Optimal Interaction Priority Calculation From Hesitant Fuzzy Preference Relations Based on the Monte Carlo Simulation Method for the Acceptable Consistency and Consensus

• Published in: IEEE transactions on cybernetics Vol. 51; no. 12; pp. 5871 - 5882
• Main Authors: Meng, Fan-Yong, Tang, Jie, Pedrycz, Witold, An, Qing-Xian
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.12.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Acceptably additive consistency (AAC); Additives; Algorithms; Analytical models; Computer simulation; Consensus; consensus analysis; Consistency; decision analysis; Decision Making; Fuzzy Logic; hesitant fuzzy preference relation (HFPR); Maximization; Monte Carlo Method; Monte Carlo methods; Monte Carlo simulation; Optimization; optimization model; ordinal consistency (OC); Programming
• ISSN: 2168-2267; 2168-2275
• DOI: 10.1109/TCYB.2019.2962095

To address the situation where the complete consistency is unnecessary, a stepwise optimization model-based method for testing the acceptably additive consistency (AAC) of hesitant fuzzy preference relations (HFPRs) is introduced. Then, an AAC concept for HFPRs is defined. Meanwhile, incomplete HFPRs (iHFPRs) are discussed and a series of optimization models to acquire complete HFPRs is constructed. If the consistency is unacceptable, an optimization model for revising unacceptably consistent HFPRs under the conditions of the AAC and maximizing the ordinal consistency (OC) is offered. Subsequently, a model for minimizing the number of adjusted variables is presented. Considering the weighting information and the consensus for group decision making (GDM), the weights of fuzzy preference relations (FPRs) obtained from each individual HFPR and the decision makers (DMs) are determined using the distance measure. With regard to the consensus, two models for reaching the consensus requirement and minimizing the amount of revised variables are separately constructed, which are both based on the analysis of maximizing the OC. Furthermore, the thresholds of the additive consistency and the consensus are studied using the Monte Carlo simulation method. A GDM algorithm with HFPRs is offered. Finally, an example and comparison are provided to show the efficiency of the new procedure.