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

Li, Hongyan; Wang, Kai

J. Nonlinear Convex Anal. 21, No. 12, 2783-2793 (2020).

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)

Keywords:

complete residuated lattice; \(L\)-ordered neighborhood system; \(L\)-ordered interior operator; stratified \(L\)-concave structure