A new compatibility model for fuzzy group decision making by using trapezoidal fuzzy preference relations with COWA operator

Considering the conflicting opinions and different risk attitudes among decision-makers (DMs) in group decision making (GDM), this paper develops a novel compatibility model with additive trapezoidal fuzzy environment based on continuous ordered weighted averaging (COWA) operator to handle the conflicts. First, some concepts of COWA operator-based compatibility index and characteristic preference relation for additive trapezoidal fuzzy preference relation (ATFPR) are discussed. Then a compatibility reaching algorithm is designed to assist each ATFPR in achieving acceptable compatibility. Moreover, the expert weight optimization model based on the criterion of minimum compatibility of preference relation in GDM is established. Furthermore, a GDM process based on compatibility measures with ATFPRs is introduced, and an application of the proposed approach is put forward. The novelties of our approach are that: (1) COWA operator can deal with the compatibility of all arguments by using controlled parameters that consider the risk attitudes of DMs rather than the compatibility of the simply two points in intervals; (2) compatibility improving algorithm makes sure that the original opinions are retained as much as possible because only one pair of preference relation elements are revised in each round; (3) optimal weights model ensures that weights of DMs in group aggregation are determined availably.