(L, M)-fuzzy internal relations and (L, M)-fuzzy enclosed relations

Article type: Research Article

Authors: Shi, Yi^{a; b} | Shi, Fu-Gui^{a; b; *}

Affiliations: [a] School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P.R. China | [b] Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing 100081, P.R. China

Correspondence: [*] Corresponding author. Fu-Gui Shi, Tel.:+86 13488811735; E-mail: fuguishi@bit.edu.cn.

Abstract: In this paper, the concepts of (L, M)-fuzzy internal relations and (L, M)-fuzzy enclosed relations between two L-fuzzy sets are introduced. They are defined respectively to be M-fuzzy subsets of LX × LX satisfying a set of axioms. A categorical approach is provided to present these relations. It is proved that the category of (L, M)-fuzzy internal relation spaces, the category of (L, M)-fuzzy enclosed relation spaces and the category of (L, M)-fuzzy topological spaces are isomorphic. In addition, some (L, M)-fuzzy internal relations and (L, M)-fuzzy enclosed relations are naturally constructed from (L, M)-fuzzy quasi-uniformities and (L, M)-fuzzy S-quasi-proximities.

Keywords: (L, M)-fuzzy topology; (L, M)-fuzzy internal relation; (L, M)-fuzzy enclosed relation; (L, M)-fuzzy IRDP mapping; (L, M)-fuzzy ERDP mapping

DOI: 10.3233/JIFS-172129

Journal: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 6, pp. 5153-5165, 2019