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On the construction of adjunctions between a fuzzy preposet and an unstructured set. (English) Zbl 1387.06004

Galois connections can be identified in several research areas, and they have shown to be an interesting tool both for theory and for applications. R. Bělohlávek [Math. Log. Q. 45, No. 4, 497–504 (1999; Zbl 0938.03079)] generalized the Galois connections from the point of view of fuzzy logic and the fuzzy Galois connections have been studied by many authors. The purpose of this paper is to investigate the construction of adjunctions (isotone Galois connections) between a fuzzy preposet and an unstructured set. Given a fuzzy preposet \(\mathbb A=(A,\rho_A)\) and an unstructured set \(B\), the authors consider the mapping \(f:\mathbb A\longrightarrow B\) and characterize those situations in which \(B\) can be endowed with a fuzzy preorder relation and an isotone mapping \(f:B\longrightarrow \mathbb A\) can be built such that the pair \((f, g)\) becomes an adjunction.

MSC:

06A15 Galois correspondences, closure operators (in relation to ordered sets)
06A75 Generalizations of ordered sets
03E72 Theory of fuzzy sets, etc.

Citations:

Zbl 0938.03079
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References:

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