4-Designing a Decision-support System for New Product Sales Forecasting

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Fuzzy decision support system for risk analysis in e-commerce development E.W.T. Ngai * , F.K.T. Wat Department of Management and Marketing, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, People’s Republic of China Received 1 December 2001; accepted 1 December 2003 Available online 14 March 2004 Abstract This paper describes the development of a fuzzy decision support system (FDSS) for the assessment of risk in e-commerce (EC) development. A Web-based prototype FDSS is designed and developed to assist EC project managers in identifying potential EC risk factors and the corresponding project risks. A risk analysis model for EC development using a fuzzy set approach is proposed and incorporated into the FDSS. The results of an evaluation indicate that the prototype performs to expectations. D 2004 Elsevier B.V. All rights reserved. Keywords: Electronic commerce; Fuzzy decision support system; Fuzzy set; Risk analysis 1. Introduction E-commerce (EC) is ‘‘a modern business method- ology that addresses the needs of organizations, mer- chants, and consumers to cut costs while improving the quality of goods and services and increasing the speed of service delivery. The term also applies to the use of computer networks to search and retrieve information in support of human and corporate deci- sion making’’ [21]. It has been adopted widely in most enterprises. Although EC offers various business opportuni- ties, EC development is plagued by various kinds of risk and risk management is necessary to avoid these problems. Indeed, a task that is critical to the proper management of EC development is the assessment of risk. An important step in advancing our knowledge requires that we understand and address these risks. According to Leung et al. [26], most project manag- ers worry about the time involved in risk management when it comes to identifying and assessing risks. However, with the aid of computers and the use of software systems, the time for risk analysis can be significantly reduced. Risk analysis can be conducted by using the theory of probability, which estimates the likelihood and consequences of any given risk. EC development is relatively new to most companies, and only limited information is available on the associated risks. The application of fuzzy set theory (FST) to risk analysis seems appropriate, as such analysis is highly subjective and related to inexact and vague information. There is a need to design and develop a fuzzy decision support system (FDSS) to assist EC practitioners to evaluate the risks associated with EC development. 0167-9236/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.dss.2003.12.002 * Corresponding author. Fax: +86-2765-0611. E-mail address: [email protected] (E.W.T. Ngai). www.elsevier.com/locate/dsw Decision Support Systems 40 (2005) 235 – 255

Transcript of 4-Designing a Decision-support System for New Product Sales Forecasting

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www.elsevier.com/locate/dsw

Decision Support Systems 40 (2005) 235–255

Fuzzy decision support system for risk analysis in

e-commerce development

E.W.T. Ngai*, F.K.T. Wat

Department of Management and Marketing, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong,

People’s Republic of China

Received 1 December 2001; accepted 1 December 2003

Available online 14 March 2004

Abstract

This paper describes the development of a fuzzy decision support system (FDSS) for the assessment of risk in e-commerce

(EC) development. A Web-based prototype FDSS is designed and developed to assist EC project managers in identifying

potential EC risk factors and the corresponding project risks. A risk analysis model for EC development using a fuzzy set

approach is proposed and incorporated into the FDSS. The results of an evaluation indicate that the prototype performs to

expectations.

D 2004 Elsevier B.V. All rights reserved.

Keywords: Electronic commerce; Fuzzy decision support system; Fuzzy set; Risk analysis

1. Introduction risk. An important step in advancing our knowledge

E-commerce (EC) is ‘‘a modern business method-

ology that addresses the needs of organizations, mer-

chants, and consumers to cut costs while improving

the quality of goods and services and increasing the

speed of service delivery. The term also applies to the

use of computer networks to search and retrieve

information in support of human and corporate deci-

sion making’’ [21]. It has been adopted widely in most

enterprises.

Although EC offers various business opportuni-

ties, EC development is plagued by various kinds of

risk and risk management is necessary to avoid these

problems. Indeed, a task that is critical to the proper

management of EC development is the assessment of

0167-9236/$ - see front matter D 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.dss.2003.12.002

* Corresponding author. Fax: +86-2765-0611.

E-mail address: [email protected] (E.W.T. Ngai).

requires that we understand and address these risks.

According to Leung et al. [26], most project manag-

ers worry about the time involved in risk management

when it comes to identifying and assessing risks.

However, with the aid of computers and the use of

software systems, the time for risk analysis can be

significantly reduced. Risk analysis can be conducted

by using the theory of probability, which estimates

the likelihood and consequences of any given risk.

EC development is relatively new to most companies,

and only limited information is available on the

associated risks. The application of fuzzy set theory

(FST) to risk analysis seems appropriate, as such

analysis is highly subjective and related to inexact

and vague information. There is a need to design and

develop a fuzzy decision support system (FDSS) to

assist EC practitioners to evaluate the risks associated

with EC development.

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E.W.T. Ngai, F.K.T. Wat / Decision Support Systems 40 (2005) 235–255236

This paper describes the research and development

of a FDSS that can be used to effectively support EC

project managers in conducting risk assessment in EC

development. The motivation for the present work is

the recognized absence and need for such system that

help in the evaluation of a company’s risk level and

provides an overall risk evaluation of EC development.

2. Literature review

2.1. Definitions of risks associated with EC

development

The concept of ‘‘risk’’ became popular in econom-

ics during the 1920s. Since then, it has been success-

fully used in theories of decision making in economics,

finance, and the decision science. The Merriam-Web-

ster [48] dictionary defines risk as the ‘‘possibility of

loss or injury’’ or ‘‘someone or something that creates

or suggests a hazard’’. At present, there is no agreed

upon universal definition of EC risk but information

security is a widely recognized aspect of EC risk [44].

Greenstein [17] views risks associated with EC as the

possibility of loss of confidential data or the destruc-

tion, generation, or use of data or programs that

physically, mentally or financially harms another party,

as well as the possibility of causing harm to hardware.

Mceachern [29] uses the term ‘‘cyber risk’’ to define

any risk associated with EC, including, for example,

Web site destruction and manipulation, unauthorized

access to customer records, Internet fraud, telecommu-

nications theft, copyright infringement and denial of

access. On the other hand, Viehlandm [44] focuses on

managing business risk in EC. He defines EC risk as

the likelihood of a negative impact to organization

itself when developing or operating EC strategy. In this

paper, risks associated with EC development are the

risks of direct or indirect loss to the organization in

development an EC project, which refers to any project

that involves development stages as planning, analysis,

design and implementation of an EC system.

2.2. The significance of fuzzy risk analysis for EC

development

Through using EC, companies are able to connect

with their trading partners for ‘‘just in time produc-

tion’’ and ‘‘just in time delivery’’, which improves

their competitiveness globally. Although EC offers

great opportunities, there is no doubt that EC devel-

opment involves many risks. In this study, we do not

intend to present risks to EC only but also risks that

EC development shares with traditional systems. Ev-

ery EC development is linked to a different degree of

risk. However, most companies do not identify and

assess EC-related risk. EC development has a lot in

common with IT project development. Many IT and

EC development cannot be completed on-time and

on-budget [39]. Proper risk management is an essen-

tial element of project success [39] because without

appropriate risk management it fails to achieve sig-

nificant return on investment or defensive/competitive

purpose. One of the important phases in risk manage-

ment is risk analysis, which involves a process of risk

identification and risk assessment. Proper risk assess-

ment can enhance the chance of successful project

implementation [1]. McDonald [28] and Stoehr [39]

point out that companies need to perform a risk

analysis before engaging EC development.

2.3. Fuzzy risk analysis research

The techniques of risk analysis are powerful tools to

help people manage uncertainty. Thorough risk anal-

ysis estimation and evaluation can provide valuable

support for decision making. There are many risk

analysis techniques currently in use that attempt to

evaluate and estimate risk. These techniques can be

either qualitative or quantitative depending on the

information available and the level of detail that is

required [4]. Quantitative techniques rely heavily on

statistical approaches, which include Monte Carlo

Simulation [49], Fault and Event Tree Analysis

[4,49], Sensitivity Analysis [49], Annual Loss Expec-

tancy [35], Risk Exposure [5], Failure Mode and

Effects Analysis [49], etc. On the other hand, qualita-

tive techniques rely more on judgment than on statis-

tical calculations such as Scenario Analysis [35], FST

[35], etc. Quantitative and qualitative techniques have

their own advantages and disadvantages. Among these

techniques, the application of FST to risk analysis

seems appropriate, as such analysis is highly subjec-

tive and related to inexact and vague information.

Since FST was introduced by Zadeh [51] to deal

with problems in which vagueness was present, lin-

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Table 1

Fuzzy risk analysis applications

Research area Description References

Information technology

Database gateway processor Applies basic concepts of fuzzy logic modeling to risk analysis in database gateway systems. [30]

Information security Presents a methodology for the modeling of the risk analysis process within a computing facility. [10]

Software development Applies FST to evaluate the rate of aggregative risk in software development. [23]

Environmental

Natural hazards Employs fuzzy methods to calculate the risk of release, exposure to, and consequence of

natural urban hazards.

[19]

Ground water nitrate

risk management

Presents a nitrate risk-management methodology using fuzzy sets in combination with a

multi-criterion decision-making (MCDM) technique to assist decision makers in evaluating,

with uncertain information, possible regulatory actions along with the various nitrate

risk-management strategies to determine an appropriate strategy.

[25]

Hazardous materials Provides an application of fuzzy logic to the risk assessment of the transport of hazardous

materials by road and pipeline to evaluate the uncertainties that affect both individual and

societal risk estimates.

[7]

Engineering

System failure Presents a fuzzy logic-based technique for prioritizing failures for corrective actions in a

Failure Mode, Effects and Criticality Analysis. The method allows the analyst to evaluate

the risks associated with item failure modes directly by using the linguistic terms employed

in the criticality assessment. Ambiguous, qualitative, or imprecise information, as well as

quantitative data, can be used in the assessment.

[8]

Construction Outlines an approach to the assessment of construction project risk by linguistic analysis

using FST.

[40,50]

Civil Involves fuzzy set representations of structural damage and related safety analyzes in civil

engineering.

[32,36,41]

Others

Bank Develops a fuzzy set approach in planning system for liquidity management in bank industry. [15]

Tourism Applies a fuzzy multiple criteria decision-making method to conduct an evaluation of tourist risks. [42]

E.W.T. Ngai, F.K.T. Wat / Decision Support Systems 40 (2005) 235–255 237

guistic values have been widely used to approximate

reasoning. Numerous studies of FST in risk assess-

ment have appeared in different areas, and are sum-

marized in Table 1. FST has been effective in such a

variety of areas because it can handle inexact yet

useful information.

2.4. Fuzzy weighted average

An operation commonly used in risk and decision

analysis is the weighted average operation [20], which

takes the following form:

�W ¼

Xni¼1

Wi � Ri

XnWi

i¼1

where W̄ is the weighted average of ratings, Ri is the

rating according to criterion i, and Wi is the weight

assigned to criterion i. When the terms Ri and Wi are

represented by fuzzy sets or fuzzy numbers, the above

operation is referred to as a fuzzy weighted average

(FWA). Bass and Kwakernaak [3] were amongst the

earliest researchers to determine the ranking of mul-

tiple alternatives with this weighted average. Later,

Schmucker [37] used the FWA to propose an approx-

imate numerical method known as the ‘‘Fuzzy Risk

Analyzer’’. Furthermore, many applications such as

Refs. [40,50] follow Schmucker’s procedure, and it is

widely applied in risk analysis, particularly in relation

to construction projects. However, Dong et al. [13]

have shown that Schmucker’s discretization method

can give quite irregular and incorrect membership

functions because information is lost in the process

of ensuring its convexity. They introduced the DSW

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E.W.T. Ngai, F.K.T. Wat / Decision Support Systems 40 (2005) 235–255238

algorithm [13] as an alternative, and dealt with the

problem through interval analysis and alpha-cut rep-

resentations of fuzzy sets. Later, Dong and Wong [12]

employed a simple, efficient, and systemic method to

develop an FWA algorithm based on the DSW algo-

rithm. The FWA algorithm has been widely adopted in

civil engineering, especially in damage assessment

such as [32,36,41].

However, as this algorithm requires O(2n) compar-

isons and arithmetic operations, Liou and Wang [27]

suggested an improved fuzzy weighted average algo-

rithm (IFWA), whilst Lee and Park [24] proposed an

efficient fuzzy weighted average algorithm (EFWA).

In the present study, a risk assessment model based on

the fuzzy weighted average of FST will be used to

calculate the overall risk faced by EC projects. The

EFWA algorithm is used because it can reduce the

number of comparisons and arithmetic operations to

O(n log n) rather than O(n2), as is the case with the

IFWA [27].

Fig. 1. FDSS development methodology framework.

3. System development methodology for the FDSS

The purpose of this study is to design and develop

a FDSS to assist EC project managers in identifying

potential risk factors and evaluating the corresponding

EC development risks. FDSS is constructed following

the five-stage system development methodology,

which is based on a generic IS development [31],

incorporated with the method for fuzzy risk analysis

[37,40,41,46]. Although this system development

methodology is developed for the FDSS, we believe

that other researchers can easily follow as a guideline

to design and develop other FDSS for risk analysis in

other application areas. The system development

process consists of five stages, namely, construction

of fuzzy risk analysis model, development of system

architecture, analyzing and designing of the system,

building of the prototype, and evaluation of the

system. An overview of these five stages of system

development is shown in Fig. 1. First, a fuzzy risk

analysis model was constructed as the kernel of the

system. Second, system architecture was developed.

Third, system design and analysis were carried out in

modularity with defining functionalities of the system

components and an understanding of how they inter-

act with one. Fourth, the prototype system was built in

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Table 2

Potential risks associated with EC development

Variables Potential risks associated with EC development

V1 Hacker gaining unauthorized access

V2 Absence of firewall

V3 Lack of using cryptography

V4 Poor ‘‘key’’ management

V5 Malicious code attacks

V6 Disclosure of sensitive information

V7 Loss of audit trail

V8 Natural disaster-caused equipment failure

V9 Human factor-caused equipment failure

V10 Threat of sabotage in internal network

V11 Inadequate backup systems

V12 Software or hardware problem-caused system

failure

V13 Site or network overload and disruption

V14 Poor design, code or maintenance procedure

V15 Wrong functions and properties development

V16 Wrong user interface development

V17 Project complexity

V18 Wrong project size estimation

V19 Technological newness

V20 Continuous change of system requirements

V21 Wrong schedule estimation

V22 Project behind schedule

V23 Project over budget

V24 Inadequate cash flow

V25 Personnel shortfalls

V26 Lack of expertise and experience in e-commerce

V27 Loss of key person

V28 Lack of top management support

V29 Poor project planning

V30 Unclear project objectives

V31 Indefinite project scope

V32 Lack of contingency plans

V33 Business process redesign

V34 Organizational restructuring

V35 Lack of trust between your organization and

merchant or customer

V36 Inappropriate media for the product and service

V37 Lack of international legal standards

V38 New laws, regulations, and judicial decisions

constantly change the online legal landscape

V39 Uncertain legal jurisdiction

V40 Incompletion of contract terms

V41 Difficult to change outsourcing decision/vendor

V42 Loss of data control

V43 Loss of control over vendor

V44 Loss of control over information technology

V45 Hidden cost

V46 Lack of vendor expertise and experience

V47 Lock-in situation

V48 Vendor offers outdated technology skill

V49 Vendor provides poor quality service

Table 2 (continued)

Variables Potential risks associated with EC development

V50 Difference users with different in culture customers,

and business styles

V51 Language barrier

Source: Based on Wat et al. [43].

E.W.T. Ngai, F.K.T. Wat / Decision Support Systems 40 (2005) 235–255 239

order to learn more about the concepts, framework,

and design through the system-building process. Fi-

nally, the prototype system was evaluated by EC

experts and potential users. Detailed descriptions of

each phase are presented in the following sections.

3.1. Phase 1: construct a fuzzy risk analysis model

Most existing risk analysis models are based on

quantitative techniques such as Monte Carlo Simula-

tion and Annual Loss Expectancy. However, the infor-

mation that is related to most uncertainty factors is not

numerical. FST provides an approximate model for the

evaluation of the risk faced by EC projects through a

linguistic approach. The procedure for fuzzy risk

analysis is based on the works from Refs. [37,40,

41,46] that consisted of five steps: risk identification,

natural language representation, fuzzy assessment ag-

gregation, fuzzy weighted average computation, and

linguistic approximation. The details of each stage are

described in the following sections.

3.1.1. Risk identification

The first step is to conduct risk identification and

compile a list of the most significant uncertainty

factors and their descriptions. Before conducting fuzzy

risk analysis, one must identify the components of

risks associated with EC development. However, little

empirical research has focused on identifying the

potential risk factors that threaten EC development.

In the study of Wat et al. [47], a source-based approach

to categorizing EC development risks is initially used,

with technical, organizational, and environmental risks

as three primary source categories. Then the potential

risks associated with EC development was identified

with 51 risk items (see Table 2) associated with EC

development based on a comprehensive literature

review and interviewed with EC practitioners.

An empirical study was conducted with 330 valid

returns used for the analysis. An exploratory factor

analysis (EFA) of the survey data revealed 10 major

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Table 3

Results of EFA

Factor Variables Factor

loading

Eigen

value

Percentage

of variance

Cumulative

variance

Factor 1: V21 0.640 11.567 26.900 26.900

Resources V22 0.768

Risk V23 0.758

V24 0.644

V25 0.464

V27 0.416

Factor 2: V14 0.535 3.050 7.094 33.994

Requirements V15 0.506

Risk V16 0.627

V17 0.638

V19 0.699

V20 0.694

Factor 3: V46 0.679 2.349 5.463 39.457

Vendor V47 0.712

Quality V48 0.769

Risk V49 0.749

Factor 4: V1 0.630 2.034 4.730 44.187

Client– V2 0.745

Server V3 0.750

Security V4 0.732

Risk V5 0.445

Factor 5: V37 0.786 1.608 3.739 47.926

Legal Risk V38 0.817

V39 0.796

Factor 6: V28 0.522 1.451 3.375 51.302

Managerial V29 0.648

Risk V30 0.728

V31 0.500

V32 0.605

Factor 7: V40 0.539 1.343 3.124 54.426

Outsourcing V41 0.641

Risk V42 0.698

V43 0.751

V45 0.439

Factor 8: V7 0.519 1.197 2.785 57.210

Physical V8 0.794

Security V9 0.821

Risk V10 0.493

Factor 9: V50 0.804 1.112 2.586 59.796

Cultural

Risk

V51 0.828

Factor 10: V33 0.606 1.075 2.501 62.297

Reengineering

Risk

V34 0.774

E.W.T. Ngai, F.K.T. Wat / Decision Support Systems 40 (2005) 235–255240

dimensions of risks associated with EC development,

namely: (1) resources risk, (2) requirements risk, (3)

vendor quality risk, (4) client–server security risk, (5)

legal risk, (6) managerial risk, (7) outsourcing risk, (8)

physical security risk, (9) cultural risk, and (10) re-

engineering risk (see Table 3). As a result of the study

[47], the risk classification framework as shown in

Fig. 2 helps in the formulation of ways of accessing

risks to EC development.

3.1.2. Natural language representation

According to Karwowski and Mital [22], tradition-

al approaches to risk assessment obtain their overall

risk scores by calculating the product of exposure,

likelihood, and the consequences of a possible acci-

dent due to the hazard. A simpler approach that is

advocated by some risk experts is to multiply the

severity of consequences by the likelihood of their

occurrence, as the likelihood of occurrence automat-

ically includes exposure [45]. For example, Boehm

[5] defined risk impact as the product of the proba-

bility of an unsatisfactory outcome (Likelihood) and

the loss to the parties affected when the outcome is

unsatisfactory (Severity). Consequently, two linguistic

variables, ‘‘Likelihood’’ and ‘‘Severity’’, are defined

to calculate the overall risk. In FWA, ‘‘Likelihood’’ is

the rating factor (Ri), and ‘‘Severity’’ is the weighting

factor (Wi) that corresponds to rating factor i. Both

linguistic variables have five terms. ‘‘Likelihood’’ is

expressed in terms of ‘‘Very Unlikely’’, ‘‘Unlikely’’,

‘‘Medium’’, ‘‘Likely’’, and ‘‘Very Likely’’ (see Fig.

3). ‘‘Severity’’ is expressed as ‘‘Minimal’’, ‘‘Low’’,

‘‘Moderate’’, ‘‘High’’, and ‘‘Critical’’ (see Fig. 4).

In this study, the membership functions of the

linguistic terms are characterized by triangular fuzzy

numbers, as these are very often used in applications

such as fuzzy controllers, and in managerial decision

making, business and finance, and the social sciences,

etc. [6]. Table 4 shows the membership functions and

the triangular fuzzy numbers of each linguistic term.

3.1.3. Fuzzy assessment aggregation

In this stage, an aggregate of several evaluators’

fuzzy assessment is performed by using the fuzzy

average operation for aggregate method. By allowing

more than one evaluator to assess the risks associated

with an EC project, a more objective and unbiased

result can be obtained. The fuzzy average operation

for aggregate method that is known as the ‘‘Triangular

Average Formula’’ [6] is used to determine the mean

of evaluator opinions. Hence, the fuzzy average of

each risk factor question from the risk assessment

form can be obtained. The Triangular Average For-

mula is as follows:

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Fig. 2. A classification framework for risk management in EC development.

E.W.T. Ngai, F.K.T. Wat / Decision Support Systems 40 (2005) 235–255 241

Page 8: 4-Designing a Decision-support System for New Product Sales Forecasting

Fig. 3. Membership function of likelihood.

E.W.T. Ngai, F.K.T. Wat / Decision Support Systems 40 (2005) 235–255242

Consider n evaluators and let Ai=(a1(i), aM

(i), a2(i)) be

the fuzzy numbers, i=1,. . .,n. Thus, the triangular

average mean:

Aaverage ¼A1 þ : : : þ An

n

¼ ðað1Þ1 ; að1ÞM ; a

ð1Þ2 Þ þ : : : þ ðaðnÞ1 ; a

ðnÞM ; a

ðnÞ2 Þ

n

¼

Xni¼1

aðiÞ1 ;Xni¼1

aðiÞm1;Xni¼1

aðiÞ2

!

n

Fig. 4. Membership fun

Aaverage ¼ ðm1;mm;m2Þ

¼ 1

n

Xni¼1

aðiÞ1 ;

1

n

Xni¼1

aðiÞM ;

1

n

Xni¼1

aðiÞ2

!

3.1.4. Fuzzy weighted average computation

Based on the classification framework in Fig. 2,

overall EC project risk has three dimensions, which

consist of 10 components. The lowest-level node

encompasses a list of risks factors that are associated

with EC development. Having obtained the fuzzy

average with the likelihood and severity of each risk

derived from previous step, the EFWA algorithm (see

ction of severity.

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Table 4

Fuzzy set representation for each linguistic terms

Likelihood Severity

Very unlikely minimal =1�4x (0, 0, 0.25) 0VxV0.25Unlikely low =4x (0, 0.25, 0.5) 0VxV0.25

=2(1�2x) 0.25VxV0.5Medium moderate =4x�1 (0.25, 0.5, 0.75) 0.25VxV0.5

=3�4x 0.5VxV0.75Likely high =2x�1 (0.5, 0.75, 1) 0.5VxV0.75

=4(1�x) 0.75VxV1Very likely critical =4x-3 (0.75, 1, 1) 0.75VxV1

E.W.T. Ngai, F.K.T. Wat / Decision Support Systems 40 (2005) 235–255 243

Appendix A) can be applied. For a better understand-

ing, let us consider an example. Fig. 5 illustrates a

simple hierarchical structure that is designed to iden-

tify the severity of loss for ‘‘Legal Risk’’. There are

three risk factors associated with ‘‘Legal Risk’’, and

the fuzzy weighted average for the severity of loss is

calculated as follows:

W̄ ¼ W1 � R1 þW2 � R2 þW3 � R3

W1 þW2 þW3

A numerical illustration of this calculation is

shown in Appendix B.

3.1.5. Linguistic approximation

As the result of the calculated fuzzy weighted

average is a fuzzy number, it is necessary to translate

it back into linguistic terms for easy interpretation.

Fig. 5. Simple hierarchical s

The goal of linguistic approximation is to find the

linguistic term with the closest possible meaning to

that of a defined fuzzy set. There are three techniques

in linguistic approximation: best fit, successive ap-

proximation, and piecewise decomposition. The dif-

ference between these three techniques was discussed

by Schmucker [37]. In the present study, the best fit

method is adopted because it is easy to understand and

easy to implement on computers [37]. This method is

based on the ‘‘Euclidean distance’’ between two fuzzy

sets, as proposed by Dubois and Prade [14]. Euclidean

distance is defined as:

dðX ;AÞ ¼X1

½X ðiÞ � AðiÞ�2( )1=2

d=Euclidean distance between two fuzzy sets. X=re-

sultant fuzzy set, and A=defined fuzzy set.

However, it is necessary to map the resultant fuzzy

interval back to one of the fuzzy numbers that are

defined in Fig. 4. Therefore, a modified Euclidean

approach was proposed by Ross et al. [36]. The

difference measure d is given as follows:

dðX ;AÞ ¼�Xn

i

½fXminðiÞ � AminðiÞg2

þ fXmaxðiÞ � AmaxðiÞg2��1=2

where i is the a value and n is the number of a-cut.

tructure of legal risk.

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E.W.T. Ngai, F.K.T. Wat / Decision Sup244

Applying the above equation, the Euclidean

distance between fuzzy set X and predefined natu-

ral language expressions (e.g. low, moderate, and

high) is calculated. The model then assigns the

appropriate natural language expression to the low-

est Euclidian distance associated with fuzzy set X.

For example, if fuzzy set X, which represents the

total risk faced by an EC project, has a low

Euclidian distance with a predefined natural lan-

guage expression of ‘‘high’’, then the model assumes

that fuzzy set X is translated as ‘‘high’’, which

indicates that the total risk faced by the project is

high. Refer to Appendix B for detailed numerical

illustration of the application to the example of

‘‘Legal Risk’’.

3.2. Phase 2: develop system architecture

Good system architecture provides a road map for

the system building process by placing components

into perspective, defining their functionalities, and

demonstrating how they will interact with one an-

other [31]. The Web is the center of activity in

developing decision support systems (DSS) [38]

while client–server architecture has been widely

adopted in the integration of Web-based applications

[9]. The client–server relationship describes the

distribution of tasks between a server and the clients

who access that server. The FDSS is a client–server

system with a two-tiered architecture. On the client

side it is a front-end system that works with Web

clients to obtain service requests and present results.

On the server side, it is a back-end system that

executes a fuzzy risk analysis and access database

for data management. Indeed, such a two-tiered

architecture is suitable when developing non-critical

applications with light transaction loads such as DSS

or departmental applications [11]. Since the FDSS is

a client–server system, it will be executed on the

Web server. Whenever a Web browser (Client) sends

a request for a page to the FDSS, the code is

processed at that time by the Web server. For the

system components contain in the FDSS, it is com-

posed of three interrelated components, which are (1)

database, (2) model base subsystem, and (3) user

interface. These three components are the basic

elements in DSS [33]. Fig. 6 depicts the basic

architecture of the FDSS.

3.3. Phase 3: analyze and design the system

Analysis and design are important aspects of the

system development process. Design involves an

understanding of the domain being studied, the appli-

cation of various alternatives, and the synthesis and

evaluation of proposed solutions. Design specifica-

tions are used as a blueprint for the implementation of

the system [31]. The determination of system compo-

nents and development platform is made during this

phase. The design of DSS can be divided into three

interrelated components, which are database, model

base subsystem, and user interface [33]. The detailed

specifications of these three system components,

structure, and features are determined as follows.

3.3.1. Database

The database system is responsible for the storage

of data and its management. It maintains the necessary

information on each EC project. The data is obtained

from an external source through manual or automated

processes and the results generated by the FDSS. To

manipulate databases on the Web, ActiveX Data

Object (ADO) is used to interface with relational

databases via the Open Database Connectivity

(ODBC) protocol [2]. ADO was chosen as the data

access mechanism due to its high speed, ease of use,

and low memory overheads. The underlying database

can be any application that supports the ODBC

protocol. The current implementation makes use of

Microsoft Access.

3.3.2. Model base subsystem (fuzzy risk analysis

COM component)

The model base performs activities to provide

analytical capabilities for the DSS [43]. Users can

write their own models or use standard models at

times. Fuzzy risk analysis model described in Section

3.1 is employed as a model base subsystem in FDSS.

This model is translated into programming code and is

integrated as the Component Object Model (COM).

COM defines the binary interface between objects. It

is a binary interoperability specification. The two

most common reasons for using components are

breaking up complex applications into manageable

chunks and packaging code for re-use [2]. ASP

scripting is mainly used to implement the FDSS.

ASP script has the ability to interface with COM

port Systems 40 (2005) 235–255

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Fig. 6. System architecture.

E.W.T. Ngai, F.K.T. Wat / Decision Support Systems 40 (2005) 235–255 245

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E.W.T. Ngai, F.K.T. Wat / Decision Support Systems 40 (2005) 235–255246

compliant software components. If functionality is

needed but cannot be provided by scripting, then

ASP components can be used. ASP components are

COM-based, encapsulate a specific functionality, and

are invoked either directly from an ASP page or

indirectly via another ASP component [34].

Fuzzy risk analysis is implemented as the COM

object that is stored in DLL for performing fuzzy risk

analysis. When clients invoke the calculation of the

overall risk faced by the EC project, the fuzzy risk

analysis COM component is called to access neces-

sary information from the database, such as the

likelihood and severity of each risk factor, to perform

fuzzy averaging, calculate the fuzzy weighted aver-

age, and obtain linguistic approximations. Eventually,

the overall risk and risk score of each risk dimension

are obtained.

3.3.3. User interface

The design of the user interface is a key element in

DSS functionality. The DSS interface should provide

easy communication between the user and the system

[43]. Web browser serves as the user interface com-

ponent of the DSS, which make the technology easy

to understand and use [38]. Besides, the FDSS con-

sists mainly of menus and graphics, which are sup-

plemented by natural language. A client invokes the

system by connecting to the Web site through the

standard HTTP protocol, which causes the interface

component to be loaded from the server to the client

station. Pull-down menus allow users to specify their

needs, such the creation of a new project and the

addition of an evaluator record (see Fig. 7).

3.4. Phase 4: build the prototype system

The implementation of a system demonstrates the

feasibility of the design and the utility of the function-

alities that are envisaged [31]. Building a prototype

system is one of the processes that allow insight into

the problems and the complexity of a system during

development research. FDSS is constructed using

various commercial software packages and program-

ming techniques. The detail descriptions of construc-

tion of the FDSS using these software packages and

programming skills are given as below.

The prototype was run on the Windows 2000

Serverk platform. IIS was the Web server which

accepted the ASP request forms that were sent from

client browsers. Internet Explorer 5.0 was selected as

the Web browser in the client computers. Macromedia

Dreamweaverk was selected as the HTML editor for

Web site and page design, and it was incorporated

with Macromedia Fireworksk for the creation and

editing of images, and Macromedia Flashk for the

creation of animated openings.

The main body of the FDSS was written using ASP

script language. VBScript was chosen for the server-

side script because it is the default scripting language

on the IIS server. To create more functional and

interactive Web pages, JavaScript was selected as

the client-side script because it is widely supported,

and some browsers (e.g. Netscape Communicator 4.5)

do not have the capability to interpret VBScript except

with the aid of proprietary add-ons from third-party

vendors. In the FDSS, JavaScript embedded in ASP

code was mainly responsible for HTML form and data

validation, and pull-down menus were used in the

interface design. Microsoft Visual InterDev (VI) was

also used to design dynamic Web applications, as it

provides a development environment and collection of

useful tools and utilities [9].

Visual Basick was selected for development of the

fuzzy risk analysis component. According to Ander-

son et al. [2], there are several advantages of using

Visual Basick to develop COM components. Firstly,

it allows the user to write components quickly without

having to spend much time learning COM. Secondly,

it gives quite respectable performance. Thirdly, it is

often seen as the natural progression for ASP devel-

opers learning to write components. Power [34]

argues that the most common, and the simplest,

component to create is Visual Basic, especially using

an ActiveX DLL that is an in-process component.

The ODBC protocol was selected to communicate

with the Access database because it is compatible with

a variety of database systems. ADO was used to

provide the database connection, as it is a set of

objects that allows programmers to program their data

access logic in languages such as Visual Basic, as well

as in scripting languages [9].

3.5. Phase 5: evaluate the system

Once the system is developed, the testing and

evaluation of the prototype can be performed.

Page 13: 4-Designing a Decision-support System for New Product Sales Forecasting

Fig. 7. Screen for creating new project.

E.W.T. Ngai, F.K.T. Wat / Decision Support Systems 40 (2005) 235–255 247

Through system evaluation, information can be cap-

tured on what users like and dislike, and what the

system does and does not do to meet their needs.

Firstly, testing and evaluation of the system were

performed. All of the FDSS modules were tested for

accuracy and completeness, and the outputs gener-

ated were checked and validated. These tests en-

sured that the system was performing functions that

would meet the requirements of users by assisting

them in conducting risk management for EC devel-

opment. Secondly, once the FDSS was built, out-

come evaluation was conducted in two phases. The

first phase was domain expert evaluation, and the

second phase was potential user (EC practitioner)

evaluation.

There are a number of approaches to evaluate DSS.

One of the criteria for the evaluation of a DSS is the

measurement of the effectiveness of the system.

Another evaluation criterion is to measuring user

satisfaction. An evaluation form with several sections

was designed. The first section measured the effec-

tiveness and usability of the system with five-point

Likert scales (1=strongly disagree, 3=undecided,

5=strongly agree). Through measuring the effective-

ness of the system, we can see the ability of the

system to accomplish its objectives or mission. Items

to measure the usability of the system reflect the

usefulness and ease of use of the system. We can

therefore assess user satisfaction as one of the poten-

tial indicators of the system’s success. The second

Page 14: 4-Designing a Decision-support System for New Product Sales Forecasting

Table 5

Result of prototype evaluations by potential users

Mean S.D. t-test Significant

level

Effectiveness of the system

The system can

(1) Assist in assessing

risks associated with

EC development.

3.59 0.96 2.890 0.009**

(2) Provide an effective

mean to collect,

store and analyze

perception on potential

risk to EC development.

3.64 0.95 3.130 0.005**

(3) Monitor and mitigate risk. 3.55 0.86 2.982 0.007**

Usability of the system

(4) Learning to operate

the system would be

easy for me.

3.32 0.72 2.084 0.050*

(5) My interaction with

the system would be

clear and understandable.

3.86 0.77 5.231 0.000***

(6) I find the system to be

flexible to interact with.

3.18 1.05 0.810 0.427

(7) The system’s commands

are self-explained and

easy to understand.

4.05 0.72 6.789 0.000***

(8) I find the system

easy to use.

3.14 1.21 0.530 0.602

(9) The system is

user friendly.

4.09 0.81 6.308 0.000***

(10) Likely to recommend

to other users.

3.59 0.67 4.161 0.000***

*pV0.05.**pV0.01.***pV0.001.

E.W.T. Ngai, F.K.T. Wat / Decision Support Systems 40 (2005) 235–255248

section of the evaluation form included several open-

ended questions that were analogous to an interview

in that they gave the respondents an opportunity to

express themselves openly, particularly about the

problems that they encountered and how the prototype

could be improved. The final section collected the

evaluators’ personal information.

3.5.1. Expert evaluation

Evaluations by domain experts help to determine

the accuracy of embedded knowledge [16]. The FDSS

system was validated by a group of six participants

attending the ‘‘Fuzziness and Soft Computing in the

New Millennium’’ session of the 9th International

Fuzzy System Association World Congress and the

20th North American Fuzzy Information Processing

Society International Conference. The FDSS was

demonstrated and an evaluation form was distributed

to the experts who presented papers in the fuzzy

modeling session of the meeting. All experts were

university professors and researchers with average

more than 10 years working experience and good

knowledge of FST. They were asked to evaluate the

prototype from two perspectives: effectiveness and

usability of the FDSS. For the effectiveness of the

system, most respondents agreed that the prototype

system was an effective risk assessment tool, in

particular indicating that it can assist in assessing

risks associated with EC development. For the us-

ability of the system, most respondents considered the

system quite easy to use. User’s interaction with the

system was clear and understandable. They were

likely to recommend the prototype system to other

users.

3.5.2. Potential user evaluation

Evaluations by users help to determine the utility

of a system according to the following criteria: ease

of interaction, the extent of its capabilities, its

efficiency and speed, its reliability and whether it

produces useful results [16]. The evaluation form

was transformed electronically and was integrated in

the FDSS for user to conduct online evaluation. A

total of 50 e-mails were sent to a randomly selected

sample from our mailing list directory of EC practi-

tioners in Hong Kong. Twenty-two responses were

collected and stored in the FDSS database for further

analysis.

The responses from the potential users are summa-

rized in Table 5. The potential users rated the system

highly on ‘‘effectiveness of the system’’ and ‘‘usabil-

ity’’, with a mean score of at least 3.14 on a five-point

scale (1=strongly disagree, 3=undecided, 5=strongly

agree). Based on the results of the evaluation, the

prototype was seen as a promising system for the

management of risk in EC development.

In order to ensure the values of most the mean

responses were statistically significantly different

from the neutral value of the scale, which is ‘‘3—

undecided’’, one-sample t-test using test value ‘‘3’’

was conducted for the 10 items. Results of t-test are

presented in Table 5. Overall, the prototype evalu-

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E.W.T. Ngai, F.K.T. Wat / Decision Support Systems 40 (2005) 235–255 249

ation is satisfactory because items 6 and 8 are not

significant from the value ‘‘3’’, which is ‘‘undecid-

ed’’. The significant level for other items are

smaller than 0.05 and their mean values are larger

than 3.00. The viability of the FDSS in supporting

risk management in EC development has been

ascertained by positive feedback obtained from the

evaluation form.

4. Benefits of using FDSS

FDSS had been implemented and the results of

the system evaluation showed that FDSS can be

applied effectively for managing risks associated

with EC development. The computations involved

in the model of fuzzy risk analysis are tedious if

performed manually. It is an easy task and the time

for risk analysis can be significantly reduced. The

Web-based FDSS automates a questionnaire instru-

ment for risk assessment that helps the EC project

managers to determine the overall risk of EC devel-

opment. The benefits of using the system are as

follows.

� Risks associated with EC development are identi-

fied. These risk items serve as a checklist that cover

possible risks associated with EC development in

technical, organizational, and environmental

dimensions. EC project managers or EC practi-

tioners can be informed and be able to recognize

the risks associated with EC development.� EC project managers can predict the overall risk of

the project before start the implementation. An

overall risk index can be used as early indicators of

project problems or potential difficulties. Evalua-

tors can keep track to evaluate the current risk level

of their EC development.� The system provides an effective, systematic, and

more natural way by using the proposed fuzzy risk

analysis model. Evaluators can just simply use the

risk evaluation checklist and use the linguistic

terms to evaluate the EC development risk level.� Prioritization is necessary to provide focus for

important risks [18]. A list of ranked risk items

associated with EC development will be produced.

Therefore, the most serious risk item will be

addressed first.

5. Conclusions and further enhancements

EC development takes place in a complex and

dynamic environment that includes high levels of risk

and uncertainty. This study has outlined an approach

to the assessment of the risks associated with EC

development using FST. A model of fuzzy risk

analysis was proposed to assist EC project managers

and decision makers in formalizing the types of

thinking that are required in assessing the current risk

environment of their EC development in a more

systematic manner than before.

A Web-based FDSS was designed and developed

to incorporate the proposed risk analysis model.

System evaluation was performed to ascertain

whether the FDSS achieved its designed purpose,

and the results were satisfactory. The feedback and

comments collected from respondents were used to

make necessary adjustments. The results of the

evaluation strongly support the viability of the study

approach to risk analysis using fuzzy sets, and

demonstrated the feasibility of evaluating EC project

risk.

The FDSS prototype focused on risk identifica-

tion, analysis, and prioritization. Less attention

was given to the risk management planning, reso-

lution, and monitoring that is associated with EC

development. Further research should be conducted

into such risk management planning. In addition,

risk monitoring should be conducted regularly to

track the status of the identified risks. With such

insight and improvement, the FDSS could be

further enhanced to handle the functionality of risk

management.

Moreover, it was assumed that the ‘‘weighting’’

assigned by each evaluator in the risk evaluation was

the same, but the relative importance placed on

certain factors by individual decision makers and

experts could be widely different. Further research

is needed to develop different ‘‘weightings’’ for

different evaluators.

6. Limitations of this study

Although the prototype comes out with many

advantages, it still has some limitations. The limita-

tions of the prototype are summarized below.

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E.W.T. Ngai, F.K.T. Wat / Decision Support Systems 40 (2005) 235–255250

� In spite of the fact that the prototype evaluation

shows a satisfactory outcome in the effectiveness

and usability of the prototype, but FDSS do not get

the chance to test it with real-life EC projects. The

validity of the system can be established through

in-depth case studies.� The prototype only provides the risk items based

on the risk classification framework shown in Fig.

2. The list of risks shown in Table 2 is not

exhaustive, but it is comprehensive enough for the

purpose of this study.� For simplification, the membership functions were

evenly distributed by triangular fuzzy numbers.

Various membership functions need to be estimat-

ed to be as realistic as possible.

Acknowledgements

The authors are grateful for the constructive

comments of the referees and the Area Editor on an

earlier version of this paper. They wish to thank all the

people who have participated in the evaluation of the

system as well.

e1 þ e2 þ þ en

Appendix A. Algorithm procedure of EFWA

(source: Ref. [24])

1. Sort a’s in non-decreasing order. Let (a1, a2, . . .an) be the resulting sequence. Let first:=1 and

last:=n.

2. Let d�threshold:= t(first +last)/2 b. For each

i=1,2,. . ., d�threshold, let ei:=di and for each

Table 6

Input values of two evaluators

Risk factors Evaluator A

Likelihood

(1) Lack of international legal

standard

likely

(0.5, 0.75, 1)

(2) New laws, regulations, and judicial

decisions constantly change the

online legal landscape

medium

(0.25, 0.5, 0.75)

(3) Uncertain legal jurisdiction medium

(0.25, 0.5, 0.75)

i=d�threshold+1,. . ., n, let ei:=ci. For an n-tuple

S=(e1, e2,. . .,en), evaluate dSd�thresholdand dS(d�threshold+1)

.

3. If dSd�threshold>0 and dS(d�threshold+1)

V0 then L=fL (e1,

e2,. . .,en) and goto Step 4; otherwise execute the

following step.

3.1. If dSd�threshold>0 then first:=d�threshold+1; oth-

erwise last:=d�threshold, and goto Step 2.

4. Sort b’s in non-decreasing order. Let (b1, b2,. . .,bn) be the resulting sequence. Let first:=1 and

last:=n.

5. Let f�threshold:=t(first+last)/2b. For each i=1,

2,. . ., fSf�threshold+1, let ei:=ci and for each i=f�thres-

hold+1,. . ., n, let ei:=di. For an n-tuple S=(e1,

e2, . . ., en), evaluate fSf�thresholdand fSf�threshold+1

.

6. If fSf�threshold>0 and fSf�threshold+1

V0 then U=fU (e1, e2,

. . ., en) and stop; otherwise execute the following

step.

6.1. If fSf�threshold>0, then first:=f�threshold+1; oth-

erwise last:=f�threshold, and goto Step 5.

where

dSi ¼ða1 � aiÞe1 þ ða2 � aiÞe2 þ : : : þ ðan � aiÞen

e1 þ e2 þ : : : þ en

fSi ¼ðb1 � biÞe1 þ ðb2 � biÞe2 þ : : : þ ðbn � biÞen

: : :

Appendix B. Illustrative example of fuzzy risk

analysis

Based on Fig. 5, an illustrative example is de-

scribed below. Suppose that two evaluators assess an

EC project. Table 6 shows the two different evalua-

tors’ perceptions.

Evaluator B

Severity Likelihood Severity

high

(0.5, 0.75, 1)

medium

(0.25, 0.5, 0.75)

critical

(0.75, 1, 1)

high

(0.5, 0.75, 1)

very likely

(0.75, 1, 1)

moderate

(0.25, 0.5, 0.75)

moderate

(0.25, 0.5, 0.75)

medium

(0.25, 0.5, 0.75)

low

(0, 0.25, 0.5)

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E.W.T. Ngai, F.K.T. Wat / Decision Support Systems 40 (2005) 235–255 251

The fuzzy average of the likelihood of risk factor 1

(lack of international legal standard) is:

¼ ð0:25þ 0:5Þ; ð0:5þ 0:75Þ; ð0:75þ 1Þ2

¼ ð0:375; 0:625; 0:875Þ

Whilst the fuzzy average of the severity of risk

factor 1 is:

¼ ðHighþ CriticalÞ=2

¼ ð0:5þ 0:75Þ; ð0:75þ 1Þ; ð1þ 1Þ2

¼ ð0:625; 0:875; 1Þ

Table 7 shows the fuzzy average of all risk factors.

After obtaining the fuzzy average, the FWA can be

calculated with the EFWA algorithm. Consider the

three-term weighted average from Table 7,

y ¼ f ðR1;R2;R3;W1;W2;W3Þ

¼ R1 �W1 þ R2 �W2 þ R3 �W3

W1 þW2 þW3

Two values for a, viz., 0 and 1, are chosen. For

a=0, the intervals of Ri and Wi are:

½a1 ¼ 0:375; b1 ¼ 0:875�; ½a2 ¼ 0:5; b2 ¼ 0:875�;½a3 ¼ 0:25; b3 ¼ 0:75�;

Table 7

Results of fuzzy average

Risk factors Fuzzy average

of likelihood

Fuzzy average

of severity

(1) Lack of international

legal standard

R1 (0.375,

0.625, 0.875)

W1 (0.625,

0.875, 1)

(2) New laws, regulations,

and judicial decisions

constantly change the

online legal landscape

R2 (0.5, 0.75,

0.875)

W2 (0.375,

0.625, 0.875)

(3) Uncertain legal

jurisdiction

R3 (0.25, 0.5,

0.75)

W3 (0.125,

0.375, 0.625)

½c1 ¼ 0:625; d1 ¼ 1�; ½c2 ¼ 0:375; d2 ¼ 0:875�;½c3 ¼ 0:125; d3 ¼ 0:625�

respectively for i=1, 2, 3.

The computational procedure is as follows:

Step 1

Sort a’s into non-decreasing order, and the result-

ing sequence is

½a1 ¼ 0:25; b1 ¼ 0:75�; ½a2 ¼ 0:375; b2 ¼ 0:875�;½a3 ¼ 0:5; b3 ¼ 0:875�; ½c1 ¼ 0:125; d1 ¼ 0:625�;½c2 ¼ 0:625; d2 ¼ 1�; ½c3 ¼ 0:375; d3 ¼ 0:875�ða1; a2; a3Þ ¼ ð0:25; 0:375; 0:5Þ; first:¼ 1; last:¼ 3

Step 2

d�threshold:=t(1+3)/2b=2, S=(0.625, 1, 0.375),

dS2 ¼ð0:25� 0:375Þ � 0:625þ ð0:5� 0:375Þ � 0:375

0:625þ 1þ 0:375

¼ �0:0156

dS3 ¼ð0:25� 0:5Þ � 0:625þ ð0:375� 0:5Þ � 1

0:625þ 1þ 0:375

¼ �0:1406

Step 3

As dS2<0 and dS3<0, execute the following step.

Step 3.1

Let last:=2 and go to Step 2.

Step 2

d�threshold:=t(1+2)/2b=1, S=(0.625, 0.625, 0.375)

dS1 ¼ð0:375� 0:25Þ� 0:625þ ð0:5� 0:25Þ � 0:375

0:625þ 0:625þ 0:375

¼ 0:1058

dS2 ¼ð0:25� 0:375Þ � 0:625þ ð0:5� 0:375Þ � 0:375

0:625þ 0:625þ 0:375

¼ �0:0192

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Fig. 8. Risk assessment form.

E.W.T. Ngai, F.K.T. Wat / Decision Support Systems 40 (2005) 235–255252

Since dS1>0 and dS2<0,

L ¼ fLðc1; d2; d3Þ ¼ a1 þ dS1 ¼ 0:25þ 0:1058

¼ 0:3558

Min fL is 0.3194 and go to Step 4.

Step 4

Sort b’s into non-decreasing order, and the result-

ing sequence is

½a1 ¼ 0:25; b1 ¼ 0:75�; ½a2 ¼ 0:375; b2 ¼ 0:875�;½a3 ¼ 0:5; b3 ¼ 0:875�; ½c1 ¼ 0:125; d1 ¼ 0:625�;½c2 ¼ 0:625; d2 ¼ 1�; ½c3 ¼ 0:375; d3 ¼ 0:875�ðb1; b2; b3Þ ¼ ð0:75; 0:875; 0:875Þ; first:¼ 1; last:¼ 3

Step 5

d�threshold:=t(1+3)/2b=2, S=(0.125, 0.625, 0.875),

dS2 ¼ð0:75� 0:875Þ � 0:125þ ð0:875� 0:875Þ � 0:875

0:125þ 0:625þ 0:875

¼ �0:0096

dS3 ¼ð0:75� 0:875Þ � 0:125þ ð0:875� 0:875Þ � 0:625

0:125þ 0:625þ 0:875

¼ �0:0096

Step 6

As dS2<0 and dS3<0, execute the following step.

Step 6.1

Let last:=2 and go to Step 5.

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E.W.T. Ngai, F.K.T. Wat / Decision Support Systems 40 (2005) 235–255 253

Step 5

d�threshold:=t(1+2)/2b=1, S=(0.125, 1, 0.875),

dS1 ¼ð0:875� 0:75Þ � 1þ ð0:875� 0:75Þ � 0:875

0:125þ 1þ 0:875

¼ 0:1172

dS2 ¼ð0:75� 0:875Þ � 0:125þ ð0:875� 0:875Þ � 0:875

0:125þ 1þ 0:875

¼ �0:0078

As dS1>0 and dS2<0,

U ¼ fU ðd1; c2; c3Þ ¼ b1 þ dS1 ¼ 0:75þ 0:1172

¼ 0:8672

Max fU is 0.8672 and stop.

Accordingly, the interval for a=0 is (0.3558,

0.8672), in which each point corresponds to the end

Fig. 9. Risk assess

points of the triangle that represent the membership

functions. The process is repeated for a=1, and the

result obtained is (0.6417, 0.6417), which corresponds

to the center of the triangle.

As the results are fuzzy numbers, Euclidean dis-

tances are used to map the resultant fuzzy interval

back to linguistic terms.

dðX ;AÞ ¼�Xn

i

½fXminðiÞ � AminðiÞg2 þ fXmaxðiÞ

� AmaxðiÞg2��1=2

where i is the a value and n is the number of a-cut.Based on the results, the Euclidean distances are:

dðX ;MinimalÞ ¼ 0:9588; dðX ;LowÞ ¼ 0:6441;

dðX ;ModerateÞ ¼ 0:2122; dðX ;HighÞ ¼ 0:2240;

dðX ;CriticalÞ ¼ 0:5490

ment result.

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E.W.T. Ngai, F.K.T. Wat / Decision Support Systems 40 (2005) 235–255254

The closest Euclidean distance is 0.2122, which

means the legal risk is considered as moderate.

Appendix C. Illustrative example of the use of the

FDSS for risk assessment in EC development

In this appendix, examples of a dialogue between a

user and the prototype FDSS are shown. Annotations

are added to give a deeper insight into the operation of

the FDSS.

To conduct a risk analysis for a new project, the

evaluator first creates a project evaluation record by

clicking on ‘‘New’’ in the ‘‘Project’’ menu (see Fig.

7). The evaluator can then click on the Assessment

button to start the fuzzy risk analysis. The risk

assessment form is displayed and lists all of the

identified risk factors from the database. Based on

previous project development experience and their

own perception, the evaluator can proceed to define

the likelihood and severity of each risk factor in

natural language. The first page of the risk evaluation

form consists of technical risk factors. The evaluator

can click on the radio button for the risk factor,

‘‘Hacker gaining unauthorized access’’, to indicate

its likelihood (e.g. ‘‘very unlikely’’) and severity

(e.g. ‘‘critical’’). The evaluator can click on the risk

factor for further explanation (see Fig. 8). He/she can

then go to the next risk assessment form by clicking

on the Next button. When all of the risk factors are

evaluated, the fuzzy risk analysis COM component is

invoked and the overall risk faced by the project is

assessed. Fig. 9 shows the results based on inputted

information and other evaluator answers for a partic-

ular project. The FDSS indicates that the overall risk

for the selected project is moderate, and the score for

each risk dimension is represented by an image bar.

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Dr. Eric W.T. Ngai is currently an Associ-

ate Professor in the Department of Man-

agement and Marketing at The Hong Kong

Polytechnic University. His research inter-

ests are in the areas of e-commerce, deci-

sion support systems, supply chain systems

and knowledge management systems. He

has published in a number of journals

including IEEE Transactions on Systems,

Man and Cybernetics, Information and

Management, Expert Systems and Applica-

tions, Expert Systems, International Journal of Operations and

Production Management, Omega, European Journal of Marketing,

European Journal of Operational Research, International Journal

of Production Economics, Transportation Review and others. Dr.

Ngai serves on the Editorial Board of International Journal of

Production Research.

Mr. Francis K.T. Wat is currently a

Research Associate in the Department

of Management and Marketing at The

Hong Kong Polytechnic University. He

was awarded the degrees of BSc (Hons)

and MPhil from The Hong Kong Poly-

technic University. His current research

interests are in the areas of e-commerce,

management information systems and

fuzzy systems. He has published in

journal such as Information & Manage-

ment, Omega, International Journal of Services Technology and

Management.