Equivalent fuzzy sets. (English) Zbl 1249.03088

Summary: Necessary and sufficient conditions under which two fuzzy sets (in the most general, poset-valued setting) with the same domain have equal families of cut sets are given. The corresponding equivalence relation on the related fuzzy power set is investigated. The relationship of poset-valued fuzzy sets and fuzzy sets for which the co-domain is the Dedekind-MacNeille completion of that poset is deduced.


03E72 Theory of fuzzy sets, etc.
06A15 Galois correspondences, closure operators (in relation to ordered sets)
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