The solution for fuzzy large-scale group decision making problems combining internal preference information and external social network structures

Owing to the advancement of information technique, people in large groups usually have some social relationships with others and also have their own unique preferences. It is important to consider internal preference information and external social network relationships simultaneously in decision making. To handle the subjective uncertainty of DMs, the interval preference and connection strength are represented by interval type-2 fuzzy linguistic variables. To deal with the large-scale group decision making (LGDM) under uncertainty, an interval type-2 fuzzy k-means solution is proposed with the internal preference information and external social network relationship information considered in decision making. The corresponding interval type-2 fuzzy similarity matrices for these two kinds of decision information are computed, respectively. Then, the large-scale DMs are classified into separate partitions by an extended interval type-2 fuzzy k-means clustering analysis with the computed similarity matrices. Finally, the optimal alternative of the LGDM is determined by an interval type-2 fuzzy aggregation operator with weights and preferences of partitions. The importance of these two kinds of information in LGDM and the validity of the proposed method are verified by an illustrative example and corresponding comparisons. The proposed method can reduce the dimension and handle the uncertainty for LGDM in some extent.