7 research outputs found

    The f -index of inclusion as optimal adjoint pair for fuzzy modus ponens

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    We continue studying the properties of the f -index of inclusion and show that, given a fixed pair of fuzzy sets, their f -index of inclusion can be linked to a fuzzy conjunction which is part of an adjoint pair. We also show that, when this pair is used as the underlying structure to provide a fuzzy interpretation of the modus ponens inference rule, it provides the maximum possible truth-value in the conclusion among all those values obtained by fuzzy modus ponens using any other possible adjoint pair.Partially supported by the Spanish Ministry of Science, Innovation and Universities (MCIU), State Agency of Research (AEI), Junta de Andalucía (JA), Universidad de Málaga (UMA) and European Regional Development Fund (FEDER) through the projects PGC2018-095869-B-I00 (MCIU/AEI/FEDER) and UMA2018-FEDERJA-001 (JA/UMA/FEDER). Funding for open access charge: Universidad de Málaga / CBU

    Fuzzy closure systems: Motivation, definition and properties

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    The aim of this paper is to extend closure systems from being crisp sets with certain fuzzy properties to proper fuzzy sets. The presentation of the paper shows a thorough discussion on the different alternatives that could be taken to define the desired fuzzy closure systems. These plausible alternatives are discarded if they are proven impossible to be in a bijective correspondence with closure operators. Finally, a definition of fuzzy closure system is established and a one-to-one relation with closure operators is proved.The aim of this paper is to extend closure systems from being crisp sets with certain fuzzy properties to proper fuzzy sets. The presentation of the paper shows a thorough discussion on the different alternatives that could be taken to define the desired fuzzy closure systems. These plausible alternatives are discarded if they are proven impossible to be in a bijective correspondence with closure operators. Finally, a definition of fuzzy closure system is established and a one-to-one relation with closure operators is proved. Funding for open access charge: Universidad de Málaga / CBU

    Fuzzy relational Galois connections between fuzzy transitive digraphs

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    We present a fuzzy version of the notion of relational Galois connection between fuzzy transitive directed graphs (fuzzy T-digraphs) on the specific setting in which the underlying algebra of truth values is a complete Heyting algebra. The components of such fuzzy Galois connection are fuzzy relations satisfying certain reasonable properties expressed in terms of the so-called full powering. Moreover, we provide a necessary and sufficient condition under which it is possible to construct a right adjoint for a given fuzzy relation between a fuzzy T-digraph and an unstructured set.This research is partially supported by the State Agency of Research (AEI), the Spanish Ministry of Science, Innovation and Universities (MCIU), the European Social Fund (FEDER), the Junta de Andalucía (JA), and the Universidad de Málaga (UMA) through the research projects with reference PGC2018-095869-B-I00, PID2021-127870OB-I00, (MCIU/AEI/FEDER, UE) and UMA18-FEDERJA-001 (JA/ UMA/ FEDER, UE). B. De Baets was supported by the Flemish Government under the “Onderzoeksprogramma Artificiële Intelligentie (AI) Vlaanderen” programme. Funding for open access charge: Universidad de Málaga / CBU

    Relational Galois connections between transitive fuzzy digraphs

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    Fuzzy-directed graphs are often chosen as the data structure to model and implement solutions to several problems in the applied sciences. Galois connections have also shown to be useful both in theoretical and in practical problems. In this paper, the notion of relational Galois connection is extended to be applied between transitive fuzzy directed graphs. In this framework, the components of the connection are crisp relations satisfying certain reasonable properties given in terms of the so-called full powering

    Relation-based Galois connections: towards the residual of a relation

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    Inma P. Cabrera, Pablo Cordero, Manuel Ojeda-Aciego, Relation-based Galois connections: towards the residual of a relation, CMMSE 2017: Proceedings of the 17th International Conference on Mathematical Methods in Science and Engineering ( ISBN: 978-84-617-8694-7) , pp. 469--475We explore a suitable generalization of the notion of Galois connection in which their components are binary relations. Many different approaches are possible depending both on the (pre-)order relation between subsets in the underlying powerdomain and the chosen type of relational composition.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

    Fuzzy Adjunctions revisited

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    En este trabajo se intenta obtener la noción de adjunción más débil entre estructuras difusas. Este trabajo continúa la línea de investigación en el estudio y construcción d adjunciones que han realizado los autores en contribuciones anteriores. Nos centraremos ahora en la noción de relación difusa que es en cierto sentido interpretable como una función difusa. Existen varios trabajos en la literatura relacionados con este tema. Entre todos ellos, trabajaremos con un enfoque próximo al de Ciric et al cuando definen las denominadas funciones parciales difusas. El nuevo concepto estudiado es el de relaciones difusas funcionales y la construcción de adjunciones entre ellas.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech
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