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On generalized modus ponens with multiple rules and a residuated implication. (English) Zbl 1001.03024

Summary: We consider a multiple-rule, generalized modus ponens inference scheme, with an interpretation based on compositional rule of inference (CRI) and a residuated implication. We show that such a system is equivalent, as far as CRI is concerned, to a system that satisfies the “basic requirement for fuzzy reasoning”, proposed by I. B. Türksen and Y. Tian [Fuzzy Sets Syst. 58, 3-40 (1993)]. We establish an analogous conclusion for an alternative interpretation (due to Magrez and Smets) of generalized modus ponens, which we call consequent dilation rule (CDR). This method is computationally faster than CRI, but it produces less specific inference results.

MSC:

03B52 Fuzzy logic; logic of vagueness
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