On Consensus in Group Decision Making Based on Fuzzy Preference Relations

In the process of decision making, the decision makers usually provide inconsistent fuzzy preference relations, and it is unreasonable to get the priority from an inconsistent preference relation. In this paper, we propose a method to derive the multiplicative consistent fuzzy preference relation from an inconsistent fuzzy preference relation. The fundamental characteristic of the method is that it can get a consistent fuzzy preference relation considering all the original preference values without translation. Then, we develop an algorithm to repair a fuzzy preference relation into the one with weak transitivity by using the original fuzzy preference relation and the constructed consistent one. After that, we propose an algorithm to help the decision makers reach an acceptable consensus in group decision making. It is worth pointing out that group fuzzy preference relation derived by using our method is also multiplicative consistent if all individual fuzzy preference relations are multiplicative consistent. Some examples are also given to illustrate our results.