A Note on “A New Method for Triangular Fuzzy Compare Wise Judgment Matrix Process Based on Consistency Analysis”

Abstract

In the paper “A new method for triangular fuzzy compare wise judgment matrix process based on consistency analysis” (Meng and Chen in Int J Fuzzy Syst 19(1):27–46, 2017), the authors defined consistency of triangular fuzzy pairwise comparison matrices (TFPCMs), and presented theorems and propositions used to derive a computation formula of ]0, 1[-valued fuzzy priority weights for consistent TFPCMs. This note shows that under such a consistency definition, there is not any consistent $$n \\times n$$n×n TFPCM ($$n \\ge 3$$n≥3) with fuzzy judgments. Two counterexamples are provided to illustrate that the presented theorems and propositions are not true, and the given computation formula of fuzzy priority weights is incorrect and thus it should be replaced with a new formula.