A new version of distance and similarity measures for hesitant fuzzy linguistic term sets and its application

Article type: Research Article

Authors: Tao, Zhifu^a | Han, Bing^b | Chen, Huayou^{b; *} | Zhu, Jiaming^b

Affiliations: [a] School of Economics, Anhui University, Hefei, Anhui, China | [b] School of Mathematical Sciences, Anhui University, Hefei, Anhui, China

Correspondence: [*] Corresponding author. Huayou Chen, School of Mathematical Sciences, Anhui University, Hefei, Anhui 230601, China. Tel.: +86 136 156 90958; E-mail: [email protected].

Abstract: In this paper, a new version of distance measure for hesitant fuzzy linguistic term sets is developed. The new version of distance measure provides an objective way to handle the diverse dimensions of two HFLTSs, i.e., without shortening the HFLTS to be a linguistic interval or extending the shorter one by adding linguistic terms. The Hamming distance, the Euclidean distance and the corresponding forms are put forward. By the relationship between the distance measure and the similarity measure, some parallel similarity measures are also investigated. As applications of the proposed measures, the issues of pattern recognition, clustering analysis and multi-criteria decision making are considered.

Keywords: Distance measure, similarity measure, hesitant fuzzy linguistic term sets, pattern recognition, decision making

DOI: 10.3233/JIFS-16381

Journal: Journal of Intelligent & Fuzzy Systems, vol. 34, no. 3, pp. 1801-1811, 2018