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Title:
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On the Induction of New Fuzzy Relations, New Fuzzy Operators and Their Aggregation
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Author:
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Carmona Cervelló, Neus; Elorza, Jorge; Recasens Ferrés, Jorge; Bragard, Jean
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Other authors:
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Universitat Politècnica de Catalunya. Departament d'Estructures a l'Arquitectura; Universitat Politècnica de Catalunya. FIA - Modelització Matemàtica Funcional i Aplicacions |
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Abstract:
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In this paper we generate fuzzy relations and fuzzy operators using different kind of generators and we study the relationship between them. Firstly, we introduce a new fuzzy preorder induced by a fuzzy operator. We generalize this preorder to a fuzzy relation generated by two fuzzy operators and we analyze its properties. Secondly, we introduce and explore two ways of inducing a fuzzy operator, one from a fuzzy operator and a fuzzy relation and the other one from two fuzzy operators. The first one is an extension of the well-known fuzzy operator induced by a fuzzy relation through Zadeh’s compositional rule. Finally, we aggregate these operators using the quasi-arithmetic mean associated to a continuous Archimedean t-norm. The aim is to compare the operator induced by the quasi-arithmetic mean of the generators with the quasi-arithmetic mean of the generated operators. |
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Abstract:
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Peer Reviewed |
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Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Lògica matemàtica
-Fuzzy logic
-Lògica difusa |
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Rights:
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Document type:
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Article - Submitted version
Article |
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Published by:
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Springer
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