Deviation measures of linguistic preference relations in group decision making

In this paper, we study the group decision making problem with linguistic preference relations. We first show that the weighted combination of A1,A2,...,Am is linguistic preference relation under the condition that all of A1,A2,...,Am are linguistic preference relations. Then we define the concepts of deviation degree and similarity degree between two linguistic values, and deviation degree and similarity degree between two linguistic preference relations. We also show that the deviation degree between linguistic preference relation Ai of A1,A2,...,Am and their group linguistic preference relation is no greater than the largest deviation degree between the linguistic preference relation Ai and each of the linguistic preference relations A1,A2,...,Am. Thus, a theoretic basis has been established for the application of linguistic preference relations in group decision making.