A generalization of the power aggregation operators for linguistic environment and its application in group decision making

We introduce a wide range of linguistic generalized power aggregation operators. First, we present the generalized power average (GPA) operator and the generalized power ordered weighted average (GPOWA) operator. Then we extend the GPA operator and the GPOWA operator to linguistic environment and propose the linguistic generalized power average (LGPA) operator, the weighted linguistic generalized power average (WLGPA) operator and the linguistic generalized power ordered weighted average (LGPOWA) operator, which are aggregation functions that use linguistic information and generalized mean in the power average (PA) operator. We give their particular cases such as the linguistic power ordered weighted average (LPOWA) operator, the linguistic power ordered weighted geometric average (LPOWGA) operator, the linguistic power ordered weighted harmonic average (LPOWHA) operator and the linguistic power ordered weighted quadratic average (LPOWQA) operator. Finally, we develop an application of the new approach in a multiple attribute group decision making problem concerning the evaluation of university faculty for tenure and promotion.

► Linguistic generalized power aggregation operators are developed.
► Properties of the new operators are discussed.
► An approach to group decision making with the new operator is proposed.
► The new operator is applied to group decision making.