Convex hull and closure of a fuzzy set

Authors:
Yuanguo Zhu
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
Venue:
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
Year:
2005

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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.