Fuzzy functions: a fuzzy extension of the category SET and some related categories

[EN] In research Works where fuzzy sets are used, mostly certain usual functions are taken as morphisms. On the other hand, the aim of this paper is to fuzzify the concept of a function itself. Namely, a certain class of L-relations F : X x Y -> L is distinguished which could be considered as...

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Bibliographic Details
Authors: Höhle, Ulrich, Porst, Hans-E., Sostak, Alexander P.
Format: article
Publication Date:2000
Country:España
Institution:Universitat Politècnica de València (UPV)
Repository:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Language:English
OAI Identifier:oai:riunet.upv.es:10251/81900
Online Access:https://riunet.upv.es/handle/10251/81900
Access Level:Open access
Keyword:L-relation
L-fuzzy function
Fuzzy category
Fuzzy topology
Fuzzy group
Description
Summary:[EN] In research Works where fuzzy sets are used, mostly certain usual functions are taken as morphisms. On the other hand, the aim of this paper is to fuzzify the concept of a function itself. Namely, a certain class of L-relations F : X x Y -> L is distinguished which could be considered as fuzzy functions from an L-valued set (X,Ex) to an L-valued set (Y,Ey). We study basic properties of these functions, consider some properties of the corresponding category of L-valued sets and fuzzy functions as well as briefly describe some categories related to algebra and topology with fuzzy functions in the role of morphisms.