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.

中文翻译：

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区间值模糊偏好关系的三角有界一致性


区间值模糊偏好关系（IFPR）的一致性是IFPR在实际问题中应用的前提。为了支持 IFPR 的应用，已经开发了各种类型的 IFPR 一致性。在决策者完全理性的假设下，它们都满足一些固定的数学条件。在实践中，这一假设通常会被违反，因为决策者通常具有有限理性。考虑到决策者的有限理性，本文提出了一种新型的 IFPR 一致性，称为三角有界一致性，它基于决策者的历史偏好。三角框架旨在描述任意三种替代方案的三个 IFPR。 IFPR的严格传递性被定义为IFPR的受限最大-最大传递性，并在三角框架中进行了重构。在这种情况下，假设决策者的偏好在相似情况下是一致的，则利用决策者的历史IFPR来定义IFPR的三角有界一致性。基于所开发的一致性，开发了确定不完整 IFPR 矩阵中缺失 IFPR 的最佳估计的过程。利用具有 IFPR 三角有界一致性的多准则群体决策 (MCGDM) 过程分析了仿真系统供应商的选择问题，以证明所开发的一致性在 MCGDM 中的应用。