Filtration-and-weighting-based triangular bounded consistency of interval-valued fuzzy preference relations

Abstract

Consistency of interval-valued fuzzy preference relations (IVFPRs) is an essential property in decision-making to characterize the logic of decision-makers’ preferences. The triangular bounded consistency (TBC) of IVFPRs is a newly proposed type of consistency that corresponds to the bounded rationality of decision-makers, considering their historical preferences. The effectiveness and coherence of historical preferences should be considered to help characterize decision-makers’ real preferences under the assumption that their preferences are consistent in previous and current decision-making scenarios. To address this issue, this paper proposes a new type of consistency of IVFPRs called filtration-and-weighting-based triangular bounded consistency (FWTBC) based on the bounded rationality of decision-makers. By transforming historical IVFPRs into triangle pairs, a process of filtering abnormal triangle pairs is created based on the box plot to guarantee their effectiveness, and a process of determining the weights of the remaining triangle pairs is constructed to improve their coherence. These two processes are then integrated into the TBC of IVFPRs to generate the FWTBC of IVFPRs. A multi-criteria group decision-making method with the FWTBC of IVFPRs is presented and then applied to a thyroid biopsy needle supplier selection problem for a tertiary hospital located in Hefei City, Anhui Province, China.