A method for improving the multiplicative inconsistency based on indeterminacy of an intuitionistic fuzzy preference relation

Abstract

In this paper, we propose a method for improving the multiplicative inconsistency of an intuitionistic fuzzy preference relation (IFPR) without computing any model to derive an underlying priority weight's vector with respect to alternatives. For this, a necessary and sufficient condition for the IFPR to be multiplicative consistent is proposed and proved. Based on it, a ratio-based deviation identifying matrix that takes an accurate measurement of deviation of every element in the IFPR is constructed. We prove that the greater the value of the deviation matrix is, the more inconsistent is its corresponding element in the IFPR and based on it, a convergent iterative algorithm of improving the multiplicative consistency is presented. The algorithm uses the fact that all the indeterminacy degrees of the IFPR are never changed in the revising process of multiplicative inconsistency and as a result, the most inconsistent elements are uniquely determined by suitable elements in the IFPR, respectively. The proposed method makes a great difference from the previous methods that derived the underlying priority weight's vector with respect to alternatives based on the given IFPR for improving consistency. A numerical example is provided to show the feasibility and efficiency of the proposed method.