Group decision making with double hierarchy hesitant fuzzy linguistic preference relations: Consistency based measures, index and repairing algorithms and decision model

Group decision making, refers to inviting a group of decision makers to evaluate, prioritize or select the optimal one among some available alternatives in the actual decision making process. Considering that the double hierarchy hesitant fuzzy linguistic term set can describe natural languages clearly, in this paper, we define the concept of double hierarchy hesitant fuzzy linguistic preference relation (DHHFLPR) and propose some additive consistency measures. To judge whether a DHHFLPR is of acceptable consistency or not, we introduce a consistency index, and develop some novel threshold values for judging whether a DHHFLPR is of acceptable consistency or not. Furthermore, we develop two consistency repairing algorithms based on the automatic improving method and the feedback improving method respectively, to improve the DHHFLPR with unacceptable consistency. Additionally, a method is set up to deal with group decision making problems with double hierarchy hesitant fuzzy linguistic preference information. Finally, the proposed method is validated by a case study that is used to evaluate the water resource situations of some important cities in Sichuan Province, and some comparative analyses are given to show the efficiency of the proposed method. (C) 2019 Elsevier Inc. All rights reserved.