Convex hull and closure of a fuzzy set

Article type: Research Article

Authors: Zhu, Yuanguo

Affiliations: Department of Information and Computational Sciences, Nanjing University of Science and Technology, Nanjing 210094, China. Tel.: +86 25 8431 5878; E-mail: ygzhu@mail.njust.edu.cn

Abstract: Convex fuzzy set and closed fuzzy set are important concepts in the fuzzy set theory. In this paper, concepts of convex hull, closure, convex closure and closed convex hull of a fuzzy set are presented. Some properties of these concepts are studied, and the relations among these concepts are also investigated. Furthermore, the expression theorems for points in level sets of convex hull and closure of a fuzzy set are given.

Keywords: convex hull, closure, convex closure, closed convex hull, fuzzy set

Journal: Journal of Intelligent & Fuzzy Systems, vol. 16, no. 1, pp. 67-73, 2005