A unifying approach to defuzzification and comparison of the outputs of fuzzy controllers

This paper addresses the defuzzification of the fuzzy set outputs of fuzzy controllers from a comparison or ranking perspective. This is done by emphasizing the fuzzy controller as a decision-making system. Based on the extensive study and justification of the fuzzy-set comparison criteria that were developed and published elsewhere by the author, a ranking and, thus, a defuzzification index is introduced. This index is shown to overcome the disadvantages of the commonly used defuzzification methods whose attempted justifications based on probabilistic arguments have not been successful. In addition, the proposed index is based on the generalization of the Hurwicz criterion that is usually adopted in decision making under nonprobabilistic uncertainty and it encompasses the pessimistic maximin and the optimistic maximax criteria as special cases.

[1]  M. Tribus.  Rational descriptions, decisions, and designs , 1969 .

[2]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[3]  H. Zimmermann,et al.  Advanced fuzzy logic control of a model car in extreme situations , 1992 .

[4]  R. Yager,et al.  An adaptive approach to defuzzification based on level sets , 1993 .

[5]  P.J. King,et al.  The application of fuzzy control systems to industrial processes , 1977, Autom..

[6]  Jean J. Saade,et al.  Towards intelligent radar systems , 1994 .

[7]  R. Yager.  Ranking fuzzy subsets over the unit interval , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[8]  Witold Pedrycz,et al.  Fuzzy control and fuzzy systems , 1989 .

[9]  J. J. Saade,et al.  Ordering fuzzy sets over the real line: an approach based on decision making under uncertainty , 1992 .

[10]  Frank Klawonn,et al.  Equality Relations as a Basis for Fuzzy Control , 1993 .

[11]  R. Yager,et al.  On the issue of defuzzification and selection based on a fuzzy set , 1993 .

[12]  J. Baldwin,et al.  Comparison of fuzzy sets on the same decision space , 1979 .

[13]  Ebrahim H. Mamdani,et al.  A linguistic self-organizing process controller , 1979, Autom..

[14]  Ronald R. Yager,et al.  A procedure for ordering fuzzy subsets of the unit interval , 1981, Inf. Sci..

[15]  E. Mamdani,et al.  Developments in fuzzy logic control , 1984, The 23rd IEEE Conference on Decision and Control.

[16]  Ramesh C. Jain.  A procedure for multiple-aspect decision making using fuzzy sets , 1977 .

[17]  Huibert Kwakernaak,et al.  Rating and ranking of multiple-aspect alternatives using fuzzy sets , 1976, Autom..

[18]  Witold Pedrycz,et al.  Fuzzy control and fuzzy systems (2nd, extended ed.) , 1993 .

[19]  C. Howson.  Theories of Probability , 1995 .

[20]  K. H. Chiang,et al.  Fuzzy logic controllers: from development to deployment , 1993, IEEE International Conference on Neural Networks.

[21]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[22]  Jean J. Saade,et al.  Application of fuzzy hypothesis testing to signal detection under uncertainty , 1994 .

[23]  George J. Klir,et al.  A principle of uncertainty and information invariance , 1990 .

[24]  Lotfi A. Zadeh,et al.  Outline of a New Approach to the Analysis of Complex Systems and Decision Processes , 1973, IEEE Trans. Syst. Man Cybern..