一类三角模糊层次分析法的无效性分析

The analysis of the invalidity of one kind triangular fuzzy AHP

模糊层次分析法是非常流行的决策方法,已经有上千篇文献使用它进行决策分析.本文针对Laarhoven等^([1])提出的三角模糊AHP方法,使用几何平均法对来自单个判断的多个专家打分进行合成,从而简化原有模型.对简化模型进行求解得到其解析解.通过理论的和数值的分析,我们发现三角模糊AHP得出的结果是无效的,因为它违反了三角模糊数的基本假设:1)下限值、最有可能值和上限值应该是非减排序;2)最终的三角模糊权重的下限值和上限值应该仅仅与三角模糊判断的下限值和上限值相关;此外,3)三角模糊AHP方法无法应用于2×2或某些残缺三角模糊判断矩阵中.本文展示三角模糊AHP存在的问题并希望AHP的使用者注意这些.我们建议纠正这种错误的方法是坚持传统的判断方法,即基于最大特征值法得AHP以及在此基础上发展的考虑相关与反馈的ANP方法.

The fuzzy analytic hierarchy process （fuzzy AHP） is a very popular decision making method and literally thousands of papers have been published about it. This paper is mainly on the triangular fuzzy AHP proposed by Laarhoven et al[11, we simplify it by combining multiple judgments for a single comparison into one unit. Along this path, we derive an analytic solution for the simple model. Through the analytic solution, we find that the triangular fuzzy AHP also has some limitations that it cannot be used in any 2~2 pairwise comparison fuzzy judgment matrix and some incomplete judgment matrices. Meanwhile, we further find that the resulting priorities are invalid because it violates the basic logic of itself. We show these and hope that who use triangular fuzzy AHP would understand the limitations even flaws in this method. Hence, we recommend the key to correct these flaws is to stick to the traditional judgments, the principal eigenvector approach of AHP and the generalization to dependence and feedback, the ANP.