Fuzzy implications: alpha migrativity and generalised laws of importation

Baczyński, Michał and Jayaram, Balasubramaniam and Mesiar, Radko (2020) Fuzzy implications: alpha migrativity and generalised laws of importation. Information Sciences, 531. pp. 87-96. ISSN 0020-0255

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Abstract

n this work, we discuss the law of α-migrativity as applied to fuzzy implication functions in a meaningful way. A generalisation of this law leads us to Pexider-type functional equations connected with the law of importation, viz., the generalised law of importation I(C(x,α),y)=I(x,J(α,y)) (GLI) and the generalised cross-law of importation I(C(x,α),y)=J(x,I(α,y)) (CLI), where C is a generalised conjunction. In this article we investigate only (GLI). We begin by showing that the satisfaction of law of importation by the pairs (C, I) and/or (C, J) does not necessarily lead to the satisfaction of (GLI). Hence, we study the conditions under which these three laws are related.

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