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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.

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