6 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

    Invariability, orbits and fuzzy attractors

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    In this paper, we present a generalization of a new systemic approach to abstract fuzzy systems. Using a fuzzy relations structure will retain the information provided by degrees of membership. In addition, to better suit the situation to be modelled, it is advisable to use T-norm or T-conorm distinct from the minimum and maximum, respectively. This gain in generality is due to the completeness of the work on a higher level of abstraction. You cannot always reproduce the results obtained previously, and also sometimes different definitions with different views are obtained. In any case this approach proves to be much more effective when modelling reality

    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

    An extension of the migrative property for uninorms

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