Fuzzy convergence structures in the framework of L-convex spaces

Document Type : Research Paper

Authors

1 College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, China

2 School of Mathematics and Information Sciences, Yantai University, Yantai, China

3 School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, China

Abstract

In this paper,  fuzzy convergence theory in the framework of $L$-convex spaces is introduced. Firstly, the concept of $L$-convex remote-neighborhood spaces is introduced and it is shown that the  resulting category is isomorphic to that of $L$-convex spaces. Secondly, by means of $L$-convex ideals, the notion of $L$-convergence spaces is introduced and it is proved that the  category of $L$-convex spaces can be embedded in that of $L$-convergence spaces as a reflective subcategory.  Finally, the concepts of  convex and preconvex $L$-convergence spaces are introduced and it is shown that  the  resulting categories are isomorphic to  the  categories of $L$-convex spaces  and  $L$-preconvex remote-neighborhood spaces, respectively.

Keywords

Iranian Journal of Fuzzy Systems
Volume 17, Issue 4
July and August 2020
Pages 139-150

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