16 research outputs found

    Migrativity properties of 2-uninorms over semi-t-operators

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    summary:In this paper, we analyze and characterize all solutions about α\alpha-migrativity properties of the five subclasses of 2-uninorms, i. e. CkC^{k}, Ck0C^{0}_{k}, Ck1C^{1}_{k}, C10C^{0}_{1}, C01C^{1}_{0}, over semi-t-operators. We give the sufficient and necessary conditions that make these α\alpha-migrativity equations hold for all possible combinations of 2-uninorms over semi-t-operators. The results obtained show that for GCkG\in C^{k}, the α\alpha-migrativity of GG over a semi-t-operator Fμ,νF_{\mu,\nu} is closely related to the α\alpha-section of Fμ,νF_{\mu,\nu} or the ordinal sum representation of t-norm and t-conorm corresponding to Fμ,νF_{\mu,\nu}. But for the other four categories, the α\alpha-migrativity over a semi-t-operator Fμ,νF_{\mu,\nu} is fully determined by the α\alpha-section of Fμ,νF_{\mu,\nu}

    Fuzzy implications: alpha migrativity and generalised laws of importation

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    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

    Distributivity of ordinal sum implications over overlap and grouping functions

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    summary:In 2015, a new class of fuzzy implications, called ordinal sum implications, was proposed by Su et al. They then discussed the distributivity of such ordinal sum implications with respect to t-norms and t-conorms. In this paper, we continue the study of distributivity of such ordinal sum implications over two newly-born classes of aggregation operators, namely overlap and grouping functions, respectively. The main results of this paper are characterizations of the overlap and/or grouping function solutions to the four usual distributive equations of ordinal sum fuzzy implications. And then sufficient and necessary conditions for ordinal sum implications distributing over overlap and grouping functions are given

    On Some Functional Equations Related to Alpha Migrative t-conorms

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    In this contribution, we analyse in details the recently introduced definition of migrative tconorms [see Fuzzy implications: alpha migrativity and generalised laws of importation, M. Baczy´nski, B. Jayaram, R. Mesiar, 2020]. We also focus on some general functional equations, which might be obtained from such a notion. We concentrate on some particular well-known families of fuzzy implications and show solutions of those equations among this kind of fuzzy implication functions
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