L-convex convergence relation and L-convex ideal-convergence structure

Document Type : Research Paper

Authors

School of Mathematics and Statistics, Anhui Normal University, Wuhu, China

Abstract

In the framework of L-convex spaces, this paper is aim to study fuzzy convergence structures
of L-convex space in a viewpoint of fuzzy relations. For this purpose, L-directed relation is introduced
and some of its examples are proposed. Based on this, notions of L-convergence relation and L-convex convergence relation are introduced. It is proved that there is a Galois's connection between the category of L-convergence relation spaces and the category of L-convex enclosed relation spaces. In particular, L-convex convergence relation spaces and L-convex enclosed relation spaces are categorically isomorphic. Also, notions of L-ideal-convergence structure and L-convex ideal-convergence structure are introduced. It is proved that L-convergence relation spaces and L-ideal-convergence spaces are categorically isomorphic. In particular, L-convex convergence relation spaces and L-convex ideal-convergence spaces are categorically isomorphic.

Keywords

Main Subjects

References

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Iranian Journal of Fuzzy Systems
Volume 21, Issue 5
September and October 2024
Pages 31-49

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