On global requirements for implication operators in fuzzy modus ponens. (English) Zbl 0931.68117

Summary: When specifying the properties required of an operation used to manipulate fuzzy sets consideration must be given to the meaning or semantics of the whole granule resulting from these operations. Is the fuzzy granule resulting from the operation as a whole meaningful? This requires us to go beyond consideration of only pointwise performance properties of fuzzy operations and to include consideration of properties based upon the global or granular results of these operations. In this spirit we look at the process of fuzzy modus ponens and consider global requirements on the definition of the implication operator used in this process. One global requirement investigated here is implicit in the information boundedness principle, this principle requires that the information contained in a fuzzy granule resulting from an inference must be no greater than the information contained in the consequent of the if then proposition and that the information contained in inferences under two different datum should be ordered by the degree f matching of the datum and the antecedent of the if-then proposition. Using thiis principle we show that any t-conorm \(S\) used in defining implication operators must satisfy the condition of moderate growth, for \(a> b\), \(S(a,v)- S(b,v)\) must be an nonincreasing function of \(v\).


68T27 Logic in artificial intelligence
03B52 Fuzzy logic; logic of vagueness
Full Text: DOI


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