On weak consistency of interval additive reciprocal matrices
On weak consistency of interval additive reciprocal matrices
复制标题
关于区间可加倒数矩阵的弱一致性
DOI：
10.1007/s10700-020-09314-z
复制
发表时间：
2020-02-08
影响因子：
4.7
通讯作者：
Pedrycz, Witold
中科院分区：
文献类型：
--
作者：
Liu, Fang;Zhang, Jia-Wei;Pedrycz, Witold
当一个人在理性选择下估计替代品的重要性时，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维的方式遇到的不确定性，决策者总是表现出有限的理性。在层次分析法的框架下，这些判断可以表示为区间值比较矩阵。针对加性互反矩阵，提出了三个公理化性质来刻画加性一致性和乘性一致性在完全有理行为下的性质。对于区间可加互反矩阵，利用弱一致性的概念来刻画其有限合理性。通过弱化相容自回归模型的一些公理性质，给出了弱相容自回归模型的合理性质。分析了两种满足弱一致性的IARM，并进行了比较。研究表明，利用公理化性质可以精确地定义和刻画自适应映射的一致性。IARMs的一致性程度的性质应通过弱化一致ARMs的公理化性质来刻画。所提出的方法可视化的发展过程从基数一致性的数值偏好关系的区间值比较矩阵的弱一致性。
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.