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Join-meet preserving maps and Alexandrov fuzzy topologies. (English) Zbl 1351.06002

Summary: In this paper, we investigate the properties of join-meet preserving maps in complete residuated lattices. We define join-meet approximation operators as a generalization of fuzzy rough sets in complete residuated lattices. Moreover, we investigate the relations between join-meet preserving maps and Alexandrov fuzzy topologies. We give their examples.

MSC:

06A15 Galois correspondences, closure operators (in relation to ordered sets)
54A40 Fuzzy topology
06B23 Complete lattices, completions
06D72 Fuzzy lattices (soft algebras) and related topics
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