The restricted hull operator of M-fuzzifying convex structures¹

Article type: Research Article

Authors: Shi, Fugui^a | Li, Erqiang^{a; b; *}

Affiliations: [a] School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, P.R. China | [b] School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, P.R. China

Correspondence: [*] Corresponding author. Erqiang Li, Tel.: +86 15652999499; E-mail: [email protected].

Note: [1] The project is supported by the National Natural Science Foundation of China (11371002) and Specialized Research Fund for the Doctoral Program of Higher Education (20131101110048)

Abstract: In this paper, the notion of M-fuzzifying restricted hull operators is introduced and several equivalent characterizations are given. It is shown that there is a one-to-one correspondence between M-fuzzifying restricted hull operators and M-fuzzifying convex structures. As applications, some properties of the cut convex structures of an M-fuzzifying convex structure and of M-fuzzifying convexity preserving functions and of M-fuzzifying convex-to-convex functions are derived. In addition, using M-fuzzifying restricted hull operators, some M-fuzzifying convexities are naturally constructed from M-fuzzy quasi-orders.

Keywords: Convex structure, M-fuzzifying convex structure, M-fuzzifying restricted hull operator, M-fuzzifying betweenness

DOI: 10.3233/IFS-151765

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 1, pp. 409-421, 2016