Least square completion and inconsistency repair methods for additively consistent fuzzy preference relations

In this paper, we explore the group decision making (GDM) problems with incomplete additively consistent fuzzy preference relations. Some properties of additively consistent fuzzy preference relations are also discussed. A sufficient and necessary condition is proposed to keep the additive consistency of fuzzy preference relations. Methods for determining the priority weights of fuzzy preference relations are provided. Least square completion and inconsistency repair methods are developed to deal with incomplete and inconsistent fuzzy preference relations. Some numerical examples are also given to illustrate the proposed approaches.