What are fuzzy rules and how to use them

Abstract Fuzzy rules have been advocated as a key tool for expressing pieces of knowledge in “fuzzy logic”. However, there does not exist a unique kind of fuzzy rules, nor is there only one type of “fuzzy logic”. This diversity has caused many a misunderstanding in the literature of fuzzy control. The paper is a survey of different possible semantics for a fuzzy rule and shows how they can be captured in the framework of fuzzy set and possibility theory. It is pointed out that the interpretation of fuzzy rules dictates the way the fuzzy rules should be combined. The various kinds of fuzzy rules considered in the paper (gradual rules, certainty rules, possibility rules, and others) have different inference behaviors and correspond to various intended uses and applications. The representation of fuzzy unless-rules is briefly investigated on the basis of their intended meaning. The problem of defining and checking the coherence of a block of parallel fuzzy rules is also briefly addressed. This issue has been neglected in the fuzzy control literature although it looks important for validation purposes.

[1]  J. Baldwin.  A new approach to approximate reasoning using a fuzzy logic , 1979 .

[2]  Didier Dubois,et al.  Fuzzy rules in knowledge-based systems , 1992 .

[3]  Didier Dubois,et al.  On The Validation of Fuzzy Knowledge Bases , 1994 .

[4]  Hung T. Nguyen,et al.  Conditional inference and logic for intelligent systems - a theory of measure-free conditioning , 1991 .

[5]  Didier Dubois,et al.  Gradual inference rules in approximate reasoning , 1992, Inf. Sci..

[6]  Dr. Hans Hellendoorn,et al.  An Introduction to Fuzzy Control , 1996, Springer Berlin Heidelberg.

[7]  Madan M. Gupta,et al.  Approximate reasoning in expert systems , 1985 .

[8]  D. Dubois,et al.  Fuzzy sets in approximate reasoning. I, Inference with possibility distributions , 1991 .

[9]  H. Zimmermann,et al.  Comparison of fuzzy reasoning methods , 1982 .

[10]  D. Dubois,et al.  A theorem on implication functions defined from triangular norms. , 1984 .

[11]  Didier Dubois,et al.  Basic Issues on Fuzzy Rules and Their Application to Fuzzy Control , 1991, Fuzzy Logic and Fuzzy Control.

[12]  Bernadette Bouchon-Meunier,et al.  La logique floue , 1993 .

[13]  Patrick Doherty,et al.  Fuzzy if-then-Unless Rules and their Implementation , 1993, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[14]  Enrique H. Ruspini,et al.  On the semantics of fuzzy logic , 1991, Int. J. Approx. Reason..

[15]  L. Zadeh,et al.  An Introduction to Fuzzy Logic Applications in Intelligent Systems , 1992 .

[16]  Bernadette Bouchon,et al.  Fuzzy inferences and conditional possibility distributions , 1987 .

[17]  Michio Sugeno,et al.  An introductory survey of fuzzy control , 1985, Inf. Sci..

[18]  Dimiter Driankov,et al.  Fuzzy logic with unless-rules , 1992, [1992 Proceedings] IEEE International Conference on Fuzzy Systems.

[19]  Didier Dubois,et al.  On the combination of uncertain or imprecise pieces of information in rule-based systems-A discussion in the framework of possibility theory , 1988, Int. J. Approx. Reason..

[20]  Lotfi A. Zadeh,et al.  PRUF—a meaning representation language for natural languages , 1978 .

[21]  L. Valverde,et al.  ON MODE AND IMPLICATION IN APPROXIMATE REASONING , 1993 .

[22]  Didier Dubois,et al.  Automated Reasoning Using Possibilistic Logic: Semantics, Belief Revision, and Variable Certainty Weights , 1994, IEEE Trans. Knowl. Data Eng..

[23]  Michel Grabisch,et al.  Gradual rules and the approximation of control laws , 1995 .

[24]  Lotfi A. Zadeh,et al.  The Calculus of Fuzzy If/Then Rules , 1992, Fuzzy Days.

[25]  Hung T. Nguyen,et al.  Theoretical aspects of fuzzy control , 1995 .

[26]  J. Baldwin,et al.  MODELLING CONTROLLERS USING FUZZY RELATIONS , 1980 .

[27]  Lotfi A. Zadeh,et al.  Soft computing and fuzzy logic , 1994, IEEE Software.

[28]  D. Dubois,et al.  Conditional Objects as Nonmonotonic Consequence Relationships , 1994, IEEE Trans. Syst. Man Cybern. Syst..

[29]  J. Mendel.  Fuzzy logic systems for engineering: a tutorial , 1995, Proc. IEEE.

[30]  Lotfi A. Zadeh,et al.  A Theory of Approximate Reasoning , 1979 .

[31]  Didier Dubois,et al.  Representing Default Rules in Possibilistic Logic , 1992, KR.