An approach to consensus measurement of linguistic preference relations in multi-attribute group decision making and application

This paper studies the group decision making problem with linguistic preference relations. We first study the consensus measure between the individual preference relations and the collective (group) preference relation by defining the concept of degree of similarity between two linguistic values and two linguistic preference relations. Then we propose a concept of the acceptance consensus threshold value for group decision making with linguistic preference information. We show that the consensus between individual preference relations and the collective (group) preference relation is greater than the weighted similarity degree of a given individual preference relation with respect to other individual preference relations in group decision making with linguistic preference relations. The results will help in the analysis of crucial issues of conflict and agreement among preferences of decision-makers, which affect the consensus of group decision making with linguistic preference relations. Theoretical foundations are then established for the proposed method. Finally, the proposed method is applied to evaluate the degree of consensus of individual overall preference values with respect to the collective overall preference values for multi-attribute group decision making with linguistic information. The main contribution of this paper is twofold. One is to present a new way to measure the consensus between the individual preference relations and the collective (group) preference relation in group decision making with linguistic preference information. Another is to provide an effective approach to evaluating individual overall preference values with respect to the collective overall preference values in multi-attribute group decision making with linguistic information.