Yager, Ronald R. On some new classes of implication operators and their role in approximate reasoning. (English) Zbl 1095.68119 Inf. Sci. 167, No. 1-4, 193-216 (2004). Summary: The basic properties required of the multivalued implication operator are introduced. The generation of these operators using the \(S\) and \(R\) implications is discussed. We suggest two new approaches for obtaining multivalued implications based on the direct use of additive generating functions. Some new classes of implication operators using these generators methods are derived. The role of the multivalued implication within the fuzzy logic based theory of approximate reasoning is described. A discussion of the modus ponens and modus tollens inference paradigms within the framework of fuzzy logic is provided. A visualization method is then used to look at various properties of the implication operator and suggest variations of standard operators. Finally we suggest a rule based approach to defining multivalued implications which allows a user to specify an implication to met their customized performance requirements. Cited in 7 ReviewsCited in 84 Documents MSC: 68T37 Reasoning under uncertainty in the context of artificial intelligence 03B50 Many-valued logic 03B52 Fuzzy logic; logic of vagueness Keywords:Multivalued logic; Fuzzy logic; Additive generators; Implication operator PDFBibTeX XMLCite \textit{R. R. Yager}, Inf. Sci. 167, No. 1--4, 193--216 (2004; Zbl 1095.68119) Full Text: DOI References: [1] Rescher, N., Many-Valued Logic (1969), McGraw-Hill: McGraw-Hill New York · Zbl 0248.02023 [2] Zadeh, L. 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