The analysis of the invalidity of one kind triangular fuzzy AHP

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 aws in this method. Hence, we recommend the key to correct these aws is to stick to the traditional judgments, the principal eigenvector approach of AHP and the generalization to dependence and feedback, the ANP.