An axiomatic approach to approximation-consistency of triangular fuzzy reciprocal preference relations
An axiomatic approach to approximation-consistency of triangular fuzzy reciprocal preference relations
复制标题
三角模糊互惠偏好关系近似一致性的公理化方法
DOI：
10.1016/j.fss.2017.02.004
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发表时间：
2017-09-01
影响因子：
3.9
通讯作者：
Zhang, Wei-Guo
中科院分区：
文献类型：
--
作者：
Liu, Fang;Pedrycz, Witold;Zhang, Wei-Guo
在理性经济学假设下，判断的一致性是多准则决策方法的重要问题之一。本文从严格逻辑和理性的角度出发，提出了相对测量一致性判断的三个公理性质：（A1）两两比较的互反性质，（A2）一致性对备选方案排列的不变性，（A3）备选方案排序的鲁棒性。利用这些性质分别分析了正真实的数和三角模糊数所表示的判断的一致性。在层次分析法（AHP）中遇到的判断矩阵的不一致性可以被认为是减弱公理性质（A3）的情况。模糊化的判断是由于公理性质（Al）的削弱。提出了一种弱化三角模糊互反矩阵公理性质的方法，并提出了近似一致性的新概念，以区别于典型一致性。通过考虑方案的排列，一个说明性的例子来显示使用所提出的程序来解决三角模糊互惠偏好关系的决策问题。(C)2017 Elsevier B.V.版权所有。
Under the assumption of rational economics, the consistency of judgments is one of the important issues in multiple criteria decision making (MCDM) methods. We propose three axiomatic properties of the consistent judgments in relative measurements being considered from the perspective of strict logic and rationality: (Al) the reciprocal property of pairwise comparisons, (A2) the invariance of consistency with respect to permutations of alternatives, and (A3) the robustness of the ranking of alternatives. These properties are further applied to analyze the consistency of the judgments expressed by positive real numbers and triangular fuzzy numbers, respectively. The inconsistency of comparison matrices encountered in the Analytic Hierarchy Process (AHP) can be considered to be the case of weakening the axiomatic property (A3). Fuzzifying the judgments is due to the weakening of axiomatic property (Al). A method of weakening the axiomatic properties for triangular fuzzy reciprocal matrices is proposed and a new concept of approximation-consistency is put forward to distinguish from the typical consistency. By considering the permutations of alternatives, an illustrative example is presented to show the use of the proposed procedures for solving the decision making problems with triangular fuzzy reciprocal preference relations. (C) 2017 Elsevier B.V. All rights reserved.