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Non-dual fuzzy connections. (English) Zbl 1060.03042

The present paper introduces and studies fuzzy conjugated pairs, with their underlying closure operators and hierarchical structure. Isotone versions of fuzzy Galois connections and closure operators are also studied, arguing that they are not dual to the antitone ones, but providing quite similar results about them. A form of artifical common treatment of classically dual notions that fail to be fuzzily dual is concretized into the concept of \((\alpha,\beta)\)-connection, which could be seen as recovering remains of duality by means of common polynominal invariants.

MSC:

03B52 Fuzzy logic; logic of vagueness
06A15 Galois correspondences, closure operators (in relation to ordered sets)
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