Fuzzy convergence structures in the framework of L-convex spaces

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:

Fuzzy convergence structures , Fuzzy convex structures , Fuzzy remote-neighborhood systems , L-convex ideals