A consensus model for hesitant fuzzy preference relations and its application in water allocation management

This paper investigates a consensus model for hesitant fuzzy preference relations (HFPRs). First, we present a revised definition of HFPRs, in which the values are not ordered for the hesitant fuzzy element. Second, we propose an additive consistency based estimation measure to normalize the HFPRs, based on which, a consensus model is developed. Here, two feedback mechanisms are proposed, namely, interactive mechanism and automatic mechanism, to obtain a solution with desired consistency and consensus levels. In the interactive mechanism, the experts are suggested to give their new preference values in a specific range. If the experts are unwilling to offer their updated preferences, the automatic mechanism could be adopted to carry out the consensus process. Induced ordered weighted averaging (IOWA) operator is used to aggregate the individual HFPRs into a collective one. A score HFPR is proposed for collective HFPR, and then the quantifier-guided dominance degrees of alternatives by using an OWA operator are obtained to rank the alternatives. Finally, both a case of study for water allocation management in Jiangxi Province of China and a comparison with the existing approaches are carried out to show the advantages of the proposed method. © 2017 Elsevier B.V. All rights reserved.