Hesitant fuzzy linguistic correlation coefficient and its applications in group decision making
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Hesitant Fuzzy Linguistic Correlation Coefficient and Its Applications in Group Decision Making Shengli Li1,2 • Cuiping Wei2
Received: 27 July 2019 / Revised: 6 March 2020 / Accepted: 27 April 2020 Taiwan Fuzzy Systems Association 2020
Abstract Hesitant fuzzy linguistic term sets (HFLTSs) are applied to deal with situations in which people are hesitant in providing linguistic evaluations and have been widely used in qualitative group decision-making processes. Considering the fact that the correlation coefficient has been widely used in many research domains, in this paper, we first present a novel correlation coefficient for HFLTSs. The significant features of the proposed correlation coefficient are that the HFLTSs need not to be extended to the same length and the correlation coefficient lies in ½1; 1. Two examples are used to illustrate the effectiveness of the proposed correlation coefficient. Second, based on the proposed correlation coefficient and the collaborative filtering algorithm, we develop a new method to deal with incomplete hesitant fuzzy linguistic information. Furthermore, by analyzing the correlation coefficient matrix, we present a new method for determining experts’ weights based on the concept of ‘attenuation’ and ‘how much trust’ they obtained. At last, a case study is used to evaluate the performance of our method. Keywords Group decision making correlation coefficient collaborative filtering algorithm hesitant fuzzy linguistic term sets trust relationship
Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. & Cuiping Wei [email protected] 1
Department of Mathematics, Taiyuan Normal University, 030619 Jinzhong, China
2
College of Mathematical Sciences, Yangzhou University, 225002 Yangzhou, China
1 Introduction Group decision-making (GDM) problem is one of the most frequent activities occurring in our daily life, whose aim is to rank or choose alternatives from a set of feasible alternatives [22, 45, 54, 55]. In the real-world situations, various factors involved in the GDM problems are often imprecise or uncertain in nature [21, 38, 44]. For qualitative criteria in multi-criteria GDM (MCGDM), it is more suitable to evaluate them by linguistic terms. In the traditional linguistic models, experts often apply a single linguistic term to assess a linguistic variable [7, 20, 57]. However, it cannot deal with the situation that experts are hesitant to provide their linguistic evaluations. To address this problem, Rodrı´guez et al. [31] introduced the concept of hesitant fuzzy linguistic term sets (HFLTSs) to deal with experts’ hesitation and uncertainty in GDM problem. Since then, there have been many related studies in this field including hesitant fuzzy linguistic decision-making methods [18, 34, 39], aggregated operators [21, 36, 46, 58], and information measures [9, 32, 37, 38]. Information measures mainly consist of distance measure [19, 48, 50], entropy measure [29, 37, 38] and correla
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