On the strict logic foundation of fuzzy reasoning
Logic foundations of fuzzy reasoning are discussed. As an alternative to Zadeh's compositional rule of inference, the triple I method of \textit{G. J. Wang} [Inf. Sci. 117, No. 1--2, 47--88 (1999; Zbl 0939.03031)] is discussed and further developed. After building a complete first-orer formal system \(K^*\) and the many-sorted system \(K^*_{ms}\), the problem of formalization of fuzzy reasoning is studied. Based on the system \(K^*_{ms}\), the triple I algorithms of fuzzy modus ponens and of fuzzy modus tollens and their consistency are formalized.
scientific article; zbMATH DE number 2151868