Managing Multigranular Unbalanced Hesitant Fuzzy Linguistic Information in Multiattribute Large-Scale Group Decision Making: A Linguistic Distribution-Based Approach

With the increase of technological and societal demands, more and more decision makers are involved in the process of group decision making, which is called large-scale group decision making (LGDM). For an LGDM problem with linguistic information, it is common that different decision makers tend to provide linguistic assessments defined on multigranular linguistic term sets due to the difference in knowledge and culture background, and that hesitant fuzzy linguistic term sets (HFLTSs) are used by decision makers to model the hesitancy of their assessments. This article proposes first an algorithm to represent a linguistic distribution assessment (LDA) using a hesitant linguistic distribution (HLD). Two other algorithms are then proposed to transform an unbalanced HFLTS into a balanced LDA and to transform a balanced LDA into an unbalanced LDA, respectively. An approach is then proposed to deal with multiattribute LGDM problems with multigranular unbalanced hesitant fuzzy linguistic information based on these algorithms. In the proposed approach, all unbalanced hesitant fuzzy linguistic information is transformed into LDAs defined on a balanced linguistic term set, and then an LDA-based clustering algorithm is devised to cluster decision makers. Based on the clustering result, decision makers' linguistic distribution decision matrices are further fused to obtain collective assessments of alternatives. In order to provide easy-to-understand linguistic results for decision makers, all LDAs of alternatives are represented by HLDs defined on each decision maker's initial linguistic term set. Finally, an example for the selection of subway lines is used to demonstrate the proposed approach.