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On some new classes of implication operators and their role in approximate reasoning

2004; Elsevier BV; Volume: 167; Issue: 1-4 Linguagem: Inglês

10.1016/j.ins.2003.04.001

1872-6291

Ronald R. Yager,

Fuzzy Logic and Control Systems

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.