22 research outputs found

    Mathematical Fuzzy Logic in the Emerging Fields of Engineering, Finance, and Computer Sciences

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    Mathematical fuzzy logic (MFL) specifically targets many-valued logic and has significantly contributed to the logical foundations of fuzzy set theory (FST). It explores the computational and philosophical rationale behind the uncertainty due to imprecision in the backdrop of traditional mathematical logic. Since uncertainty is present in almost every real-world application, it is essential to develop novel approaches and tools for efficient processing. This book is the collection of the publications in the Special Issue “Mathematical Fuzzy Logic in the Emerging Fields of Engineering, Finance, and Computer Sciences”, which aims to cover theoretical and practical aspects of MFL and FST. Specifically, this book addresses several problems, such as:- Industrial optimization problems- Multi-criteria decision-making- Financial forecasting problems- Image processing- Educational data mining- Explainable artificial intelligence, etc

    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 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

    Funciones t-migrativas t-overlap: una generalización de migratividad en funciones t-overlap

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    Este artículo introduce una generalización de funciones migrativas por extensión de la condición de la operación producto aplicada en las variables. Más específicamente, en lugar de exigir multiplicar la variable x por un número real alfa; en este trabajo se trabaja este número alfa con las variables de acuerdo a una t-norma. Se denomina a esta generalización función t-migrativa con respecto a tal tnorma. Luego se analizan las propiedades principales de funciones t-migrativas en funciones t-overlap y se introducen algunos métodos de construcción de este tipo de funciones.This paper introduces a generalization of migrative functions by extending the conditions of the product operation applied in the variables. We operate a number with the variables according to a t-norm instead of multiplying the variable x by this number. Such generalization, whenever it occurs, is called a t-migrative function with respect to such t-norm. Furthermore, we analyse the main properties of t-migrative and t-overlap functions. We introduce some interesting methods of construction of such 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
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