Fuzzy convergence structures in the framework of L-convex spaces

Xiu, Z. Y.; Li, Q. H.; Pang, B.

doi:10.22111/ijfs.2020.5411

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	Fuzzy convergence structures in the framework of L-convex spaces
Iranian Journal of Fuzzy Systems
دوره 17، شماره 4، مهر و آبان 2020، صفحه 139-150 اصل مقاله (411.3 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22111/ijfs.2020.5411
نویسندگان
Z. Y. Xiu^* ¹؛ Q. H. Li²؛ B. Pang³
¹College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, China
²School of Mathematics and Information Sciences, Yantai University, Yantai, China
³School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, China
چکیده
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.
کلیدواژه‌ها
Fuzzy convergence structures؛ fuzzy convex structures؛ fuzzy remote-neighborhood systems؛ $L$-convex ideals

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Fuzzy convergence structures in the framework of L-convex spaces