Distance Measure and Correlation Coefficient for Linguistic Hesitant Fuzzy Sets and Their Application

Abstract

Linguistic hesitant fuzzy sets (LHFSs) permit the decision maker to apply several linguistic terms with each having several membership degrees to denote his/her preference of one thing. This type of fuzzy sets can well address the qualitative and quantitative cognitions of the decision maker as well as reflect his/her hesitancy, uncertainty and inconsistency. This paper introduces a distance measure between any two LHFSs and then defines a correlation coefficient of LHFSs. Considering the application of LHFSs, the weighted distance measure and the weighted correlation coefficient of LHFSs are defined. To address the interactions between elements in a set, the Shapley weighted distance measure and the Shapley weighted correlation coefficient are presented. It is worth noting that when the elements are independent, they degenerate to the associated weighted distance measure and the weighted correlation coefficient, respectively. After that, their application to pattern recognition is studied. Furthermore, an approach to multi-attribute decision making under linguistic hesitant fuzzy environment is developed. Meanwhile, numerical examples are offered to show the concrete application of the developed procedure.

Proportional hesitant 2‐tuple linguistic distance measurements and extended VIKOR method: Case study of evaluation and selection of green airport plans

“…In addition, the compromise solution is obtained on the premise of the ideal solution, while the application of the comparison method is of great importance in obtaining the ideal solution, and the comparison of fuzzy information also plays an important role in solving practical MAGDM problems 32 . Previous studies, on the basis of the TOPSIS method, have proposed similarity and correlation coefficients of HFSs for fuzzy decision‐making 33,34 . However, existing methods still face challenges when it comes to comparison of PH2TLTSs.…”

“…32 Previous studies, on the basis of the TOPSIS method, have proposed similarity and correlation coefficients of HFSs for fuzzy decision-making. 33,34 However, existing methods still face challenges when it comes to comparison of PH2TLTSs. Besides, distance measurement is also fundamentally important and plays a key role in determining the compromise plan.…”

A Decision Framework under a Linguistic Hesitant Fuzzy Set for Solving Multi-Criteria Group Decision Making Problems

“…They also extended power operators under an LHFS and applied the same for decision-making. Guan et al [31] extended different distance and correlation measures under an LHFS environment for the decision-making process. Recently, Dong et al [32] extended the popular VIKOR method to an LHFS environment and applied the same for intelligent transport system selection.…”

Prioritized Dual Hesitant Fuzzy Aggregation Operators Based on <italic>t</italic>-Norms and <italic>t</italic>-Conorms with Their Applications in Decision Making

“…In decision making, uncertainty is ubiquitous since objective things are uncertain and complex, and the managing and modelling of uncertain information are crucial for the acquisition of desirable solutions (Xu and Zhao, 2016). To date, a large number of tools have been proposed to model people's imprecise decision information from different angles (Atanassov, 1986;Torra, 2010;Zhu et al, 2012;Zhou et al, 2013;Pang et al, 2016;Guan et al, 2017;Gou et al, 2017;Liao et al, 2017;Zhang, 2017;Zhao et al, 2018). Among them, to fully reflect the characteristics of affirmation and negation of human's cognitive performance, Atanassov (1986) introduced intuitionistic fuzzy sets (IFSs), which assign to each element a membership degree and a non-membership degree.…”