Höhle, Ulrich; Porst, Hans-E.; Šostak, Alexander P. Fuzzy functions: A fuzzy extension of the category SET and some related categories. (English) Zbl 0977.03028 Appl. Gen. Topol. 1, No. 1, 115-127 (2000). 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. Reviewer: Zhang Dexue (Sichuan) Cited in 1 Document MSC: 03E72 Theory of fuzzy sets, etc. 18B99 Special categories 54A40 Fuzzy topology Keywords:fuzzy category; fuzzy topology; fuzzy function; \(L\)-relation; category of \(L\)-valued sets PDFBibTeX XMLCite \textit{U. Höhle} et al., Appl. Gen. Topol. 1, No. 1, 115--127 (2000; Zbl 0977.03028) Full Text: DOI