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An FMT-universal triple I\(*\) method for R-implication operators. (Chinese. English summary) Zbl 1313.68243

Summary: Focusing on the FMT (fuzzy modus tollens) problem of fuzzy reasoning, as a generalization and improvement of triple I\(*\) method, an FMT-universal triple I\(*\) method is put forward and thoroughly investigated. First of all, the attributes of the FMT-universal triple I\(*\) method are analyzed, and its basic principle is proposed, which improves the one of triple I\(*\) methods. Furthermore, the unified form of the FMT-universal triple I\(*\) method is established. Meanwhile some optimal solutions are obtained for several classical R-implication operators. Finally, the contrapositive reversibility property of the FMT-universal triple I\(*\) method is proved with excellent results.

MSC:

68T37 Reasoning under uncertainty in the context of artificial intelligence
03B52 Fuzzy logic; logic of vagueness
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