sugeno Theory of fuzzy integrals and its applications [PhDthesis] Tokyo Institute of Technology Tokyo Japan 1974

[32] K Ishii and M Sugeno ldquoA model of human evaluation processusing fuzzy measurerdquo International Journal of Man-MachineStudies vol 22 no 1 pp 19ndash38 1985

[33] Y-C Hu and H Chen ldquoChoquet integral-based hierarchicalnetworks for evaluating customer service perceptions on fastfood storesrdquo Expert Systems with Applications vol 37 no 12 pp7880ndash7887 2010

[34] T Gurbuz S E Alptekin and G Isiklar Alptekin ldquoA hybridMCDMmethodology for ERP selection problem with interact-ing criteriardquo Decision Support Systems vol 54 no 1 pp 206ndash214 2012

[35] T Murofushi and M Sugeno ldquoAn interpretation of fuzzymeasures and the Choquet integral as an integral with respectto a fuzzy measurerdquo Fuzzy Sets and Systems vol 29 no 2 pp201ndash227 1989

[36] S J Chen and C L Hwang ldquoFuzzy multiple attribute decisionmaking methodsrdquo in Fuzzy Multiple Attribute Decision Mak-ingmdashMethods and Applications vol 375 of Lecture Notes in Eco-nomics and Mathematical Systems pp 289ndash486 Springer 1992

[37] LMikhailov ldquoDeriving priorities from fuzzy pairwise compari-son judgementsrdquo Fuzzy Sets and Systems vol 134 no 3 pp 365ndash385 2003

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


information for the hostel administration (eg type ofinteractions between attributes and weights of the factors) indeciding efficient strategies In addition in several studies theoverall satisfaction score of each hostel under evaluation wassimply computed by using the common arithmetic aggregatorwhich presumes independency among attributes Howeverin reality most of the attributes used for an assessment areinteracted to each other [13] The hostel attributes hold thesame characteristic as well

Hence it is can be concluded that there is a need for aquantitative model which mainly deals with or considers theinteractions between attributes in the process of evaluatingthe performance of a set of hostels based on studentsrsquosatisfaction in order to implement more practical strategiesin enhancing their satisfaction

This paper is organized as follows Firstly the needs forenhancing studentsrsquo satisfaction towards a hostel and theexisting problems relating to hostel evaluation are elucidatedSecondly a review on past literature focusing on the usage ofChoquet integral and its associated 120582-measure is presentedThirdly the proposed hybrid MADM model is introducedFourthly the workability of the proposed model is demon-strated by conducting a real analysis involving fourteenUniversity Utara Malaysia (UUM) hostels The contributionsof the paper and the potential future research are summarizedin the final section

2 Aggregation Phase in MADM

MADMrefers to a process of selecting ranking or classifyinga set of alternatives based on varied usually conflictingattributes [14] Applying multiple attribute utility theory(MAUT) techniques appears as a well-accepted standardquantitative means for modeling MADM problems [15]There are only three basic phases in implementing any of theMAUT techniques [16] In the first phase all the pertinentattributes for evaluating the alternatives under considerationare identified The core components of a typical MAUTmodel are comprised of a set of 119898 alternatives denoted by119860 = 119886

1 1198862 119886

119898 and a set of 119899 attributes represented

by 119862 = 1198881 1198882 119888

119899 In the following phase the weights

of attributes and performance score of each alternative withrespect to each attribute are derivedwhere some judgments orpreference values from the experts or respondents are usuallyrequired for this purpose [17] In the final phase a specificfunction namely aggregation operator is used to composethe set of weights and performance scores of each alternativeinto a single global score [18] Based on these global scoresthe alternatives can be then ranked up classified or selectedwhere an alternative with highest global score signifies themost preferred alternative for the evaluation problem

21 Aggregation Based on Choquet Integral Normally addi-tive operators such as SWA which assume independencybetween attributes [19] are simply employed for the aggre-gation purpose Unfortunately this assumption is completelyirrelevant to real scenario where in many cases the attributeshold interactive characteristics [13 20] Therefore aggrega-tion should not be always performed via additive aggregators

as they failed to model the interactions between attributes[21 22] However with the aid of Choquet integral operator[23] the interactions between attributes can be capturedduring aggregation [24 25] The usage of Choquet integralrequires a prior identification of monotone measure weights119892 These weights represent not only the importance of eachattribute but also the importance of all possible combinationsor subsets of attributes [26ndash28] As a result for a MADMproblem comprising 119899 number of attributes 2119899 number ofweights needs to be identified prior to employing Choquetintegral [29 30]

120582-measure which was introduced by Sugeno [31] appearsas one of the broadly used monotone measures due to itsease of usage mathematical soundness and modest degreeof freedom characteristics [32] Let 119862 = (119888

1 1198882 119888

119899) be a

finite set A set function 119892120582(sdot) defined on the set of the subsets

of 119862 119875(119862) is called a 120582-measure if it meets the followingconditions

(a) 119892120582 119875(119862) rarr [0 1] and 119892

120582(0) = 0 119892

120582(119862) = 1

(boundary condition)

(b) forall119860 119861 isin 119875(119862) if 119860 sube 119861 then implies 119892120582(119860) le 119892

120582(119861)

(monotonic condition)

(c) 119892120582(119860 cup 119861) = 119892

120582(119860) + 119892

120582(119861) + 120582119892

120582(119860)119892120582(119861) for all

119860 119861 isin 119875(119862) where 119860 cap 119861 = 0 and 120582 isin [minus1 +infin]

According to [33 34] consider the following

(a) If 120582 lt 0 then it implies that the attributes are shar-ing subadditive (redundancy) effects This means asignificant increase in the performance of the targetcan be achieved by only enhancing some attributes in119862 which have higher individual weights

(b) If 120582 gt 0 then it interprets that the attributes are shar-ing superadditive (synergy support) effects Thismeans a significant increase in the performance of thetarget can be achieved by simultaneously enhancingall the attributes in 119862 regardless of their individualweights

(c) If 120582 = 0 then it indicates that the attributes are non-interactive

As 119862 = 119888119895= 1198881 1198882 119888

119899 is finite the entire 120582-measure

weights can be identified using

1198921205821198881 1198882 119888

119899 =

1

120582

10038161003816100381610038161003816100381610038161003816100381610038161003816

119899

prod

119895=1

(1 + 120582119892119895) minus 1

10038161003816100381610038161003816100381610038161003816100381610038161003816

for minus 1 lt 120582 lt +infin

(1)

where 119892119895= 119892120582(119888119895) 119895 = 1 119899 denotes the individual weights

of attributes Ifsum119899119895=1

119892119895= 1 120582 = 0 whereas ifsum119899

119895=1119892119895

= 1 thevalue of 120582 can be identified by solving

1 + 120582 =

119899

prod

119895=1

(1 + 120582119892119895) (2)



120582


119899) and let 119883 =

(1199091 1199092 119909




119899= (1198881 1198882 119888



Choquet119892120582(1199091 1199092 119909

119899)

= 119909119899sdot 119892120582(119879119899) + [119909


) + sdot sdot sdot

+ [1199091minus 1199092] sdot 119892120582(1198791)

= 119909119899sdot 119892120582(1198881 1198882 119888

119899) + [119909

119899minus1minus 119909119899]

sdot 119892120582(1198881 1198882 119888


1minus 1199092] sdot 119892120582(1198881)

(3)



119875) Literature (119909

119871) are 75 80 and 50


ge 119909119872

ge 119909119871 119879119899= (119875119872 119871) and


119892120582(119909119872 119909119875 119909119871) = 119909

119871sdot 119892120582(119875119872 119871) + (119909

119872minus 119909119871) sdot

119892120582(119875119872) + (119909

119875minus 119909119872) sdot 119892120582(119875)

3 Methodology











119868119895119901=1

119911

119911

sum

119890=1

119868119895119890119901 (4)

Suppose119864119890= 1198641 1198642 119864




119895= 119892120582(119888119895) 119895 = 1 2 119899















119891119887is compared to 119891




Maximize 120583


(119906119886119887minus 119898119886119887) 120583119908119887+ 119908119886minus 119906119886119887119908119887le 0

119902

sum

119901=1

119908119901= 1 119908

119901gt 0 119901 = 1 119902

(5)




119886to 119891119887 Meanwhile 119908





119902

sum

119901=1

(119908119901119910119901) (6)


119901represents


4 Real Application








































5)






1 6603 30014 30014 Cleaning (11988811) 749

2 1867 8487 38501 Washroom (11988821) 717 379

3 1247 5667 44169 Maintenance (11988810) 612

4 1215 5522 49691 Management (11988820) 602 341

5 1164 5291 54982 SRC (11988822) 527

6 929 4222 59204 TV (11988817) 786

7 871 3961 63166 Laundry (11988818) 723

8 777 3530 66696 ATM (11988816) 665

9 768 3489 70184 Sports (11988819) 638

10 710 3225 73410 Study room (11988815) 435 346

11 649 2949 76359 Population (1198884) 673

12 594 2701 79060 Size (1198887) 647 412

13 582 2644 81704 Physical (11988812) 409 583

14 570 2591 84295 Lab (11988814) 561 412

15 515 2339 86635 Wi-Fi (11988813) 547 427

16 490 2229 88864 Bus (1198883) 307 650

17 476 2163 91027 Distance (1198882) 329 649

18 458 2082 93109 Cafeteria (1198889) 449 453

19 427 1941 95050 Exterior (1198881) 453 448

20 391 1779 96829 Fees (1198888) 355 391

21 375 1705 98535 Security (1198885) 756

22 322 1465 100000 Safety (1198886) 684





5+ 25+ 25+ 22) weights In


119899 to sum119902

119901=12|119891119901| where

119891119901= (1198911 1198911 119891








1199082



4= 0065 weight of



fore

valuatingstu


UUM

hoste

ls

Goal

Evaluatin

gperfo

rmance

ofho

stelsbasedon


Factors

Service

Con

venience

Precautio

nFacility

Valuefor

mon

eyAttributes

119888 11

119888 21

119888 10

119888 20

119888 22

119888 4119888 7

119888 12

119888 14

119888 13

119888 5119888 6

119888 17

119888 18

119888 16

119888 19

119888 15

119888 3119888 2

119888 9119888 1

119888 8

Bank

Rakyat

5475

5175

4890

5243

4192

7043

6255

5783

5775

3112

4673

5685

4020

3915

6180

5303

4838

3773

4703

3045

5549

4830

SME

544

55632

6098

5430

4687

7230

6923

6885

5767

3495

5303

6255

306

03945

5288

5573

5295

4620

4575

5497

5415

5340

SimeD

arby

4350

4088

4560

4860

4755

6570

5610

5985

5775

4620

4110

5618

3150

2985

4133

4350

3795

4763

5865

300

05573

4822

EON

5227

4785

5092

5722

5258

6690

5587

5902

5947

5670

4095

5100

3975

4455

4763

5295

444

84928

564

04995

5475

5115

Muamalat

4703

4912

4845

4898

4703

4800

3855

4845

5835

3720

3998

4710

3975

4343

6120

4890

3930

5978

5535

4912

5175

4163

YAB

5310

4950

4372

5344

5520

5873

5250

5452

4343

4410

3915

4673

3368

4597

5168

5168

4433

5325

4785

4350

5018

4800

Proton

3885

3195

4613

4275

3713

6555

5483

6233

5722

4695

3735

4950

3848

4613

4230

4095

4673

3675

5888

4500

4793

4658

MAS

3975

4035

464

24725

4313

6915

6540

5677

6248

5685

4493

5213

2310

4065

3015

3825

4358

4718

4965

3893

5280

4912

Petro

nas

4860

5198

4838

5085

5205

6615

5490

6098

6675

564

04673

546

05565

5670

6518

5182

4822

4305

6930

4800

5663

4830

TNB

4433

3900

5423

4710

4335

6473

5873

5925

5745

5063

4583

544

52685

3495

4035

3870

4650

4140

5790

4793

5078

5415

Tradew

inds

4793

4875

4395

5130

4763

606

85205

5992

5317

4770

3420

4687

5280

4845

5213

4905

4845

4237

6015

3795

4590

4230

Perw

aja

5820

4568

5213

5055

4943

7297

5955

6615

6383

5550

3818

5933

4020

4350

2797

444

0444

05670

5940

6262

5258

5108

MISC

5325

3533

4815

4133

5303

6923

5820

5288

6105

4793

3427

4860

2895

3112

2250

3945

3472

5385

4935

5047

5565

5055

TM5430

4530

4875

4620

5280

7425

5925

6503

6622

5632

3922

4957

3713

4425

2880

4057

4620

5587

504

02970

4905

4815





















individualweights


1198642

1198643

1198644

1198645 119864

11198642

1198643

1198644

1198645

Service



Facility



Convenience



Value for money












17 0123 119888

4 0288 119888

3 0573

11988821 0360 119888

18 0231 119888

7 0497 119888

2 0398

11988811 11988821 0720 119888

17 11988818 0355 119888

4 1198887 0650 119888

3 1198882 0749

11988810 0599 119888

16 0141 119888

12 0582 119888

9 0551

11988811 11988810 0834 119888

17 11988816 0265 119888

4 11988812 0712 119888

3 1198889 0817

11988821 11988810 0753 119888

18 11988816 0373 119888

7 11988812 0806 119888

2 1198889 0736

11988811 11988821 11988810 0907 119888

17 11988818 11988816 0498 119888

4 1198887 11988812 0875 119888

3 1198882 1198889 0899

11988820 0664 119888

19 0351 119888

14 0263 119888

1 0436

11988811 11988820 0865 119888

17 11988819 0476 119888

4 11988814 0480 119888

3 1198881 0766

11988821 11988820 0795 119888

18 11988819 0585 119888

7 11988814 0637 119888

2 1198881 0665

11988811 11988821 11988820 0927 119888

17 11988818 11988819 0710 119888

4 1198887 11988814 0752 119888

3 1198882 1198881 0868

11988810 11988820 0883 119888

16 11988819 0494 119888

12 11988814 0701 119888

9 1198881 0753

11988811 11988810 11988820 0968 119888

17 11988816 11988819 0619 119888

4 11988812 11988814 0798 119888

3 1198889 1198881 0907

11988821 11988810 11988820 0939 119888

18 11988816 11988819 0729 119888

7 11988812 11988814 0869 119888

2 1198889 1198881 0860

11988811 11988821 11988810 11988820 0995 119888

17 11988818 11988816 11988819 0855 119888

4 1198887 11988812 11988814 0921 119888

3 1198882 1198889 1198881 0954

11988822 0099 119888

15 0141 119888

13 0599 119888

8 0633

11988811 11988822 0596 119888

17 11988815 0265 119888

4 11988813 0724 119888

3 1198888 0853

11988821 11988822 0425 119888

18 11988815 0373 119888

7 11988813 0815 119888

2 1198888 0786

11988811 11988821 11988822 0751 119888

17 11988818 11988815 0498 119888

4 1198887 11988813 0882 119888

3 1198882 1198888 0921

11988810 11988822 0641 119888

16 11988815 0283 119888

12 11988813 0852 119888

9 1198888 0845

11988811 11988810 11988822 0854 119888

17 11988816 11988815 0407 119888

4 11988812 11988813 0909 119888

3 1198889 1198888 0947

11988821 11988810 11988822 0781 119888

18 11988816 11988815 0516 119888

7 11988812 11988813 0950 119888

2 1198889 1198888 0916

11988811 11988821 11988810 11988822 0920 119888

17 11988818 11988816 11988815 0641 119888

4 1198887 11988812 11988813 0980 119888

3 1198882 1198889 1198888 0979

11988820 11988822 0762 119888

19 11988815 0494 119888

14 11988813 0713 119888

1 1198888 0801

11988811 11988820 11988822 0882 119888

17 11988819 11988815 0619 119888

4 11988814 11988813 0808 119888

3 1198881 1198888 0928

11988821 11988820 11988822 0819 119888

18 11988819 11988815 0729 119888

7 11988814 11988813 0876 119888

2 1198881 1198888 0889

11988811 11988821 11988820 11988822 0938 119888

17 11988818 11988819 11988815 0855 119888

4 1198887 11988814 11988813 0926 119888

3 1198882 1198881 1198888 0967

11988810 11988820 11988822 0898 119888

16 11988819 11988815 0637 119888

12 11988814 11988813 0904 119888

9 1198881 1198888 0923

11988811 11988810 11988820 11988822 0976 119888

17 11988816 11988819 11988815 0763 119888

4 11988812 11988814 11988813 0946 119888

3 1198889 1198881 1198888 0982

11988821 11988810 11988820 11988822 0949 119888

18 11988816 11988819 11988815 0873 119888

7 11988812 11988814 11988813 0977 119888

2 1198889 1198881 1198888 0964

11988811 11988821 11988810 11988820 11988822 1000 119888

17 11988818 11988816 11988819 11988815 1000 119888

4 1198887 11988812 11988814 11988813 1000 119888

3 1198882 1198889 1198881 1198888 1000


1198886 0367

1198885 1198886 1000






Facility(1199082= 0309)


Value formoney

(1199084= 0065)





Service (0374)


SRC 0099 0044 0016SUM 2271 1000

Facility (0309)


Study room 0141 0143 0044SUM 0987 1000

Convenience (0147)

Population 0288 0129 0019Size 0497 0223 0033





SUM 1000










119891119901= (1198911 1198911 119891









Acknowledgments


References














































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











120582


119899) and let 119883 =

(1199091 1199092 119909




119899= (1198881 1198882 119888



Choquet119892120582(1199091 1199092 119909

119899)

= 119909119899sdot 119892120582(119879119899) + [119909


) + sdot sdot sdot

+ [1199091minus 1199092] sdot 119892120582(1198791)

= 119909119899sdot 119892120582(1198881 1198882 119888

119899) + [119909

119899minus1minus 119909119899]

sdot 119892120582(1198881 1198882 119888


1minus 1199092] sdot 119892120582(1198881)

(3)



119875) Literature (119909

119871) are 75 80 and 50


ge 119909119872

ge 119909119871 119879119899= (119875119872 119871) and


119892120582(119909119872 119909119875 119909119871) = 119909

119871sdot 119892120582(119875119872 119871) + (119909

119872minus 119909119871) sdot

119892120582(119875119872) + (119909

119875minus 119909119872) sdot 119892120582(119875)

3 Methodology











119868119895119901=1

119911

119911

sum

119890=1

119868119895119890119901 (4)

Suppose119864119890= 1198641 1198642 119864




119895= 119892120582(119888119895) 119895 = 1 2 119899















119891119887is compared to 119891




Maximize 120583


(119906119886119887minus 119898119886119887) 120583119908119887+ 119908119886minus 119906119886119887119908119887le 0

119902

sum

119901=1

119908119901= 1 119908

119901gt 0 119901 = 1 119902

(5)




119886to 119891119887 Meanwhile 119908





119902

sum

119901=1

(119908119901119910119901) (6)


119901represents


4 Real Application








































5)






1 6603 30014 30014 Cleaning (11988811) 749

2 1867 8487 38501 Washroom (11988821) 717 379

3 1247 5667 44169 Maintenance (11988810) 612

4 1215 5522 49691 Management (11988820) 602 341

5 1164 5291 54982 SRC (11988822) 527

6 929 4222 59204 TV (11988817) 786

7 871 3961 63166 Laundry (11988818) 723

8 777 3530 66696 ATM (11988816) 665

9 768 3489 70184 Sports (11988819) 638

10 710 3225 73410 Study room (11988815) 435 346

11 649 2949 76359 Population (1198884) 673

12 594 2701 79060 Size (1198887) 647 412

13 582 2644 81704 Physical (11988812) 409 583

14 570 2591 84295 Lab (11988814) 561 412

15 515 2339 86635 Wi-Fi (11988813) 547 427

16 490 2229 88864 Bus (1198883) 307 650

17 476 2163 91027 Distance (1198882) 329 649

18 458 2082 93109 Cafeteria (1198889) 449 453

19 427 1941 95050 Exterior (1198881) 453 448

20 391 1779 96829 Fees (1198888) 355 391

21 375 1705 98535 Security (1198885) 756

22 322 1465 100000 Safety (1198886) 684





5+ 25+ 25+ 22) weights In


119899 to sum119902

119901=12|119891119901| where

119891119901= (1198911 1198911 119891








1199082



4= 0065 weight of



fore

valuatingstu


UUM

hoste

ls

Goal

Evaluatin

gperfo

rmance

ofho

stelsbasedon


Factors

Service

Con

venience

Precautio

nFacility

Valuefor

mon

eyAttributes

119888 11

119888 21

119888 10

119888 20

119888 22

119888 4119888 7

119888 12

119888 14

119888 13

119888 5119888 6

119888 17

119888 18

119888 16

119888 19

119888 15

119888 3119888 2

119888 9119888 1

119888 8

Bank

Rakyat

5475

5175

4890

5243

4192

7043

6255

5783

5775

3112

4673

5685

4020

3915

6180

5303

4838

3773

4703

3045

5549

4830

SME

544

55632

6098

5430

4687

7230

6923

6885

5767

3495

5303

6255

306

03945

5288

5573

5295

4620

4575

5497

5415

5340

SimeD

arby

4350

4088

4560

4860

4755

6570

5610

5985

5775

4620

4110

5618

3150

2985

4133

4350

3795

4763

5865

300

05573

4822

EON

5227

4785

5092

5722

5258

6690

5587

5902

5947

5670

4095

5100

3975

4455

4763

5295

444

84928

564

04995

5475

5115

Muamalat

4703

4912

4845

4898

4703

4800

3855

4845

5835

3720

3998

4710

3975

4343

6120

4890

3930

5978

5535

4912

5175

4163

YAB

5310

4950

4372

5344

5520

5873

5250

5452

4343

4410

3915

4673

3368

4597

5168

5168

4433

5325

4785

4350

5018

4800

Proton

3885

3195

4613

4275

3713

6555

5483

6233

5722

4695

3735

4950

3848

4613

4230

4095

4673

3675

5888

4500

4793

4658

MAS

3975

4035

464

24725

4313

6915

6540

5677

6248

5685

4493

5213

2310

4065

3015

3825

4358

4718

4965

3893

5280

4912

Petro

nas

4860

5198

4838

5085

5205

6615

5490

6098

6675

564

04673

546

05565

5670

6518

5182

4822

4305

6930

4800

5663

4830

TNB

4433

3900

5423

4710

4335

6473

5873

5925

5745

5063

4583

544

52685

3495

4035

3870

4650

4140

5790

4793

5078

5415

Tradew

inds

4793

4875

4395

5130

4763

606

85205

5992

5317

4770

3420

4687

5280

4845

5213

4905

4845

4237

6015

3795

4590

4230

Perw

aja

5820

4568

5213

5055

4943

7297

5955

6615

6383

5550

3818

5933

4020

4350

2797

444

0444

05670

5940

6262

5258

5108

MISC

5325

3533

4815

4133

5303

6923

5820

5288

6105

4793

3427

4860

2895

3112

2250

3945

3472

5385

4935

5047

5565

5055

TM5430

4530

4875

4620

5280

7425

5925

6503

6622

5632

3922

4957

3713

4425

2880

4057

4620

5587

504

02970

4905

4815





















individualweights


1198642

1198643

1198644

1198645 119864

11198642

1198643

1198644

1198645

Service



Facility



Convenience



Value for money












17 0123 119888

4 0288 119888

3 0573

11988821 0360 119888

18 0231 119888

7 0497 119888

2 0398

11988811 11988821 0720 119888

17 11988818 0355 119888

4 1198887 0650 119888

3 1198882 0749

11988810 0599 119888

16 0141 119888

12 0582 119888

9 0551

11988811 11988810 0834 119888

17 11988816 0265 119888

4 11988812 0712 119888

3 1198889 0817

11988821 11988810 0753 119888

18 11988816 0373 119888

7 11988812 0806 119888

2 1198889 0736

11988811 11988821 11988810 0907 119888

17 11988818 11988816 0498 119888

4 1198887 11988812 0875 119888

3 1198882 1198889 0899

11988820 0664 119888

19 0351 119888

14 0263 119888

1 0436

11988811 11988820 0865 119888

17 11988819 0476 119888

4 11988814 0480 119888

3 1198881 0766

11988821 11988820 0795 119888

18 11988819 0585 119888

7 11988814 0637 119888

2 1198881 0665

11988811 11988821 11988820 0927 119888

17 11988818 11988819 0710 119888

4 1198887 11988814 0752 119888

3 1198882 1198881 0868

11988810 11988820 0883 119888

16 11988819 0494 119888

12 11988814 0701 119888

9 1198881 0753

11988811 11988810 11988820 0968 119888

17 11988816 11988819 0619 119888

4 11988812 11988814 0798 119888

3 1198889 1198881 0907

11988821 11988810 11988820 0939 119888

18 11988816 11988819 0729 119888

7 11988812 11988814 0869 119888

2 1198889 1198881 0860

11988811 11988821 11988810 11988820 0995 119888

17 11988818 11988816 11988819 0855 119888

4 1198887 11988812 11988814 0921 119888

3 1198882 1198889 1198881 0954

11988822 0099 119888

15 0141 119888

13 0599 119888

8 0633

11988811 11988822 0596 119888

17 11988815 0265 119888

4 11988813 0724 119888

3 1198888 0853

11988821 11988822 0425 119888

18 11988815 0373 119888

7 11988813 0815 119888

2 1198888 0786

11988811 11988821 11988822 0751 119888

17 11988818 11988815 0498 119888

4 1198887 11988813 0882 119888

3 1198882 1198888 0921

11988810 11988822 0641 119888

16 11988815 0283 119888

12 11988813 0852 119888

9 1198888 0845

11988811 11988810 11988822 0854 119888

17 11988816 11988815 0407 119888

4 11988812 11988813 0909 119888

3 1198889 1198888 0947

11988821 11988810 11988822 0781 119888

18 11988816 11988815 0516 119888

7 11988812 11988813 0950 119888

2 1198889 1198888 0916

11988811 11988821 11988810 11988822 0920 119888

17 11988818 11988816 11988815 0641 119888

4 1198887 11988812 11988813 0980 119888

3 1198882 1198889 1198888 0979

11988820 11988822 0762 119888

19 11988815 0494 119888

14 11988813 0713 119888

1 1198888 0801

11988811 11988820 11988822 0882 119888

17 11988819 11988815 0619 119888

4 11988814 11988813 0808 119888

3 1198881 1198888 0928

11988821 11988820 11988822 0819 119888

18 11988819 11988815 0729 119888

7 11988814 11988813 0876 119888

2 1198881 1198888 0889

11988811 11988821 11988820 11988822 0938 119888

17 11988818 11988819 11988815 0855 119888

4 1198887 11988814 11988813 0926 119888

3 1198882 1198881 1198888 0967

11988810 11988820 11988822 0898 119888

16 11988819 11988815 0637 119888

12 11988814 11988813 0904 119888

9 1198881 1198888 0923

11988811 11988810 11988820 11988822 0976 119888

17 11988816 11988819 11988815 0763 119888

4 11988812 11988814 11988813 0946 119888

3 1198889 1198881 1198888 0982

11988821 11988810 11988820 11988822 0949 119888

18 11988816 11988819 11988815 0873 119888

7 11988812 11988814 11988813 0977 119888

2 1198889 1198881 1198888 0964

11988811 11988821 11988810 11988820 11988822 1000 119888

17 11988818 11988816 11988819 11988815 1000 119888

4 1198887 11988812 11988814 11988813 1000 119888

3 1198882 1198889 1198881 1198888 1000


1198886 0367

1198885 1198886 1000






Facility(1199082= 0309)


Value formoney

(1199084= 0065)





Service (0374)


SRC 0099 0044 0016SUM 2271 1000

Facility (0309)


Study room 0141 0143 0044SUM 0987 1000

Convenience (0147)

Population 0288 0129 0019Size 0497 0223 0033





SUM 1000










119891119901= (1198911 1198911 119891









Acknowledgments


References














































Volume 2014




Journal of











Journal of


Function Spaces






Algebra




















119891119887is compared to 119891




Maximize 120583


(119906119886119887minus 119898119886119887) 120583119908119887+ 119908119886minus 119906119886119887119908119887le 0

119902

sum

119901=1

119908119901= 1 119908

119901gt 0 119901 = 1 119902

(5)




119886to 119891119887 Meanwhile 119908





119902

sum

119901=1

(119908119901119910119901) (6)


119901represents


4 Real Application








































5)






1 6603 30014 30014 Cleaning (11988811) 749

2 1867 8487 38501 Washroom (11988821) 717 379

3 1247 5667 44169 Maintenance (11988810) 612

4 1215 5522 49691 Management (11988820) 602 341

5 1164 5291 54982 SRC (11988822) 527

6 929 4222 59204 TV (11988817) 786

7 871 3961 63166 Laundry (11988818) 723

8 777 3530 66696 ATM (11988816) 665

9 768 3489 70184 Sports (11988819) 638

10 710 3225 73410 Study room (11988815) 435 346

11 649 2949 76359 Population (1198884) 673

12 594 2701 79060 Size (1198887) 647 412

13 582 2644 81704 Physical (11988812) 409 583

14 570 2591 84295 Lab (11988814) 561 412

15 515 2339 86635 Wi-Fi (11988813) 547 427

16 490 2229 88864 Bus (1198883) 307 650

17 476 2163 91027 Distance (1198882) 329 649

18 458 2082 93109 Cafeteria (1198889) 449 453

19 427 1941 95050 Exterior (1198881) 453 448

20 391 1779 96829 Fees (1198888) 355 391

21 375 1705 98535 Security (1198885) 756

22 322 1465 100000 Safety (1198886) 684





5+ 25+ 25+ 22) weights In


119899 to sum119902

119901=12|119891119901| where

119891119901= (1198911 1198911 119891








1199082



4= 0065 weight of



fore

valuatingstu


UUM

hoste

ls

Goal

Evaluatin

gperfo

rmance

ofho

stelsbasedon


Factors

Service

Con

venience

Precautio

nFacility

Valuefor

mon

eyAttributes

119888 11

119888 21

119888 10

119888 20

119888 22

119888 4119888 7

119888 12

119888 14

119888 13

119888 5119888 6

119888 17

119888 18

119888 16

119888 19

119888 15

119888 3119888 2

119888 9119888 1

119888 8

Bank

Rakyat

5475

5175

4890

5243

4192

7043

6255

5783

5775

3112

4673

5685

4020

3915

6180

5303

4838

3773

4703

3045

5549

4830

SME

544

55632

6098

5430

4687

7230

6923

6885

5767

3495

5303

6255

306

03945

5288

5573

5295

4620

4575

5497

5415

5340

SimeD

arby

4350

4088

4560

4860

4755

6570

5610

5985

5775

4620

4110

5618

3150

2985

4133

4350

3795

4763

5865

300

05573

4822

EON

5227

4785

5092

5722

5258

6690

5587

5902

5947

5670

4095

5100

3975

4455

4763

5295

444

84928

564

04995

5475

5115

Muamalat

4703

4912

4845

4898

4703

4800

3855

4845

5835

3720

3998

4710

3975

4343

6120

4890

3930

5978

5535

4912

5175

4163

YAB

5310

4950

4372

5344

5520

5873

5250

5452

4343

4410

3915

4673

3368

4597

5168

5168

4433

5325

4785

4350

5018

4800

Proton

3885

3195

4613

4275

3713

6555

5483

6233

5722

4695

3735

4950

3848

4613

4230

4095

4673

3675

5888

4500

4793

4658

MAS

3975

4035

464

24725

4313

6915

6540

5677

6248

5685

4493

5213

2310

4065

3015

3825

4358

4718

4965

3893

5280

4912

Petro

nas

4860

5198

4838

5085

5205

6615

5490

6098

6675

564

04673

546

05565

5670

6518

5182

4822

4305

6930

4800

5663

4830

TNB

4433

3900

5423

4710

4335

6473

5873

5925

5745

5063

4583

544

52685

3495

4035

3870

4650

4140

5790

4793

5078

5415

Tradew

inds

4793

4875

4395

5130

4763

606

85205

5992

5317

4770

3420

4687

5280

4845

5213

4905

4845

4237

6015

3795

4590

4230

Perw

aja

5820

4568

5213

5055

4943

7297

5955

6615

6383

5550

3818

5933

4020

4350

2797

444

0444

05670

5940

6262

5258

5108

MISC

5325

3533

4815

4133

5303

6923

5820

5288

6105

4793

3427

4860

2895

3112

2250

3945

3472

5385

4935

5047

5565

5055

TM5430

4530

4875

4620

5280

7425

5925

6503

6622

5632

3922

4957

3713

4425

2880

4057

4620

5587

504

02970

4905

4815





















individualweights


1198642

1198643

1198644

1198645 119864

11198642

1198643

1198644

1198645

Service



Facility



Convenience



Value for money












17 0123 119888

4 0288 119888

3 0573

11988821 0360 119888

18 0231 119888

7 0497 119888

2 0398

11988811 11988821 0720 119888

17 11988818 0355 119888

4 1198887 0650 119888

3 1198882 0749

11988810 0599 119888

16 0141 119888

12 0582 119888

9 0551

11988811 11988810 0834 119888

17 11988816 0265 119888

4 11988812 0712 119888

3 1198889 0817

11988821 11988810 0753 119888

18 11988816 0373 119888

7 11988812 0806 119888

2 1198889 0736

11988811 11988821 11988810 0907 119888

17 11988818 11988816 0498 119888

4 1198887 11988812 0875 119888

3 1198882 1198889 0899

11988820 0664 119888

19 0351 119888

14 0263 119888

1 0436

11988811 11988820 0865 119888

17 11988819 0476 119888

4 11988814 0480 119888

3 1198881 0766

11988821 11988820 0795 119888

18 11988819 0585 119888

7 11988814 0637 119888

2 1198881 0665

11988811 11988821 11988820 0927 119888

17 11988818 11988819 0710 119888

4 1198887 11988814 0752 119888

3 1198882 1198881 0868

11988810 11988820 0883 119888

16 11988819 0494 119888

12 11988814 0701 119888

9 1198881 0753

11988811 11988810 11988820 0968 119888

17 11988816 11988819 0619 119888

4 11988812 11988814 0798 119888

3 1198889 1198881 0907

11988821 11988810 11988820 0939 119888

18 11988816 11988819 0729 119888

7 11988812 11988814 0869 119888

2 1198889 1198881 0860

11988811 11988821 11988810 11988820 0995 119888

17 11988818 11988816 11988819 0855 119888

4 1198887 11988812 11988814 0921 119888

3 1198882 1198889 1198881 0954

11988822 0099 119888

15 0141 119888

13 0599 119888

8 0633

11988811 11988822 0596 119888

17 11988815 0265 119888

4 11988813 0724 119888

3 1198888 0853

11988821 11988822 0425 119888

18 11988815 0373 119888

7 11988813 0815 119888

2 1198888 0786

11988811 11988821 11988822 0751 119888

17 11988818 11988815 0498 119888

4 1198887 11988813 0882 119888

3 1198882 1198888 0921

11988810 11988822 0641 119888

16 11988815 0283 119888

12 11988813 0852 119888

9 1198888 0845

11988811 11988810 11988822 0854 119888

17 11988816 11988815 0407 119888

4 11988812 11988813 0909 119888

3 1198889 1198888 0947

11988821 11988810 11988822 0781 119888

18 11988816 11988815 0516 119888

7 11988812 11988813 0950 119888

2 1198889 1198888 0916

11988811 11988821 11988810 11988822 0920 119888

17 11988818 11988816 11988815 0641 119888

4 1198887 11988812 11988813 0980 119888

3 1198882 1198889 1198888 0979

11988820 11988822 0762 119888

19 11988815 0494 119888

14 11988813 0713 119888

1 1198888 0801

11988811 11988820 11988822 0882 119888

17 11988819 11988815 0619 119888

4 11988814 11988813 0808 119888

3 1198881 1198888 0928

11988821 11988820 11988822 0819 119888

18 11988819 11988815 0729 119888

7 11988814 11988813 0876 119888

2 1198881 1198888 0889

11988811 11988821 11988820 11988822 0938 119888

17 11988818 11988819 11988815 0855 119888

4 1198887 11988814 11988813 0926 119888

3 1198882 1198881 1198888 0967

11988810 11988820 11988822 0898 119888

16 11988819 11988815 0637 119888

12 11988814 11988813 0904 119888

9 1198881 1198888 0923

11988811 11988810 11988820 11988822 0976 119888

17 11988816 11988819 11988815 0763 119888

4 11988812 11988814 11988813 0946 119888

3 1198889 1198881 1198888 0982

11988821 11988810 11988820 11988822 0949 119888

18 11988816 11988819 11988815 0873 119888

7 11988812 11988814 11988813 0977 119888

2 1198889 1198881 1198888 0964

11988811 11988821 11988810 11988820 11988822 1000 119888

17 11988818 11988816 11988819 11988815 1000 119888

4 1198887 11988812 11988814 11988813 1000 119888

3 1198882 1198889 1198881 1198888 1000


1198886 0367

1198885 1198886 1000






Facility(1199082= 0309)


Value formoney

(1199084= 0065)





Service (0374)


SRC 0099 0044 0016SUM 2271 1000

Facility (0309)


Study room 0141 0143 0044SUM 0987 1000

Convenience (0147)

Population 0288 0129 0019Size 0497 0223 0033





SUM 1000










119891119901= (1198911 1198911 119891









Acknowledgments


References














































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













































5)






1 6603 30014 30014 Cleaning (11988811) 749

2 1867 8487 38501 Washroom (11988821) 717 379

3 1247 5667 44169 Maintenance (11988810) 612

4 1215 5522 49691 Management (11988820) 602 341

5 1164 5291 54982 SRC (11988822) 527

6 929 4222 59204 TV (11988817) 786

7 871 3961 63166 Laundry (11988818) 723

8 777 3530 66696 ATM (11988816) 665

9 768 3489 70184 Sports (11988819) 638

10 710 3225 73410 Study room (11988815) 435 346

11 649 2949 76359 Population (1198884) 673

12 594 2701 79060 Size (1198887) 647 412

13 582 2644 81704 Physical (11988812) 409 583

14 570 2591 84295 Lab (11988814) 561 412

15 515 2339 86635 Wi-Fi (11988813) 547 427

16 490 2229 88864 Bus (1198883) 307 650

17 476 2163 91027 Distance (1198882) 329 649

18 458 2082 93109 Cafeteria (1198889) 449 453

19 427 1941 95050 Exterior (1198881) 453 448

20 391 1779 96829 Fees (1198888) 355 391

21 375 1705 98535 Security (1198885) 756

22 322 1465 100000 Safety (1198886) 684





5+ 25+ 25+ 22) weights In


119899 to sum119902

119901=12|119891119901| where

119891119901= (1198911 1198911 119891








1199082



4= 0065 weight of



fore

valuatingstu


UUM

hoste

ls

Goal

Evaluatin

gperfo

rmance

ofho

stelsbasedon


Factors

Service

Con

venience

Precautio

nFacility

Valuefor

mon

eyAttributes

119888 11

119888 21

119888 10

119888 20

119888 22

119888 4119888 7

119888 12

119888 14

119888 13

119888 5119888 6

119888 17

119888 18

119888 16

119888 19

119888 15

119888 3119888 2

119888 9119888 1

119888 8

Bank

Rakyat

5475

5175

4890

5243

4192

7043

6255

5783

5775

3112

4673

5685

4020

3915

6180

5303

4838

3773

4703

3045

5549

4830

SME

544

55632

6098

5430

4687

7230

6923

6885

5767

3495

5303

6255

306

03945

5288

5573

5295

4620

4575

5497

5415

5340

SimeD

arby

4350

4088

4560

4860

4755

6570

5610

5985

5775

4620

4110

5618

3150

2985

4133

4350

3795

4763

5865

300

05573

4822

EON

5227

4785

5092

5722

5258

6690

5587

5902

5947

5670

4095

5100

3975

4455

4763

5295

444

84928

564

04995

5475

5115

Muamalat

4703

4912

4845

4898

4703

4800

3855

4845

5835

3720

3998

4710

3975

4343

6120

4890

3930

5978

5535

4912

5175

4163

YAB

5310

4950

4372

5344

5520

5873

5250

5452

4343

4410

3915

4673

3368

4597

5168

5168

4433

5325

4785

4350

5018

4800

Proton

3885

3195

4613

4275

3713

6555

5483

6233

5722

4695

3735

4950

3848

4613

4230

4095

4673

3675

5888

4500

4793

4658

MAS

3975

4035

464

24725

4313

6915

6540

5677

6248

5685

4493

5213

2310

4065

3015

3825

4358

4718

4965

3893

5280

4912

Petro

nas

4860

5198

4838

5085

5205

6615

5490

6098

6675

564

04673

546

05565

5670

6518

5182

4822

4305

6930

4800

5663

4830

TNB

4433

3900

5423

4710

4335

6473

5873

5925

5745

5063

4583

544

52685

3495

4035

3870

4650

4140

5790

4793

5078

5415

Tradew

inds

4793

4875

4395

5130

4763

606

85205

5992

5317

4770

3420

4687

5280

4845

5213

4905

4845

4237

6015

3795

4590

4230

Perw

aja

5820

4568

5213

5055

4943

7297

5955

6615

6383

5550

3818

5933

4020

4350

2797

444

0444

05670

5940

6262

5258

5108

MISC

5325

3533

4815

4133

5303

6923

5820

5288

6105

4793

3427

4860

2895

3112

2250

3945

3472

5385

4935

5047

5565

5055

TM5430

4530

4875

4620

5280

7425

5925

6503

6622

5632

3922

4957

3713

4425

2880

4057

4620

5587

504

02970

4905

4815





















individualweights


1198642

1198643

1198644

1198645 119864

11198642

1198643

1198644

1198645

Service



Facility



Convenience



Value for money












17 0123 119888

4 0288 119888

3 0573

11988821 0360 119888

18 0231 119888

7 0497 119888

2 0398

11988811 11988821 0720 119888

17 11988818 0355 119888

4 1198887 0650 119888

3 1198882 0749

11988810 0599 119888

16 0141 119888

12 0582 119888

9 0551

11988811 11988810 0834 119888

17 11988816 0265 119888

4 11988812 0712 119888

3 1198889 0817

11988821 11988810 0753 119888

18 11988816 0373 119888

7 11988812 0806 119888

2 1198889 0736

11988811 11988821 11988810 0907 119888

17 11988818 11988816 0498 119888

4 1198887 11988812 0875 119888

3 1198882 1198889 0899

11988820 0664 119888

19 0351 119888

14 0263 119888

1 0436

11988811 11988820 0865 119888

17 11988819 0476 119888

4 11988814 0480 119888

3 1198881 0766

11988821 11988820 0795 119888

18 11988819 0585 119888

7 11988814 0637 119888

2 1198881 0665

11988811 11988821 11988820 0927 119888

17 11988818 11988819 0710 119888

4 1198887 11988814 0752 119888

3 1198882 1198881 0868

11988810 11988820 0883 119888

16 11988819 0494 119888

12 11988814 0701 119888

9 1198881 0753

11988811 11988810 11988820 0968 119888

17 11988816 11988819 0619 119888

4 11988812 11988814 0798 119888

3 1198889 1198881 0907

11988821 11988810 11988820 0939 119888

18 11988816 11988819 0729 119888

7 11988812 11988814 0869 119888

2 1198889 1198881 0860

11988811 11988821 11988810 11988820 0995 119888

17 11988818 11988816 11988819 0855 119888

4 1198887 11988812 11988814 0921 119888

3 1198882 1198889 1198881 0954

11988822 0099 119888

15 0141 119888

13 0599 119888

8 0633

11988811 11988822 0596 119888

17 11988815 0265 119888

4 11988813 0724 119888

3 1198888 0853

11988821 11988822 0425 119888

18 11988815 0373 119888

7 11988813 0815 119888

2 1198888 0786

11988811 11988821 11988822 0751 119888

17 11988818 11988815 0498 119888

4 1198887 11988813 0882 119888

3 1198882 1198888 0921

11988810 11988822 0641 119888

16 11988815 0283 119888

12 11988813 0852 119888

9 1198888 0845

11988811 11988810 11988822 0854 119888

17 11988816 11988815 0407 119888

4 11988812 11988813 0909 119888

3 1198889 1198888 0947

11988821 11988810 11988822 0781 119888

18 11988816 11988815 0516 119888

7 11988812 11988813 0950 119888

2 1198889 1198888 0916

11988811 11988821 11988810 11988822 0920 119888

17 11988818 11988816 11988815 0641 119888

4 1198887 11988812 11988813 0980 119888

3 1198882 1198889 1198888 0979

11988820 11988822 0762 119888

19 11988815 0494 119888

14 11988813 0713 119888

1 1198888 0801

11988811 11988820 11988822 0882 119888

17 11988819 11988815 0619 119888

4 11988814 11988813 0808 119888

3 1198881 1198888 0928

11988821 11988820 11988822 0819 119888

18 11988819 11988815 0729 119888

7 11988814 11988813 0876 119888

2 1198881 1198888 0889

11988811 11988821 11988820 11988822 0938 119888

17 11988818 11988819 11988815 0855 119888

4 1198887 11988814 11988813 0926 119888

3 1198882 1198881 1198888 0967

11988810 11988820 11988822 0898 119888

16 11988819 11988815 0637 119888

12 11988814 11988813 0904 119888

9 1198881 1198888 0923

11988811 11988810 11988820 11988822 0976 119888

17 11988816 11988819 11988815 0763 119888

4 11988812 11988814 11988813 0946 119888

3 1198889 1198881 1198888 0982

11988821 11988810 11988820 11988822 0949 119888

18 11988816 11988819 11988815 0873 119888

7 11988812 11988814 11988813 0977 119888

2 1198889 1198881 1198888 0964

11988811 11988821 11988810 11988820 11988822 1000 119888

17 11988818 11988816 11988819 11988815 1000 119888

4 1198887 11988812 11988814 11988813 1000 119888

3 1198882 1198889 1198881 1198888 1000


1198886 0367

1198885 1198886 1000






Facility(1199082= 0309)


Value formoney

(1199084= 0065)





Service (0374)


SRC 0099 0044 0016SUM 2271 1000

Facility (0309)


Study room 0141 0143 0044SUM 0987 1000

Convenience (0147)

Population 0288 0129 0019Size 0497 0223 0033





SUM 1000










119891119901= (1198911 1198911 119891









Acknowledgments


References














































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













1 6603 30014 30014 Cleaning (11988811) 749

2 1867 8487 38501 Washroom (11988821) 717 379

3 1247 5667 44169 Maintenance (11988810) 612

4 1215 5522 49691 Management (11988820) 602 341

5 1164 5291 54982 SRC (11988822) 527

6 929 4222 59204 TV (11988817) 786

7 871 3961 63166 Laundry (11988818) 723

8 777 3530 66696 ATM (11988816) 665

9 768 3489 70184 Sports (11988819) 638

10 710 3225 73410 Study room (11988815) 435 346

11 649 2949 76359 Population (1198884) 673

12 594 2701 79060 Size (1198887) 647 412

13 582 2644 81704 Physical (11988812) 409 583

14 570 2591 84295 Lab (11988814) 561 412

15 515 2339 86635 Wi-Fi (11988813) 547 427

16 490 2229 88864 Bus (1198883) 307 650

17 476 2163 91027 Distance (1198882) 329 649

18 458 2082 93109 Cafeteria (1198889) 449 453

19 427 1941 95050 Exterior (1198881) 453 448

20 391 1779 96829 Fees (1198888) 355 391

21 375 1705 98535 Security (1198885) 756

22 322 1465 100000 Safety (1198886) 684





5+ 25+ 25+ 22) weights In


119899 to sum119902

119901=12|119891119901| where

119891119901= (1198911 1198911 119891








1199082



4= 0065 weight of



fore

valuatingstu


UUM

hoste

ls

Goal

Evaluatin

gperfo

rmance

ofho

stelsbasedon


Factors

Service

Con

venience

Precautio

nFacility

Valuefor

mon

eyAttributes

119888 11

119888 21

119888 10

119888 20

119888 22

119888 4119888 7

119888 12

119888 14

119888 13

119888 5119888 6

119888 17

119888 18

119888 16

119888 19

119888 15

119888 3119888 2

119888 9119888 1

119888 8

Bank

Rakyat

5475

5175

4890

5243

4192

7043

6255

5783

5775

3112

4673

5685

4020

3915

6180

5303

4838

3773

4703

3045

5549

4830

SME

544

55632

6098

5430

4687

7230

6923

6885

5767

3495

5303

6255

306

03945

5288

5573

5295

4620

4575

5497

5415

5340

SimeD

arby

4350

4088

4560

4860

4755

6570

5610

5985

5775

4620

4110

5618

3150

2985

4133

4350

3795

4763

5865

300

05573

4822

EON

5227

4785

5092

5722

5258

6690

5587

5902

5947

5670

4095

5100

3975

4455

4763

5295

444

84928

564

04995

5475

5115

Muamalat

4703

4912

4845

4898

4703

4800

3855

4845

5835

3720

3998

4710

3975

4343

6120

4890

3930

5978

5535

4912

5175

4163

YAB

5310

4950

4372

5344

5520

5873

5250

5452

4343

4410

3915

4673

3368

4597

5168

5168

4433

5325

4785

4350

5018

4800

Proton

3885

3195

4613

4275

3713

6555

5483

6233

5722

4695

3735

4950

3848

4613

4230

4095

4673

3675

5888

4500

4793

4658

MAS

3975

4035

464

24725

4313

6915

6540

5677

6248

5685

4493

5213

2310

4065

3015

3825

4358

4718

4965

3893

5280

4912

Petro

nas

4860

5198

4838

5085

5205

6615

5490

6098

6675

564

04673

546

05565

5670

6518

5182

4822

4305

6930

4800

5663

4830

TNB

4433

3900

5423

4710

4335

6473

5873

5925

5745

5063

4583

544

52685

3495

4035

3870

4650

4140

5790

4793

5078

5415

Tradew

inds

4793

4875

4395

5130

4763

606

85205

5992

5317

4770

3420

4687

5280

4845

5213

4905

4845

4237

6015

3795

4590

4230

Perw

aja

5820

4568

5213

5055

4943

7297

5955

6615

6383

5550

3818

5933

4020

4350

2797

444

0444

05670

5940

6262

5258

5108

MISC

5325

3533

4815

4133

5303

6923

5820

5288

6105

4793

3427

4860

2895

3112

2250

3945

3472

5385

4935

5047

5565

5055

TM5430

4530

4875

4620

5280

7425

5925

6503

6622

5632

3922

4957

3713

4425

2880

4057

4620

5587

504

02970

4905

4815





















individualweights


1198642

1198643

1198644

1198645 119864

11198642

1198643

1198644

1198645

Service



Facility



Convenience



Value for money












17 0123 119888

4 0288 119888

3 0573

11988821 0360 119888

18 0231 119888

7 0497 119888

2 0398

11988811 11988821 0720 119888

17 11988818 0355 119888

4 1198887 0650 119888

3 1198882 0749

11988810 0599 119888

16 0141 119888

12 0582 119888

9 0551

11988811 11988810 0834 119888

17 11988816 0265 119888

4 11988812 0712 119888

3 1198889 0817

11988821 11988810 0753 119888

18 11988816 0373 119888

7 11988812 0806 119888

2 1198889 0736

11988811 11988821 11988810 0907 119888

17 11988818 11988816 0498 119888

4 1198887 11988812 0875 119888

3 1198882 1198889 0899

11988820 0664 119888

19 0351 119888

14 0263 119888

1 0436

11988811 11988820 0865 119888

17 11988819 0476 119888

4 11988814 0480 119888

3 1198881 0766

11988821 11988820 0795 119888

18 11988819 0585 119888

7 11988814 0637 119888

2 1198881 0665

11988811 11988821 11988820 0927 119888

17 11988818 11988819 0710 119888

4 1198887 11988814 0752 119888

3 1198882 1198881 0868

11988810 11988820 0883 119888

16 11988819 0494 119888

12 11988814 0701 119888

9 1198881 0753

11988811 11988810 11988820 0968 119888

17 11988816 11988819 0619 119888

4 11988812 11988814 0798 119888

3 1198889 1198881 0907

11988821 11988810 11988820 0939 119888

18 11988816 11988819 0729 119888

7 11988812 11988814 0869 119888

2 1198889 1198881 0860

11988811 11988821 11988810 11988820 0995 119888

17 11988818 11988816 11988819 0855 119888

4 1198887 11988812 11988814 0921 119888

3 1198882 1198889 1198881 0954

11988822 0099 119888

15 0141 119888

13 0599 119888

8 0633

11988811 11988822 0596 119888

17 11988815 0265 119888

4 11988813 0724 119888

3 1198888 0853

11988821 11988822 0425 119888

18 11988815 0373 119888

7 11988813 0815 119888

2 1198888 0786

11988811 11988821 11988822 0751 119888

17 11988818 11988815 0498 119888

4 1198887 11988813 0882 119888

3 1198882 1198888 0921

11988810 11988822 0641 119888

16 11988815 0283 119888

12 11988813 0852 119888

9 1198888 0845

11988811 11988810 11988822 0854 119888

17 11988816 11988815 0407 119888

4 11988812 11988813 0909 119888

3 1198889 1198888 0947

11988821 11988810 11988822 0781 119888

18 11988816 11988815 0516 119888

7 11988812 11988813 0950 119888

2 1198889 1198888 0916

11988811 11988821 11988810 11988822 0920 119888

17 11988818 11988816 11988815 0641 119888

4 1198887 11988812 11988813 0980 119888

3 1198882 1198889 1198888 0979

11988820 11988822 0762 119888

19 11988815 0494 119888

14 11988813 0713 119888

1 1198888 0801

11988811 11988820 11988822 0882 119888

17 11988819 11988815 0619 119888

4 11988814 11988813 0808 119888

3 1198881 1198888 0928

11988821 11988820 11988822 0819 119888

18 11988819 11988815 0729 119888

7 11988814 11988813 0876 119888

2 1198881 1198888 0889

11988811 11988821 11988820 11988822 0938 119888

17 11988818 11988819 11988815 0855 119888

4 1198887 11988814 11988813 0926 119888

3 1198882 1198881 1198888 0967

11988810 11988820 11988822 0898 119888

16 11988819 11988815 0637 119888

12 11988814 11988813 0904 119888

9 1198881 1198888 0923

11988811 11988810 11988820 11988822 0976 119888

17 11988816 11988819 11988815 0763 119888

4 11988812 11988814 11988813 0946 119888

3 1198889 1198881 1198888 0982

11988821 11988810 11988820 11988822 0949 119888

18 11988816 11988819 11988815 0873 119888

7 11988812 11988814 11988813 0977 119888

2 1198889 1198881 1198888 0964

11988811 11988821 11988810 11988820 11988822 1000 119888

17 11988818 11988816 11988819 11988815 1000 119888

4 1198887 11988812 11988814 11988813 1000 119888

3 1198882 1198889 1198881 1198888 1000


1198886 0367

1198885 1198886 1000






Facility(1199082= 0309)


Value formoney

(1199084= 0065)





Service (0374)


SRC 0099 0044 0016SUM 2271 1000

Facility (0309)


Study room 0141 0143 0044SUM 0987 1000

Convenience (0147)

Population 0288 0129 0019Size 0497 0223 0033





SUM 1000










119891119901= (1198911 1198911 119891









Acknowledgments


References














































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











fore

valuatingstu


UUM

hoste

ls

Goal

Evaluatin

gperfo

rmance

ofho

stelsbasedon


Factors

Service

Con

venience

Precautio

nFacility

Valuefor

mon

eyAttributes

119888 11

119888 21

119888 10

119888 20

119888 22

119888 4119888 7

119888 12

119888 14

119888 13

119888 5119888 6

119888 17

119888 18

119888 16

119888 19

119888 15

119888 3119888 2

119888 9119888 1

119888 8

Bank

Rakyat

5475

5175

4890

5243

4192

7043

6255

5783

5775

3112

4673

5685

4020

3915

6180

5303

4838

3773

4703

3045

5549

4830

SME

544

55632

6098

5430

4687

7230

6923

6885

5767

3495

5303

6255

306

03945

5288

5573

5295

4620

4575

5497

5415

5340

SimeD

arby

4350

4088

4560

4860

4755

6570

5610

5985

5775

4620

4110

5618

3150

2985

4133

4350

3795

4763

5865

300

05573

4822

EON

5227

4785

5092

5722

5258

6690

5587

5902

5947

5670

4095

5100

3975

4455

4763

5295

444

84928

564

04995

5475

5115

Muamalat

4703

4912

4845

4898

4703

4800

3855

4845

5835

3720

3998

4710

3975

4343

6120

4890

3930

5978

5535

4912

5175

4163

YAB

5310

4950

4372

5344

5520

5873

5250

5452

4343

4410

3915

4673

3368

4597

5168

5168

4433

5325

4785

4350

5018

4800

Proton

3885

3195

4613

4275

3713

6555

5483

6233

5722

4695

3735

4950

3848

4613

4230

4095

4673

3675

5888

4500

4793

4658

MAS

3975

4035

464

24725

4313

6915

6540

5677

6248

5685

4493

5213

2310

4065

3015

3825

4358

4718

4965

3893

5280

4912

Petro

nas

4860

5198

4838

5085

5205

6615

5490

6098

6675

564

04673

546

05565

5670

6518

5182

4822

4305

6930

4800

5663

4830

TNB

4433

3900

5423

4710

4335

6473

5873

5925

5745

5063

4583

544

52685

3495

4035

3870

4650

4140

5790

4793

5078

5415

Tradew

inds

4793

4875

4395

5130

4763

606

85205

5992

5317

4770

3420

4687

5280

4845

5213

4905

4845

4237

6015

3795

4590

4230

Perw

aja

5820

4568

5213

5055

4943

7297

5955

6615

6383

5550

3818

5933

4020

4350

2797

444

0444

05670

5940

6262

5258

5108

MISC

5325

3533

4815

4133

5303

6923

5820

5288

6105

4793

3427

4860

2895

3112

2250

3945

3472

5385

4935

5047

5565

5055

TM5430

4530

4875

4620

5280

7425

5925

6503

6622

5632

3922

4957

3713

4425

2880

4057

4620

5587

504

02970

4905

4815





















individualweights


1198642

1198643

1198644

1198645 119864

11198642

1198643

1198644

1198645

Service



Facility



Convenience



Value for money












17 0123 119888

4 0288 119888

3 0573

11988821 0360 119888

18 0231 119888

7 0497 119888

2 0398

11988811 11988821 0720 119888

17 11988818 0355 119888

4 1198887 0650 119888

3 1198882 0749

11988810 0599 119888

16 0141 119888

12 0582 119888

9 0551

11988811 11988810 0834 119888

17 11988816 0265 119888

4 11988812 0712 119888

3 1198889 0817

11988821 11988810 0753 119888

18 11988816 0373 119888

7 11988812 0806 119888

2 1198889 0736

11988811 11988821 11988810 0907 119888

17 11988818 11988816 0498 119888

4 1198887 11988812 0875 119888

3 1198882 1198889 0899

11988820 0664 119888

19 0351 119888

14 0263 119888

1 0436

11988811 11988820 0865 119888

17 11988819 0476 119888

4 11988814 0480 119888

3 1198881 0766

11988821 11988820 0795 119888

18 11988819 0585 119888

7 11988814 0637 119888

2 1198881 0665

11988811 11988821 11988820 0927 119888

17 11988818 11988819 0710 119888

4 1198887 11988814 0752 119888

3 1198882 1198881 0868

11988810 11988820 0883 119888

16 11988819 0494 119888

12 11988814 0701 119888

9 1198881 0753

11988811 11988810 11988820 0968 119888

17 11988816 11988819 0619 119888

4 11988812 11988814 0798 119888

3 1198889 1198881 0907

11988821 11988810 11988820 0939 119888

18 11988816 11988819 0729 119888

7 11988812 11988814 0869 119888

2 1198889 1198881 0860

11988811 11988821 11988810 11988820 0995 119888

17 11988818 11988816 11988819 0855 119888

4 1198887 11988812 11988814 0921 119888

3 1198882 1198889 1198881 0954

11988822 0099 119888

15 0141 119888

13 0599 119888

8 0633

11988811 11988822 0596 119888

17 11988815 0265 119888

4 11988813 0724 119888

3 1198888 0853

11988821 11988822 0425 119888

18 11988815 0373 119888

7 11988813 0815 119888

2 1198888 0786

11988811 11988821 11988822 0751 119888

17 11988818 11988815 0498 119888

4 1198887 11988813 0882 119888

3 1198882 1198888 0921

11988810 11988822 0641 119888

16 11988815 0283 119888

12 11988813 0852 119888

9 1198888 0845

11988811 11988810 11988822 0854 119888

17 11988816 11988815 0407 119888

4 11988812 11988813 0909 119888

3 1198889 1198888 0947

11988821 11988810 11988822 0781 119888

18 11988816 11988815 0516 119888

7 11988812 11988813 0950 119888

2 1198889 1198888 0916

11988811 11988821 11988810 11988822 0920 119888

17 11988818 11988816 11988815 0641 119888

4 1198887 11988812 11988813 0980 119888

3 1198882 1198889 1198888 0979

11988820 11988822 0762 119888

19 11988815 0494 119888

14 11988813 0713 119888

1 1198888 0801

11988811 11988820 11988822 0882 119888

17 11988819 11988815 0619 119888

4 11988814 11988813 0808 119888

3 1198881 1198888 0928

11988821 11988820 11988822 0819 119888

18 11988819 11988815 0729 119888

7 11988814 11988813 0876 119888

2 1198881 1198888 0889

11988811 11988821 11988820 11988822 0938 119888

17 11988818 11988819 11988815 0855 119888

4 1198887 11988814 11988813 0926 119888

3 1198882 1198881 1198888 0967

11988810 11988820 11988822 0898 119888

16 11988819 11988815 0637 119888

12 11988814 11988813 0904 119888

9 1198881 1198888 0923

11988811 11988810 11988820 11988822 0976 119888

17 11988816 11988819 11988815 0763 119888

4 11988812 11988814 11988813 0946 119888

3 1198889 1198881 1198888 0982

11988821 11988810 11988820 11988822 0949 119888

18 11988816 11988819 11988815 0873 119888

7 11988812 11988814 11988813 0977 119888

2 1198889 1198881 1198888 0964

11988811 11988821 11988810 11988820 11988822 1000 119888

17 11988818 11988816 11988819 11988815 1000 119888

4 1198887 11988812 11988814 11988813 1000 119888

3 1198882 1198889 1198881 1198888 1000


1198886 0367

1198885 1198886 1000






Facility(1199082= 0309)


Value formoney

(1199084= 0065)





Service (0374)


SRC 0099 0044 0016SUM 2271 1000

Facility (0309)


Study room 0141 0143 0044SUM 0987 1000

Convenience (0147)

Population 0288 0129 0019Size 0497 0223 0033





SUM 1000










119891119901= (1198911 1198911 119891









Acknowledgments


References














































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





























individualweights


1198642

1198643

1198644

1198645 119864

11198642

1198643

1198644

1198645

Service



Facility



Convenience



Value for money












17 0123 119888

4 0288 119888

3 0573

11988821 0360 119888

18 0231 119888

7 0497 119888

2 0398

11988811 11988821 0720 119888

17 11988818 0355 119888

4 1198887 0650 119888

3 1198882 0749

11988810 0599 119888

16 0141 119888

12 0582 119888

9 0551

11988811 11988810 0834 119888

17 11988816 0265 119888

4 11988812 0712 119888

3 1198889 0817

11988821 11988810 0753 119888

18 11988816 0373 119888

7 11988812 0806 119888

2 1198889 0736

11988811 11988821 11988810 0907 119888

17 11988818 11988816 0498 119888

4 1198887 11988812 0875 119888

3 1198882 1198889 0899

11988820 0664 119888

19 0351 119888

14 0263 119888

1 0436

11988811 11988820 0865 119888

17 11988819 0476 119888

4 11988814 0480 119888

3 1198881 0766

11988821 11988820 0795 119888

18 11988819 0585 119888

7 11988814 0637 119888

2 1198881 0665

11988811 11988821 11988820 0927 119888

17 11988818 11988819 0710 119888

4 1198887 11988814 0752 119888

3 1198882 1198881 0868

11988810 11988820 0883 119888

16 11988819 0494 119888

12 11988814 0701 119888

9 1198881 0753

11988811 11988810 11988820 0968 119888

17 11988816 11988819 0619 119888

4 11988812 11988814 0798 119888

3 1198889 1198881 0907

11988821 11988810 11988820 0939 119888

18 11988816 11988819 0729 119888

7 11988812 11988814 0869 119888

2 1198889 1198881 0860

11988811 11988821 11988810 11988820 0995 119888

17 11988818 11988816 11988819 0855 119888

4 1198887 11988812 11988814 0921 119888

3 1198882 1198889 1198881 0954

11988822 0099 119888

15 0141 119888

13 0599 119888

8 0633

11988811 11988822 0596 119888

17 11988815 0265 119888

4 11988813 0724 119888

3 1198888 0853

11988821 11988822 0425 119888

18 11988815 0373 119888

7 11988813 0815 119888

2 1198888 0786

11988811 11988821 11988822 0751 119888

17 11988818 11988815 0498 119888

4 1198887 11988813 0882 119888

3 1198882 1198888 0921

11988810 11988822 0641 119888

16 11988815 0283 119888

12 11988813 0852 119888

9 1198888 0845

11988811 11988810 11988822 0854 119888

17 11988816 11988815 0407 119888

4 11988812 11988813 0909 119888

3 1198889 1198888 0947

11988821 11988810 11988822 0781 119888

18 11988816 11988815 0516 119888

7 11988812 11988813 0950 119888

2 1198889 1198888 0916

11988811 11988821 11988810 11988822 0920 119888

17 11988818 11988816 11988815 0641 119888

4 1198887 11988812 11988813 0980 119888

3 1198882 1198889 1198888 0979

11988820 11988822 0762 119888

19 11988815 0494 119888

14 11988813 0713 119888

1 1198888 0801

11988811 11988820 11988822 0882 119888

17 11988819 11988815 0619 119888

4 11988814 11988813 0808 119888

3 1198881 1198888 0928

11988821 11988820 11988822 0819 119888

18 11988819 11988815 0729 119888

7 11988814 11988813 0876 119888

2 1198881 1198888 0889

11988811 11988821 11988820 11988822 0938 119888

17 11988818 11988819 11988815 0855 119888

4 1198887 11988814 11988813 0926 119888

3 1198882 1198881 1198888 0967

11988810 11988820 11988822 0898 119888

16 11988819 11988815 0637 119888

12 11988814 11988813 0904 119888

9 1198881 1198888 0923

11988811 11988810 11988820 11988822 0976 119888

17 11988816 11988819 11988815 0763 119888

4 11988812 11988814 11988813 0946 119888

3 1198889 1198881 1198888 0982

11988821 11988810 11988820 11988822 0949 119888

18 11988816 11988819 11988815 0873 119888

7 11988812 11988814 11988813 0977 119888

2 1198889 1198881 1198888 0964

11988811 11988821 11988810 11988820 11988822 1000 119888

17 11988818 11988816 11988819 11988815 1000 119888

4 1198887 11988812 11988814 11988813 1000 119888

3 1198882 1198889 1198881 1198888 1000


1198886 0367

1198885 1198886 1000






Facility(1199082= 0309)


Value formoney

(1199084= 0065)





Service (0374)


SRC 0099 0044 0016SUM 2271 1000

Facility (0309)


Study room 0141 0143 0044SUM 0987 1000

Convenience (0147)

Population 0288 0129 0019Size 0497 0223 0033





SUM 1000










119891119901= (1198911 1198911 119891









Acknowledgments


References














































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












17 0123 119888

4 0288 119888

3 0573

11988821 0360 119888

18 0231 119888

7 0497 119888

2 0398

11988811 11988821 0720 119888

17 11988818 0355 119888

4 1198887 0650 119888

3 1198882 0749

11988810 0599 119888

16 0141 119888

12 0582 119888

9 0551

11988811 11988810 0834 119888

17 11988816 0265 119888

4 11988812 0712 119888

3 1198889 0817

11988821 11988810 0753 119888

18 11988816 0373 119888

7 11988812 0806 119888

2 1198889 0736

11988811 11988821 11988810 0907 119888

17 11988818 11988816 0498 119888

4 1198887 11988812 0875 119888

3 1198882 1198889 0899

11988820 0664 119888

19 0351 119888

14 0263 119888

1 0436

11988811 11988820 0865 119888

17 11988819 0476 119888

4 11988814 0480 119888

3 1198881 0766

11988821 11988820 0795 119888

18 11988819 0585 119888

7 11988814 0637 119888

2 1198881 0665

11988811 11988821 11988820 0927 119888

17 11988818 11988819 0710 119888

4 1198887 11988814 0752 119888

3 1198882 1198881 0868

11988810 11988820 0883 119888

16 11988819 0494 119888

12 11988814 0701 119888

9 1198881 0753

11988811 11988810 11988820 0968 119888

17 11988816 11988819 0619 119888

4 11988812 11988814 0798 119888

3 1198889 1198881 0907

11988821 11988810 11988820 0939 119888

18 11988816 11988819 0729 119888

7 11988812 11988814 0869 119888

2 1198889 1198881 0860

11988811 11988821 11988810 11988820 0995 119888

17 11988818 11988816 11988819 0855 119888

4 1198887 11988812 11988814 0921 119888

3 1198882 1198889 1198881 0954

11988822 0099 119888

15 0141 119888

13 0599 119888

8 0633

11988811 11988822 0596 119888

17 11988815 0265 119888

4 11988813 0724 119888

3 1198888 0853

11988821 11988822 0425 119888

18 11988815 0373 119888

7 11988813 0815 119888

2 1198888 0786

11988811 11988821 11988822 0751 119888

17 11988818 11988815 0498 119888

4 1198887 11988813 0882 119888

3 1198882 1198888 0921

11988810 11988822 0641 119888

16 11988815 0283 119888

12 11988813 0852 119888

9 1198888 0845

11988811 11988810 11988822 0854 119888

17 11988816 11988815 0407 119888

4 11988812 11988813 0909 119888

3 1198889 1198888 0947

11988821 11988810 11988822 0781 119888

18 11988816 11988815 0516 119888

7 11988812 11988813 0950 119888

2 1198889 1198888 0916

11988811 11988821 11988810 11988822 0920 119888

17 11988818 11988816 11988815 0641 119888

4 1198887 11988812 11988813 0980 119888

3 1198882 1198889 1198888 0979

11988820 11988822 0762 119888

19 11988815 0494 119888

14 11988813 0713 119888

1 1198888 0801

11988811 11988820 11988822 0882 119888

17 11988819 11988815 0619 119888

4 11988814 11988813 0808 119888

3 1198881 1198888 0928

11988821 11988820 11988822 0819 119888

18 11988819 11988815 0729 119888

7 11988814 11988813 0876 119888

2 1198881 1198888 0889

11988811 11988821 11988820 11988822 0938 119888

17 11988818 11988819 11988815 0855 119888

4 1198887 11988814 11988813 0926 119888

3 1198882 1198881 1198888 0967

11988810 11988820 11988822 0898 119888

16 11988819 11988815 0637 119888

12 11988814 11988813 0904 119888

9 1198881 1198888 0923

11988811 11988810 11988820 11988822 0976 119888

17 11988816 11988819 11988815 0763 119888

4 11988812 11988814 11988813 0946 119888

3 1198889 1198881 1198888 0982

11988821 11988810 11988820 11988822 0949 119888

18 11988816 11988819 11988815 0873 119888

7 11988812 11988814 11988813 0977 119888

2 1198889 1198881 1198888 0964

11988811 11988821 11988810 11988820 11988822 1000 119888

17 11988818 11988816 11988819 11988815 1000 119888

4 1198887 11988812 11988814 11988813 1000 119888

3 1198882 1198889 1198881 1198888 1000


1198886 0367

1198885 1198886 1000






Facility(1199082= 0309)


Value formoney

(1199084= 0065)





Service (0374)


SRC 0099 0044 0016SUM 2271 1000

Facility (0309)


Study room 0141 0143 0044SUM 0987 1000

Convenience (0147)

Population 0288 0129 0019Size 0497 0223 0033





SUM 1000










119891119901= (1198911 1198911 119891









Acknowledgments


References














































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












Facility(1199082= 0309)


Value formoney

(1199084= 0065)





Service (0374)


SRC 0099 0044 0016SUM 2271 1000

Facility (0309)


Study room 0141 0143 0044SUM 0987 1000

Convenience (0147)

Population 0288 0129 0019Size 0497 0223 0033





SUM 1000










119891119901= (1198911 1198911 119891









Acknowledgments


References














































Volume 2014




Journal of











Journal of


Function Spaces






Algebra


















119891119901= (1198911 1198911 119891









Acknowledgments


References














































Volume 2014




Journal of











Journal of


Function Spaces






Algebra




















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









A Hybrid Multiattribute Decision Making Model for ...repo.uum.edu.my/14894/1/801308.pdf ·...

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Transcript of A Hybrid Multiattribute Decision Making Model for ...repo.uum.edu.my/14894/1/801308.pdf ·...