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) |
References:
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