Fuzzy implications: alpha migrativity and generalised laws of importation

Michał Baczyński, Balasubramaniam Jayaram, Radko Mesiar
2020 Information Sciences  
Citation style: Baczyński Michał, Jayaram Balasubramaniam, Mesiar Radko. (2020). Fuzzy implications: alpha migrativity and generalised laws of importation. a b s t r a c t 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
more » ... nd 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 fatcat:3k3ey2c2uffjnf7c5mxbaiobvi