Subtraction and division operations over hesitant fuzzy sets

Article type: Research Article

Authors: Liao, Huchang | Xu, Zeshui^;

Affiliations: Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai, China | College of Sciences, PLA University of Science and Technology, Nanjing, China

Note: [] Corresponding author. Zeshui Xu, Tel./Fax: +86 25 84483382; E-mail: xuzeshui@263.net (Z. Xu); liaohuchang@163.com (H. Liao).

Abstract: Hesitant fuzzy set (HFS), which permits the membership having a set of possible values, has turned out to be a powerful structure in expressing uncertainty and vagueness. In this paper, we propose two new basic operations over HFSs, which are the subtraction operation and the division operation. Several operational laws of these two operations over HFSs are given. The relationship between intuitionistic fuzzy set (IFS) and HFS is further verified in terms of these two operations. In addition, the relationships between these two operations are also established in this paper. The operations can be immediately extended into interval-valued hesitant fuzzy sets and dual hesitant fuzzy sets. The subtraction and division operations are significantly important in forming the integral theoretical framework of HFS and may have many practical applications in decision making.

Keywords: Hesitant fuzzy set, subtraction operation, division operation

DOI: 10.3233/IFS-130978

Journal: Journal of Intelligent & Fuzzy Systems, vol. 27, no. 1, pp. 65-72, 2014