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首页> 外文期刊>Fuzzy Optimization and Decision Making: A Journal of Modeling and Computation Under Uncertainty >On weak consistency of interval additive reciprocal matrices
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On weak consistency of interval additive reciprocal matrices

机译：关于间隔添加剂互易矩阵的弱一致性

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摘要

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.
机译：当一个人估计理性选择下替代品的重要性时，从心理学的角度来看，它很自然。由于以类似于人类思想的方式遇到的模糊性，决策者始终表现出有限的合理性。判断可以在分析层次过程框架内表示为间隔值比较矩阵。在本研究中，对于添加剂往复基质（臂），提出了三种公理性质，以表征添加剂一致性和完全合理行为下的乘法一致性。对于间隔添加剂互易矩阵（IARM），弱一致性的概念用于捕获有限的合理性。通过削弱一致臂的一些公理性质，提出了具有弱稠度的IARM的合理性质。分析了满足弱一致性性质的两种IARMS，提供了一些比较。观察到，可以通过使用公理性质准确地定义臂的一致性。表征IARMS一致性程度的特性应该通过削弱一致臂的公理组而捕获。所提出的方法可视化从数值偏好关系的基本值一致性开始的开发过程，与间隔值比较矩阵的弱一致性。

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