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Fuzzy concepts defined via residuated maps. (English) Zbl 0985.54500

Summary: We show how some concepts such as “fuzzy subset” or “fuzzy closed set of a topological space” may be identified with certain maps between complete lattices. Underlying this representation is the fact that the category of closure spaces contains the category of complete lattices and residuated maps as a reflective subcategory. This approach suggests a uniform method for fuzzifying concepts such as “ideals”, “subgroups” and other collections of subsets having a complete lattice structure.

MSC:

54A40 Fuzzy topology
03E72 Theory of fuzzy sets, etc.
06A15 Galois correspondences, closure operators (in relation to ordered sets)
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References:

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