Jcis08 Ftt 6

Toolbox for Interval Type-2 Fuzzy LogicSystems

Mohsen Zamani1 Hossein Nejati2 Amin T. Jahromi3Ali Reza Partovi4 Sadegh H. Nobari2 Ghasem N. Shirazi1

1Electrical and Computer Engineering Dept, National Universityof Singapore, Singapore

[email protected]; [email protected] of Computing, National University of Singapore, Singapore

[email protected]; [email protected] and Electronic Engineering School, Nanyang

Technological University, [email protected]

4Electrical Engineering Dept, Alame Mohaddeseh NooriTechnical University, Noor, Iran

[email protected]

Abstract

Type-2 systems has been becoming the fo-cus of research in the field of fuzzy logic inrecent years. Comparing with type-1 sys-tems, type-2 fuzzy systems are more com-plex and relatively more difficult to under-stand and implement. We developed aninteractive graphical user interface (GUI)based toolbox, MFLS tool, for intervaltype-2 fuzzy logic system. This paperpresents MFLS toolbox. Moreover, theversatility of the software is demonstratedvia an prediction problem.

Keywords: Interval Type-2 Fuzzy logicSystem; Toolbox

1. Introduction

Fuzzy logic has obtained attention of re-searchers for last couple of decades. It hasopened new horizons both in the academiaand the industry site. Fuzzy logic pro-posed by Zadeh(1965) has found his way

during ages in many different applica-tions. Although, conventional fuzzy sys-tems (FSs) or so called type-1 FSs is ca-pable of handling input uncertainties, it isnot adequate to handle all types of uncer-tainties associated with knowledge-basedsystems. Thus, [20] introduced type-2 FSsas an extension to his first theory for type-1. On the other hand, type-2 theory is ca-pable of handling 4 major type of uncer-tainties involved with type-1 FS [15] .Type-1 membership function are exact de-fined, whereas type-2 membership func-tion has one more degree of freedomwhich suites them for uncertain environ-ments but higher degree of freedom bringscomputation complexity to type-2 fuzzylogic systems(FLSs). Type-2 is muchcomputationally intensive comparing to itstype-1 counterpart. Despite their compu-tation burden, type-2 has been applied tovarious type of application such as , signalprocessing [13, 12], pattern recognition[9, 8], time-series forecasting [10, 16],decision making [17], finance[4], wire-

Proceedings of the 11th Joint Conference on Information Sciences (2008) Published by Atlantis Press the authors 1

less communication [14], noise cancella-tion [5], system identification [11], neu-ral network [18], power engineering [1],control [7, 6]. Although, type-2 has beenemerging in different branch of science,its popularity is still not comparable to itsconventional counterpart. Type-2 has notextended its domain due to following fac-tors:1) Type-2 fuzzy set are computation-ally more complex that their conventionalcounter part.2) There is still a lack of useful toolboxesto facilitate the use of type-2.

This paper presents development anddesign of a GUI and a command line pro-gramming toolbox for construction, edi-tion and observation of interval type-2Fuzzy inference systems. The MFLStool, is an environment for implementingand designing of a interval type-2 FLS(IT2FLS). MFLS covers all phases of theIT2FLS from first phase till the last. TheMFLS best qualities such as flexibilitywhich enables the user to add new file, anduser friendly which makes it suitable forversatile range of user from beginner toadvance. Moreover, it contains some func-tion which implement the inference engineas black box.In Section 2 some topics on IT2FLS isdemonstrated, in Section 3 developed tool-box is presented; in Section MFLS is ex-ploited for general approximation prob-lem. Finally, conclusion are stated in Sec-tion 5 .

2. Interval Type-2 Set and Systems

Interval type-2 fuzzy set is a special caseof general type-2 set in which there is nofuzziness in its third dimension and sec-ondary grade is just equal to identity. (1),(2) present type-2 fuzzy set for continuous

and discrete domain, respectively.

À =

xX

[vJx

1/v/

x

]Jx [0,1]

(1)

À = Ni=1[vJx [1/v ]

]/xi (2)

It is well known [15] that an interval set

À(x) can be fully expressed based on up-per

À(x)and lower membership function

À(x). Some of the most fundamentaltype-2 membership function are listed be-low:

1. Gaussian with uncertain mean

fÀ(x)=

N(m1, ;x) x < m11 m1 x m2

N(m2, ;x) x > m2

fÀ(x)=

{N(m2, ;x) x m1+m22N(m1, ;x) x > m1+m22

2. Gaussian with uncertain deviation

fÀ(x) = N(m,2;x)

fÀ(x) = N(m,1;x)

3. Triangular membership function withuncertain mean

fÀ(x) =

0 x < l1x l1p1l1

l1 x < p11 p1 x p2

r2 x

r2 p2p2 < x r2

0 x > r2

fÀ(x)=

0 x < l2xl2p2l2 x

r1(p2l2)+l2(r1p1)(p2l2)+(r1p1)

r2xr2p2

x >r1(p2l2)+l2(r1p1)

(p2l2)+(r1p1)0 x > r2

In fuzzy reasoning the consequence setcan be concluded even if the antecedentset does not completely satisfy so, fuzzyreasoning is not as precise as conventionallogic. The IT2FLS is depicted in Figure 1.


Fig. 1: IT2FLS inference structure

3. MFLS Toolbox

Mamdani IT2FLS is designed and imple-mented in MFLS toolbox. Intersection op-erators such as product and minimum andunion operators like maximum or summa-tion. Moreover, MFLS allows the userto either choose center of sum, center ofset or centroid as desired type reductionprocedure. The package exploits Karnik-Mendel algorithm to obtain the type re-duced set. This package offers the userflexibility for handling computation timeby adjusting quantization step. MFLS hastwo main parts a GUI based part and aMATLAB part. Visual C# based GUIhelps the user to set all the parameter andthen exports set parameters in to MAT-LAB environment as a structure variable.For instance, Figure 2 depicted the frontpanel of MFLS, and Figures 3, 4, 5 depictMFLS windows for some of well knowntype-2 membership function.

Fig. 2: MFLS main panel

In this part we demonstrate a re-quired procedure for implementing FS

Fig. 3: Gaussian membership functionwith uncertain mean

Fig. 4: Gaussian membership functionwith uncertain deviation

Fig. 5: Triangular membership functionwith uncertain mean

Fig. 6: Rule Base in MFLS

with MFLS. Firstly, the cardinality of an-tecedent and consequent must be set. Sec-ondly, fuzzy rules must be created, a


set of fuzzy rules are shown in Figure6. Thirdly, for exploiting the designedIT2FLS in MATLAB, user needs to ex-port the IT2FLS in to MATLAB mfile us-ing file \ export system menu. The resultof this part is structure variable which re-flects the designed system. The block dia-gram in Figure 7 demonstrates the linkingvariable between GUI and MATLAB. Theuser can modify the structure for his ownpersonal purpose.

Fig. 7: Structure variable which links theGUI and MATLAB

On the other hand, some mfiles are re-sponsible for linkage between GUI andMATLAB software. This makes the prob-lem easy for user. Some of the functionare as follows plottype2.m, kmim.m, in-ference.m and etc. also, for sake of sim-plicity all the required functions are inte-grated in to one function called type2fls.mwhich helps user to deal with IT2FLS asblack box. This way user does not need toworry about detail material and user just

need to concern about top level issues. Theprocess of design based on MFLS is de-picted in Figure 8.

Fig. 8: FS design sequence with MFLS

4. Application

In this section a general approximationproblem is introduced and the MFLS tool-box is exploited for solving this problem.There is approximation based on noisydata [15]. The objective is to approximatey = 100 x2 where x [10,10]. Theonly access is just available to noisy mea-surement. For any test point xi, yi boundsto [yli,yui] so, it means that FS relies onnon-crisp data value. The Gaussian mem-bership function with uncertain mean isdesired for the outputs. There is no un-certainty involved with inputs. Thus, in-put membership function is considered tobe type-1. The input and output rangesare x [10,10], y [190,190], respec-tively. The singleton fuzzification andminimum, product and center of sum areassigned for intersection operator, productoperator and type reduction method, re-spectively.

All antecedent sets assumed to be Gaus-sian function and their parameters arelisted in Table 1 . On the other hand, theconsequent sets are Gaussian membershipfunction with uncertain mean. The conse-quent parameters are reported in Table 2.The FS use the simple rule base as follow-ing:

IF x is Ai THEN y is Ci.


mean deviationA1 -10 1.25A2 -7.5 1.25A3 -5 1.25A4 -2.5 1.25A5 0 1.25A6 2.5 1.25A7 5 1.25A8 7.5 1.25A9 10 1.25

Table 1: Antecedent set parameters

mean1 mean2 deviationC1 -7.79 6.49 40C2 34.72 52.93 40C3 66.12 84.1 40C4 84.93 101.75 40C5 93.09 109.95 40C6 88.02 103.53 40C7 65.37 84.32 40C8 34.14 50.85 40C9 -9.62 9.62 40

Table 2: Consequent set parameters

The design steps are mentioned in Figure8 and resultant output is depicted in Figure9. Although,in this example there were notprecise access to value of y and it variesin large scale, the type-2 FS approximatesthe function with close approximation.

Fig. 9: Output response

5. Conclusion

In this paper MFLS toolbox, a toolbox fortype-2 FS was presented and versatility oftoolbox is demonstrated via an general ap-proximation example. Our future work isto improve MFLS by adding new func-tions, developing more advanced GUI andintegrating intelligent learning techniquesuch as genetic algorithm and neural net-work.

References

[1] J. R. Agero and A. Vargas, Usingtype-2 fuzzy logic systems to infer theoperative configuration of distributionnetworks, in Proceedings IEEE PowerEngineering Society General Meeting,pages 2379-2386, June 2005.

[2] S. Auephanwiriyakul, A. Adrian, andJ.M. Keller, Type 2 fuzzy set analy-sis in management surveys. in ProcceIEEE International Conference onFuzzy Systems, vol. 2, pages 1321-1325, 2002.

[3] S. Auephanwiriyakul, A. Adrian, andJ.M. Keller, Type 2 fuzzy set analy-sis in management surveys. in ProcceIEEE International Conference onFuzzy Systems, vol. 2, pages 1321-1325, 2002.

[4] P. Baguley, T. Page, V. Koliza, and P.Maropoulos, Time to market predic-tion using type-2 fuzzy sets. Journal ofManufacturing Technology Msanage-ment, 17(4):513-520, 2006.

[5] O. Castillo and P. Melin, Adaptivenoise cancellation using type-2 fuzzylogic and neural networks. in IEEEConference on Cybernetics and Intel-ligent Systems, vol. 2, pages 1351-1355, 2004.

[6] J. Figuero, J. Posada, M. Melgarejo,and S. Rojas, A type-2 fuzzy con-troller for tracking mobile objects inthe context of robotic soccer games.in


Proceedings 2005 IEEE InternationalConference on Fuzzy Systems, pages359-364, May 2005.

[7] H. Hagras. A hierarchical type-2fuzzy logic control architecture for au-tonomous mobile robots. IEEE Trans-actions on Fuzzy Systems, 12(4):524-539, August 2004.

[8] P. Herman, G. Prasad, and T. M.McGinnity, Investigation of the type-2fuzzy logic approach to classificationin an EEG-based brain-computer in-terface. In Proceedings of the AnnualInternational Conference-IEEE Engi-neering in Medicine and Biology So-ciety , pages 5354-5357, 2005.

[9] Jia Zeng and Zhi-Qiang Liu. Type-2fuzzy sets for handling uncertainty inpattern recognition, in Procceding ofFUZZ-IEEE, pages 6597-6602, Van-couver, Canada, July 2006.

[10] N. N. Karnik and J. M. Mendel, Ap-plications of type-2 fuzzy logic sys-tems to forecasting of timeseries, In-formation Sciences, vol. 120, pages89-111, 1999.

[11] C. H. Lee, Y.C. Lin, and W. Y.Lai, Systems identification using type-2 fuzzy neural network (type-2 FNN)systems. in Proceedings of IEEE In-ternational Symposium on Computa-tional Intelligence in Robotics andAutomation. Computational Intelli-gence in Robotics and Automation forthe New Millennium, vol. 3, pages1264-1269, 2003.

[12] Q. Liang and J. M. Mendel, Equal-ization of nonlinear time-varyingchannels using type-2 fuzzy adaptivefilters, IEEE Transactions on FuzzySystems, 2000.

[13] Q. Liang and J.M. Mendel, ModelingMPEG VBR video traffic using type-2 fuzzy logic systems, In GranularComputing: An Emerging Paradigm,Springer-Verlag, 2000.

[14] Q. Liang and L. Wang, Sensed signal

strength forecasting for wireless sen-sors using interval type-2 fuzzy logicsystem. in Proceedings 2005 IEEE In-ternational Conference on Fuzzy Sys-tems, pages 25-30, Reno, NV, May2005.

[15] J. M. Mendel, Uncertain Rule-Based Fuzzy Logic Systems Introduc-tion and New Directions, EnglewoodCliffs, NJ: Prentice-Hall, 2001.

[16] J. M. Mendel, Uncertainty, fuzzylogic, and signal processing, SignalProccessing , vol. 80, pages 913-933,2000.

[17] T. Ozen and J.M. Garibaldi. Effectof type-2 fuzzy membership functionshape on modelling variation in hu-man decision making. In Proceedings2004 IEEE International Conferenceon Fuzzy Systems, vol. 2, pages 971-976, 2004.

[18] F.C.H. Rhee and C. Hwang, An inter-val type-2 fuzzy perceptron. in IEEEInternational Conference on FuzzySystems, FUZZ-IEEE vol. 2, pages1331-1335, 2002.

[19] H. Shu and Q. Liang, Wireless sen-sor network lifetime analysis using in-terval type-2 fuzzy logic systems.inProceedings 2005 IEEE InternationalConference on Fuzzy Systems, pages19-24, May 2005.

[20] Zadeh, L.A,The concept of a linguis-tic variable and its application to ap-proximate reasoning, Parts 1, 2, and3 Information Sciences, 1975, 8:199-249, 8:301-357, 9:43-80.


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