A clustering method for large-scale group decision-making with multi-stage hesitant fuzzy linguistic terms

A large-scale group decision-making (LGDM) problem is studied from the perspective of multi-stage hesitant fuzzy linguistic term sets (MHFLTSs). Solving an LGDM problem requires two processes: a clustering process is helpful for breaking down the larger problem into smaller pieces for simplification purposes, and a selection process is utilized for obtaining a final solution. Along with the MHFLTSs, the decision-making process should include consideration of the distinctiveness of the term sets. With this idea in mind, we propose a clustering method and a selection method based on consideration of multiple reference points derived from the MHFLTSs. First, taking into account the HFLTS characteristics, an expert similarity measurement is proposed based on both the expectation distance and hesitancy similarity between two HFLTSs. Second, multiple reference points are examined: a positive ideal reference point and a development reference point. Reference similarity is then measured by combining these two points. With the goal of maximizing the reference similarity of the alternatives, the third element is the establishment of an optimization model for determining the stage and attribute weights based on consideration of the sensitivity of these two weights to the problem. In the fourth step, a fuzzy clustering method is applied in order to create expert clusters based on expert similarity as well as on the stage and attribute weights. An additional feature is a selection analysis based on the reference similarity between the cluster centers, which entails consideration of the degree of certainty of each cluster as a measure of cluster weighting. The final phase of the research is the application of the proposed method to two cases as a means of illustrating the applicability and feasibility of the new method.