Triangular Bounded Consistency of Interval-Valued Fuzzy Preference Relations

The consistency of interval-valued fuzzy preference relations (IFPRs) is a prerequisite for the application of IFPRs in real problems. To support the application of IFPRs, various types of consistency of IFPRs have been developed. They all satisfy some fixed mathematical conditions under the assumption that decision makers are perfectly rational. In practice, this assumption is usually violated because decision makers generally have bounded rationality. Considering the bounded rationality of decision makers, this article develops a new type of consistency of IFPRs called triangular bounded consistency, which is based on the historical preferences of decision makers. A triangular framework is designed to describe the three IFPRs of any three alternatives. The strict transitivity of IFPRs is defined as the restricted max-max transitivity of IFPRs, which is reconstructed in the triangular framework. In this situation, under the assumption that the preferences of a decision maker are consistent in similar circumstances, the triangular bounded consistency of IFPRs is defined by use of the historical IFPRs of decision makers. Based on the developed consistency, the process of determining the optimal estimations of missing IFPRs in an incomplete IFPR matrix is developed. A problem of selecting suppliers of simulation systems is analyzed using the multicriteria group decision-making (MCGDM) process with the triangular bounded consistency of IFPRs to demonstrate the application of the developed consistency in MCGDM.