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Title: Fuzzy implications: alpha migrativity and generalised laws of importation
Authors: Baczyński, Michał
Jayaram, Balasubramaniam
Mesiar, Radko
Keywords: Fuzzy connectives; T-norm; Fuzzy implication; Law of importation; Alpha-migrativity
Issue Date: 2020
Citation: "Information Sciences" Vol. 531, (2020), s. 87-96
Abstract: In 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.
DOI: 10.1016/j.ins.2020.04.033
ISSN: 0020-0255
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