Abstract: Extended probabilistic linguistic term set (EPLTS) can be transformed into several linguistic information representation models by adjusting the probability distribution, such as uncertain linguistic variable, linguistic distribution assessment, extended hesitant fuzzy linguistic term set, probabilistic linguistic term set and so on. EPLTS can describe the original evaluation information more fully and objectively so that it is an important tool for dealing with uncertain information. In view of this, with respect to multiple attribute group decision making problems under extended probabilistic linguistic environment, this paper proposes an extended probabilistic linguistic group decision making method based on evidential reasoning and generalized Shapley value. Firstly, the concept and relative theories of extended probabilistic linguistic term set are given. Secondly, the combination of generalized Shapley value and evidential reasoning is used to aggregate evaluation information from multiple decision makers, and the combination of generalized Shapley value and classical TODIM method is utilized to rank multiple alternatives. Thirdly, the weight determination models based on grey relational method are proposed to calculate weights of decision makers and weights of attributes respectively. Finally, taking the green supplier selection as an example, the effectiveness and superiority of the proposed method are verified by comparative analysis with the existing methods.

Key words: multiple attribute group decision making, extended probabilistic linguistic term set, evidential reasoning, TODIM method, generalized Shapley value