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Automorphisms, negations and implication operators. (English) Zbl 1010.03017

Summary: In this paper we study conditions under which the implication operators satisfy the property \(I(x,c(x))=c(x\)) for all \(x\in [0,1], c\) being any strong negation. This study has led us to present different implication operator characterization theorems from automorphisms, obtaining a theorem similar to the one presented by P. Smets and P. Magrez [Int. J. Approx. Reasoning 1, 327-347 (1987; Zbl 0643.03018)], in which the strong negation \(c\) used is not generated by the same automorphism that generates the implication.

MSC:

03B52 Fuzzy logic; logic of vagueness

Citations:

Zbl 0643.03018
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References:

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