The power average operator for unbalanced linguistic term sets

In order to aggregate linguistic values of unbalanced linguistic term sets, this paper introduces the linguistic proportional 2-tuple power average operator, which can reflect the relationship among the aggregated values by considering the support for each value from others. Its advantage regarding other linguistic power average operators enables it to be used in such cases in which the linguistic term sets are not necessarily to be balanced, and the membership functions of the linguistic terms are utilized in the computational processes. In this operator, a linguistic proportional 2-tuple is represented by a normalized numerical representation. Some properties of the operator are discussed. A group decision making model based on the proposed operator is introduced. Finally an illustrative example is presented.