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\(L\)-ordered neighborhood systems of stratified \(L\)-concave structures. (English) Zbl 1465.52004

Summary: Based on a complete residuated lattice \(L\), the notion of stratified \(L\)-concave structures is introduced, which is the dual structure of convex structures in the \(L\)-setting. For characterizing it, \(L\)-ordered neighborhood systems and \(L\)-ordered interior operators in the framework of stratified \(L\)-concave spaces are introduced. Moreover, it is shown that \(L\)-ordered neighborhood spaces, \(L\)-ordered interior spaces and stratified \(L\)-concave spaces are isomorphic from the view of category.

MSC:

52A01 Axiomatic and generalized convexity
03E72 Theory of fuzzy sets, etc.
06A15 Galois correspondences, closure operators (in relation to ordered sets)
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