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Fuzzy implications: alpha migrativity and generalised laws of importation
پیامدهای فازی: مهاجرت آلفا و قوانین کلی واردات-2020 In this work, we discuss the law of α-migrativity as applied to fuzzy implication func- tions in a meaningful way. A generalisation of this law leads us to Pexider-type func- tional equations connected with the law of importation, viz., the generalised law of im- portation 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. Keywords: Fuzzy connectives | T-norm | Fuzzy implication | Law of importation | Alpha-migrativity |
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