Hesitant fuzzy linguistic correlation coefficient and its applications in group decision making

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 $$[-1,1]$$ . Two examples are used to illustrate the effectiveness of the proposed correlation coefficient. Secondly, 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 analysing 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.