Novel Distance and Similarity Measures on Hesitant Fuzzy Linguistic Term Sets and Their Application in Clustering Analysis

Abstract

The existing distance and similarity measures of hesitant fuzzy linguistic term sets (HFLTSs) only cover the difference of linguistic terms but have no consideration of the difference between the numbers of linguistic terms. Thus, the concept of hesitance degree of HFLTSs is introduced to describe the hesitant degree among several linguistic terms in each HFLTS during the decision-makers' evaluating process. Considering the hesitance degree of HFLTSs, several novel distance and similarity measures of HFLTSs are developed, and their properties are discussed. Afterward, a novel hesitant fuzzy linguistic-based on the novel similarity measures and the Boole matrix is developed to classify the objects with hesitant fuzzy linguistic information and a numerical example of the automobile recommendation is given to illustrate the performance of our developed clustering method. The results indicate that our developed clustering method can fully express the original evaluation information and has less computational effects on clustering results than the previous method.

Clustering algorithms based on correlation coefficients for probabilistic linguistic term sets

“…In the decision‐making problems, the collected data for cluster analysis usually are uncertain and fuzzy . To analyze this kind of data, many clustering algorithms have been studied for fuzzy sets, IFSs, and HFSs . For instance, Giordani and Ramos‐Guajardo put forward a so‐called non‐Euclidean fuzzy relational data clustering (NE‐FRC) algorithm to cluster random fuzzy sets.…”

“…Xu and Wu put forward an intuitionistic fuzzy C‐means algorithm for clustering IFSs. Zhang and Xu defined some novel distance and similarity formulas for measuring the degree of deviation between any two HFSs and then used them into cluster analysis. However, through our detailed survey, it is noticed that there are no investigation and research over the cluster analysis for PLTSs.…”

Informational Paradigm, management of uncertainty and theoretical formalisms in the clustering framework: A review

“…Zhang and Xu [343] proposed a novel concept of hesitancy index of hesitant fuzzy set to measure the hesitancy degree among the possible values in each hesitant fuzzy element of the hesitant fuzzy set. By taking into account their hesitancy indices, they suggested new methods for measuring the distances between hesitant fuzzy sets and discuss their properties.…”

Multi-Attribute Group Decision Making Based on Hesitant Fuzzy Sets, Topsis Method and Fuzzy Preference Relations

“…Dong, Chen, and Herrera (2015) proposed a novel distance-based consensus measure for hesitant linguistic group decision making. Zhang and Xu (2015) believed that distance and similarity measures were inaccurate in some cases. Therefore, a new concept of fuzzy set hesitant fuzzy index was proposed to measure the hesitation degree among the possible values in each hesitant fuzzy element of the HFS.…”

“…(1) When using aggregation operators or score functions to rank HFSs, the results are not consistent with the actual situation (Lan, Jin, Zheng, & Hu, 2017); (2) When some MAGDM methods of using distance and similarity measures, HFEs need to be extended to the same length (Li et al, 2015;Zeng et al, 2016;Zhang & Xu, 2015), these methods have changed the original decision information, which may lead to inaccurate decision results; (3) When using fuzzy preference relations for MAGDM problems, in the decision process, it is often difficult to ensure consistency, and thus the algorithm is modified (Khalid & Beg, 2016;Zhang et al, 2015b), which resulting in the changes in decision information, which may lead to inconsistent results, thus may make decision failure. To overcome the flaws, the rest of this paper is arranged as follows: In Section 1, some basic concepts of HFSs and fuzzy preference relations are reviewed.…”