Fuzzy functions: a fuzzy extension of the category SET and some related categories
<p>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.</p>
2020 ◽
Vol 11
(SPL1)
◽
pp. 171-174
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2021 ◽
Vol 1
(1)
◽
pp. 71-88
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2021 ◽
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