A clustering-based method for large-scale group decision making in the hesitant fuzzy set environment

The hesitant fuzzy set (HFS) has received wide attention because it can neatly describe the fuzziness and hesitancy of decision information with several possible values. Hence, this paper proposes a clustering-based method for resolving large-scale group decision making problems with HFSs. Considering the different risk attitudes of decision makers (DMs), a new score function of hesitant fuzzy elements (HFEs) is defined by introducing weight factors of all possible values. According to the scores of attribute values, a neighborhood-based approach is put forward to detect and process abnormal evaluations that may influence decision results. Afterwards, a two-stage clustering approach along with three algorithms is presented to cluster DMs into sub-groups. The first stage clusters DMs with finite possible cluster numbers based on the supporters of each DM and the separations between DMs. In the second stage, according to intra and inter-differences among DMs, an index is introduced to evaluate clustering results and select the best cluster number from the finite ones given in the first stage. Finally, by fusing the information densities and cluster sizes, cluster weights are determined and ranking values of alternatives are generated by aggregating evaluation information of the alternatives. At length, a case study is provided to illustrate the applications of the proposed method. Furthermore, the experiments and comparative analyses are conducted to show the effectiveness and superiority of the proposed method.