When one estimates the importance of alternatives under rational choice, it is natural to avoid self-contradiction from the viewpoint of psychology. Due to the vagueness encountered in a manner analogous to human thought, decision makers always exhibit limited rationality. The judgements could be expressed as interval-valued comparison matrices within the framework of analytic hierarchy process. In this study, for additive reciprocal matrices (ARMs), three axiomatic properties are proposed to characterize the additive consistency and the multiplicative consistency under fully rational behavior. For interval additive reciprocal matrices (IARMs), the concept of weak consistency is used to capture the limited rationality. By weakening some axiomatic properties of consistent ARMs, the reasonable properties of IARMs with weak consistency are presented. Two kinds of IARMs satisfying the properties of weak consistency are analyzed and some comparisons are offered. It is observed that the consistency of ARMs can be defined exactly and characterized by using the axiomatic properties. The properties of characterizing the consistency degree of IARMs should be captured by weakening the axiomatic ones of consistent ARMs. The proposed approach visualizes the development process starting from cardinal consistency of numeric-valued preference relations to weak consistency of interval-valued comparison matrices.

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关于区间可加倒数矩阵的弱一致性

当人们估计理性选择下的选择的重要性时，从心理学的角度来看，避免自相矛盾是很自然的。由于以类似于人类思想的方式遇到的模糊性，决策者总是表现出有限的理性。这些判断可以在层次分析法框架内表示为区间值比较矩阵。在这项研究中，对于加性互惠矩阵（ARMs），提出了三种公理性质来表征完全有理行为下的加性一致性和乘法一致性。对于区间加法倒数矩阵（IARM），弱一致性的概念用于捕获有限的合理性。通过削弱一致性ARM的一些公理性质，提出了一致性较弱的IARM的合理性质。分析了满足弱一致性特性的两种IARM，并进行了比较。可以观察到，通过使用公理属性可以准确定义ARM的一致性并对其进行表征。应该通过削弱一致性ARM的公理化来捕获表征IARM一致性程度的特性。所提出的方法将开发过程形象化，从数值优先关系的基本一致性到区间值比较矩阵的弱一致性开始。应该通过削弱一致性ARM的公理化来捕获表征IARM一致性程度的特性。所提出的方法将开发过程形象化，从数值优先关系的基本一致性到区间值比较矩阵的弱一致性开始。应该通过削弱一致性ARM的公理化来捕获表征IARM一致性程度的特性。所提出的方法将开发过程形象化，从数值优先关系的基本一致性到区间值比较矩阵的弱一致性开始。