Local feedback strategy for consensus building with probability-hesitant fuzzy preference relations

A consensus reaching process is an iteratively developed negotiation process designed to ensure that a mutual agreement is reached by decision makers. To incorporate distribution information of hesitant fuzzy sets, probability-hesitant fuzzy sets have recently been proposed. In the context of probability hesitant fuzzy preference relations (PHFPR), this paper aims to provide a novel consensus reaching process for group decision making problems. By means of fuzzy preference relations, an optimization based consistency improvement process is proposed to deal with the inconsistencies in a given PHFPR. Consensus measures that are developed based on the distances between the individuals are computed on three levels: an alternative pair level, an alternatives level, and a preference relations level. An algorithm that adopts a local feedback strategy is designed to improve the consensus reaching process. The feedback strategy sequentially identifies the preferences with respect to the position and the anti-ideal individuals who need to change, after which the convergence of the proposed algorithm is proven. The novelty of the proposed strategy is that it avoids the need to compute the collective preference relations and recommendations are generated for the individuals in their original domains. Finally, some numerical examples taken from the literature are given to compare the proposed approaches with existing studies. The obtained results confirm the theoretical analysis and highlight the advantages of the proposed approaches. (C) 2017 Elsevier B.V. All rights reserved.