Acceptable consistency analysis of interval reciprocal comparison matrices
Acceptable consistency analysis of interval reciprocal comparison matrices
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DOI：
10.1016/j.fss.2009.01.010
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发表时间：
2009-09-16
影响因子：
3.9
通讯作者：
Liu, Fang
中科院分区：
文献类型：
--
作者：
Liu, Fang
当决策者通过区间互反比较矩阵来表达自己的意见时，为了避免产生误导性的解决方案，一致性的研究就成为决策过程中一个非常重要的方面。在本文中。定义了一个可接受一致的区间互易比较矩阵，当区间变为精确数时，可将其简化为可接受一致的清晰互易比较矩阵。具有不可接受一致性的区间互反比较矩阵可以很容易地调整，使修正后的矩阵具有可接受的一致性。利用凸组合方法，可以得到一组具有可接受一致性的清晰的互易比较矩阵，进一步发现其权值表现出一种凸组合的风格，并从可接受一致性的区间互易比较矩阵中聚合得到区间权值。提出了一种新颖、简单、有效的区间权值排序可能性度公式。数值计算结果显示了所提出方法的质量和数量，并与其他现有方法进行了比较。(C) 2009 Elsevier B.V.版权所有
When a decision maker expresses his/her opinions by means of an interval reciprocal comparison matrix, the study of consistency becomes a very important aspect in decision making in order to avoid a misleading solution. In the present paper. an acceptably consistent interval reciprocal comparison matrix is defined, which can be reduced to an acceptably consistent crisp reciprocal comparison matrix when the intervals become exact numbers. An interval reciprocal comparison matrix with unacceptable consistency can be easily adjusted such that the revised matrix possesses acceptable consistency. Utilizing a convex combination method, a family of crisp reciprocal comparison matrices with acceptable consistency can be obtained, whose weights are further found to exhibit a style of convex combination, and aggregated to obtain interval weights from an acceptably consistent interval reciprocal comparison matrix. A novel, simple yet effective formula of possibility degree is presented to rank interval weights. Numerical results are calculated to show the quality and quantity of the proposed approaches and compare with other existing procedures. (C) 2009 Elsevier B.V. All rights reserved.