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Reinterpreting a fuzzy subset by means of a Sincov’s functional equation. (English) Zbl 1309.03021
Summary: Throughout the paper it is shown that the classical definition of a fuzzy subset carries additional structures. The concept of a fuzzy subset is regarded from an alternative point of view: namely, the characteristic function of a fuzzy subset may be reinterpreted in terms of a Sincov’s functional equation in two variables. Since the solutions of a Sincov’s functional equation are also closely related to the existence of representable total preorders, an special attention is paid to the relationship between fuzzy subsets and total preorders defined on a universe. Some possible applications of this approach are pointed out in the final section of the manuscript.

03E72 Theory of fuzzy sets, etc.
39B52 Functional equations for functions with more general domains and/or ranges
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