Approximate Reasoning Using Fodor's Implication

Using generalized modus ponens reasoning, we examine the values of the inferred conclusion using the Fodor’s implication in order to interpret a fuzzy if-then rule with a single input single output and the T-norms t1(x, y) = min(x, y), t2(x, y) = xy and t3(x, y) = max(0, x + y − 1) for composition operation. These are the very used T-norms in generalized modus ponens reasoning.

[1]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[2]  James M. Keller,et al.  A new approach to inference in approximate reasoning , 1991 .

[3]  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..

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

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

[6]  Ronald R. Yager,et al.  An Approach to Inference in Approximate Reasoning , 1980, Int. J. Man Mach. Stud..

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

[8]  Satoru Fukami,et al.  Some considerations on fuzzy conditional inference , 1980 .

[9]  Jacek M. Leski,et al.  On equivalence of approximate reasoning results using different interpretations of fuzzy if-then rules , 2001, Fuzzy Sets Syst..

[10]  Satoru Fukami SOME CONSIDERATIONS ON FUZZY CONDITIONAL INFERENCE , 1993 .

[11]  D. Dubois,et al.  FUZZY LOGICS AND THE GENERALIZED MODUS PONENS REVISITED , 1984 .

[12]  Ion Iancu,et al.  Propagation of uncertainty and imprecision in knowledge-based systems , 1998, Fuzzy Sets Syst..

[13]  Masaharu Mizumoto,et al.  FUZZY REASONING UNDER NEW COMPOSITIONAL RULES OF INFERENCE , 1985 .

[14]  Sylvie Despres,et al.  Un apport a la conception de systemes a base de connaissances : les operations de deduction floues , 1988 .

[15]  Yahachiro Tsukamoto,et al.  AN APPROACH TO FUZZY REASONING METHOD , 1993 .

[16]  M. Mizumoto NOTE ON THE ARITHMETIC RULE BY ZADEH FOR FUZZY CONDITIONAL INFERENCE , 1981 .

[17]  Brian R. Gaines,et al.  Foundations of fuzzy reasoning , 1976 .

[18]  L. Zadeh Fuzzy sets as a basis for a theory of possibility , 1999 .

[19]  Didier Dubois,et al.  Operations in a Fuzzy-Valued Logic , 1979, Inf. Control..