Hesitant sets and hesitant relations

Article type: Research Article

Authors: Hu, Bao Qing^{; *}

Affiliations: School of Mathematics and Statistics, Wuhan University, Wuhan, P.R. China

Correspondence: [*] Corresponding author. Bao Qing Hu, School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P.R. China. E-mail: bqhu@whu.edu.cn.

Abstract: Firstly, this paper is intended to point out the lack of mathematical rigor in logic operation definition of hesitant fuzzy sets and to revise these operations. Then, new logical operations and partially ordered relations are introduced on a linearly ordered set, whose properties are studied accordingly. Finally, the concepts of hesitant set and hesitant relation are given together with their operations and corresponding properties. It can be found that some existing concepts are special examples of hesitant sets, such as shadowed sets, hesitant fuzzy sets and interval-valued hesitant fuzzy sets etc.

Keywords: Posets, fuzzy sets, hesitant fuzzy sets, hesitant fuzzy relations

DOI: 10.3233/JIFS-17314

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 6, pp. 3629-3640, 2017