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 A(1),A(2),...,A(3), is linguistic preference relation under the condition that all of A(1),A(2),...,A(3) 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 A(i) of A(1), A(2),...,A(m) and their group linguistic preference relation is no greater than the largest deviation degree between the linguistic preference relation A(i) and each of the linguistic preference relations A(1),A(2),...,A(m). Thus, a theoretic basis has been established for the application of linguistic preference relations in group decision making. (c) 2004 Elsevier Ltd. All rights reserved.