一种调整AHP不一致判断矩阵的优化方法
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1. 空军工程大学
2. 空军工程大学工程学院六系
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吴诗辉

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C934

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New Optimization Method to Improve the Inconsistent Comparison Matrix in the Analytic Hierarchy Process
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    摘要:

    针对AHP中不一致判断矩阵,提出了一种新的调整方法. 通过将AHP不一致判断矩阵的调整问题等价转化为一个带约束条件的优化问题,能够保证判断矩阵满足一致性要求条件下,使得调整后判断矩阵与原始判断矩阵的差异程度最小. 给出了决策容许区间的概念,使得元素的变动值在规定的范围内,同时,采取逐渐增大扰动变量的方法控制决策容许区间,以保证最小的改动实现一致性要求,并设计了改进的模式搜索算法求解优化问题. 最后,通过算例说明了方法的可行性. 该方法与现有方法相比,不仅具有直观性,易于计算机编程实现,而且能够真正做到以最小的改动量实现判断矩阵满足一致性要求.

    Abstract:

    To solve the inconsistency of comparison matrix in the Analytic Hierarchy Process (AHP), a new method is proposed. The inconsistency improving problem is equally converted to a optimization problem with constraints, which can minimize the modification of the original comparison matrix while reach the consistency requirement of AHP. In addition, the concept of allowable Interval is proposed to make sure the modification of elements in comparison matrix to be within the acceptable range. In order to minimize the modification, a method is designed to increase the allowable Interval step by step till the optimal solution is reached and the optimizing algorithm is realized by the improved pattern search method. An example is given to illustrate the feasibility of the approach. Compared with the present method, our approach is straightforward and easy to realize through computer programing, while truly find the improved comparison matrix with minimal modifications.

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吴诗辉 刘晓东 贺波 解江.一种调整AHP不一致判断矩阵的优化方法[J].控制与决策,2016,31(11):2106-2112

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历史
  • 收稿日期:2015-09-14
  • 最后修改日期:2016-01-02
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  • 在线发布日期: 2016-11-20
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