Distance and similarity measures for dual hesitant fuzzy sets and their applications in pattern recognition

Article type: Research Article

Authors: Su, Zhan^a | Xu, Zeshui^{b; *} | Liu, Haifeng^a | Liu, Shousheng^a

Affiliations: [a] College of Sciences, PLA University of Science and Technology, Nanjing, Jiangsu, China | [b] Business School, Sichuan University, Chengdu, Sichuan, China

Correspondence: [*] Correspondence to: Zeshui Xu, Business School, Sichuan University, Chengdu, 610064, China. xuzeshui@263.net

Abstract: Dual hesitant fuzzy set (DHFS) is a very comprehensive set which includes fuzzy set, intuition fuzzy set and hesitant fuzzy set as its special cases. Distance and similarity measures play great roles in many areas, such as decision making, pattern recognition, etc. In this paper, we introduce some distance and similarity measures for DHFSs based on Hamming distance, Euclidean distance and Hausdorff distance. Two examples are used to illustrate these distance and similarity measures and their applications in pattern recognition. Finally, the comparisons among DHFSs and the corresponding IVIFSs and HFSs are made in detail by utilizing the developed distance measures.

Keywords: Dual hesitant fuzzy set (DHFS), hesitant fuzzy set (HFS), distance measures, similarity measures, pattern recognition

DOI: 10.3233/IFS-141474

Journal: Journal of Intelligent & Fuzzy Systems, vol. 29, no. 2, pp. 731-745, 2015