The analysis of the invalidity of one kind triangular fuzzy AHP

ZHU Ke-yu, DONG Qing-xing, LIANG Chang-yong, YANG Shan-lin

Systems Engineering - Theory & Practice ›› 2015, Vol. 35 ›› Issue (8) : 2104-2112.

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Systems Engineering - Theory & Practice ›› 2015, Vol. 35 ›› Issue (8) : 2104-2112. DOI: 10.12011/1000-6788(2015)8-2104

The analysis of the invalidity of one kind triangular fuzzy AHP

  • ZHU Ke-yu1,3, DONG Qing-xing2, LIANG Chang-yong1, YANG Shan-lin1
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Abstract

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[1], 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.

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AHP / fuzzy AHP / triangular fuzzy number

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ZHU Ke-yu , DONG Qing-xing , LIANG Chang-yong , YANG Shan-lin. The analysis of the invalidity of one kind triangular fuzzy AHP. Systems Engineering - Theory & Practice, 2015, 35(8): 2104-2112 https://doi.org/10.12011/1000-6788(2015)8-2104

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