Modus ponens and modus tollens under the compositional rule of inference with triangular norms
説明
This work focuses on modus ponens and modus tollens in fuzzy reasoning methods. The authors consider t-norms as conjunctive functions for relational composition in "the compositional rule of inference", and pick up t-norms and four classes of implication (i.e. S-implication, R-implication, n-reciprocal R-implication and QL-implication) as the functions for "the translating rule". The necessary and sufficient conditions for satisfaction of modus ponens and modus tollens are proved. A number of numerical examples with various combinations of functions illustrate the application of our theoretical results.
収録刊行物
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- Proceedings of IEEE 5th International Fuzzy Systems
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Proceedings of IEEE 5th International Fuzzy Systems 2 912-917, 2002-12-23
IEEE