Power Geometric Operators For Group Decision Making Under Multiplicative Linguistic Preference Relations

The aim of this paper is to develop some new linguistic aggregation operators, such as linguistic power geometric (LPG) operator, linguistic weighted PG operator, LPOWG operator which are based on PG operator. We have studied some desired properties of the developed operators, such as commutativity, idempotency, boundary, etc. Moreover, we have developed two approaches to deal with group decision making problems under multiplicative linguistic preference relations. If the weighting vector of the decision makers is known, we develop an approach which is based on the linguistic weighted PG operator. On the other hand, if the weighting vector of the decision makers is unknown, we develop another approach which is based on the LPOWG. Finally, a practical example is given to illustrate the multiple attribute group decision making process; a comparative study to the linguistic weighted geometric average (LWGA) operator method is also demonstrated.