4 research outputs found

    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

    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

    Fuzzy Sets, Fuzzy Logic and Their Applications 2020

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    The present book contains the 24 total articles accepted and published in the Special Issue “Fuzzy Sets, Fuzzy Logic and Their Applications, 2020” of the MDPI Mathematics journal, which covers a wide range of topics connected to the theory and applications of fuzzy sets and systems of fuzzy logic and their extensions/generalizations. These topics include, among others, elements from fuzzy graphs; fuzzy numbers; fuzzy equations; fuzzy linear spaces; intuitionistic fuzzy sets; soft sets; type-2 fuzzy sets, bipolar fuzzy sets, plithogenic sets, fuzzy decision making, fuzzy governance, fuzzy models in mathematics of finance, a philosophical treatise on the connection of the scientific reasoning with fuzzy logic, etc. It is hoped that the book will be interesting and useful for those working in the area of fuzzy sets, fuzzy systems and fuzzy logic, as well as for those with the proper mathematical background and willing to become familiar with recent advances in fuzzy mathematics, which has become prevalent in almost all sectors of the human life and activity

    On alpha-Migrativity of Fuzzy Implications and the 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 generalisations of the law of importation, viz., the generalised law of importation I(C(α,x),y) = I(x,J(α,y)) (GLI) and the generalised cross-law of importation I(C(α,x),y)=J(x,I(α,y)) (CLI), where C is a generalised conjunction. We firstly show 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 may be related
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