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Fuzzy functions: A fuzzy extension of the category SET and some related categories. (English) Zbl 0977.03028

Since functions \(f:X\to Y\) between two sets can be regarded as a special kind of relations between \(X\) and \(Y\), that is to say, a special kind of subsets of \(X\times Y\) with certain conditions, in this paper the authors define a fuzzy function between two \(L\)-subsets of \(L\)-valued sets \(X\) and \(Y\), respectively, as a certain \(L\)-relation between \(X\) and \(Y\), that is, a function \(X\times Y\to L\) with certain conditions. Basic properties such as preimages, images, injectivity, surjectivity of these functions etc. are investigated. The corresponding category of \(L\)-valued sets and fuzzy functions and some categories related to algebra and topology are discussed.

MSC:

03E72 Theory of fuzzy sets, etc.
18B99 Special categories
54A40 Fuzzy topology
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