Limited Rationality and Its Quantification Through the Interval Number Judgments With Permutations
Limited Rationality and Its Quantification Through the Interval Number Judgments With Permutations
复制标题
有限理性及其通过区间数判断与排列的量化
DOI：
10.1109/tcyb.2016.2594491
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发表时间：
2017-12
影响因子：
11.8
通讯作者：
Wei-Guo Zhang
中科院分区：
文献类型：
--
作者：
Fang Liu;Witold Pedrycz;Wei-Guo Zhang
在模糊层次分析法中，以区间数表示的方案的相对重要性旨在捕捉决策者（DM）在进行一系列比较时所经历的不确定性。在完全合理性假设下，典型层次分析法中话语标记语的判断是一致的。然而，由于话语标记语表达意见的不确定性是不可避免的，因此区间数判断与有限理性有关。本文通过引入区间乘互反比较矩阵，研究了有限理性的概念。通过分析区间互反判断矩阵的一致性，发现区间数判断是不一致的。通过考虑方案的置换，提出了区间乘互反比较矩阵的近似一致性和可接受近似一致性的概念。交换方法被设计为生成所有的排列。考虑方案比较的随机性，提出了一种确定区间权重向量的新方法，确定了区间权重向量。提出了一种求解区间乘互惠偏好决策问题的新算法。两个数值例子来说明所提出的方法，并提供了文献中的方法进行比较。
The relative importance of alternatives expressed in terms of interval numbers in the fuzzy analytic hierarchy process aims to capture the uncertainty experienced by decision makers (DMs) when making a series of comparisons. Under the assumption of full rationality, the judgements of DMs in the typical analytic hierarchy process could be consistent. However, since the uncertainty in articulating the opinions of DMs is unavoidable, the interval number judgements are associated with the limited rationality. In this paper, we investigate the concept of limited rationality by introducing interval multiplicative reciprocal comparison matrices. By analyzing the consistency of interval multiplicative reciprocal comparison matrices, it is observed that the interval number judgements are inconsistent. By considering the permutations of alternatives, the concepts of approximation-consistency and acceptable approximation-consistency of interval multiplicative reciprocal comparison matrices are proposed. The exchange method is designed to generate all the permutations. A novel method of determining the interval weight vector is proposed under the consideration of randomness in comparing alternatives, and a vector of interval weights is determined. A new algorithm of solving decision making problems with interval multiplicative reciprocal preference relations is provided. Two numerical examples are carried out to illustrate the proposed approach and offer a comparison with the methods available in the literature.
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