A Method to Improve the Multiplicative Inconsistency Preserving the Preference Information of Every Element of an Intuitionistic Fuzzy Preference Relation

Abstract

In general, almost intuitionistic fuzzy preference relations (IFPRs) provided by experts are multiplicutively inconsistent because of the complexity of a problem, lack of correct or sufficient knowledge about the problem domain, the ambiguity inherent in human thinking and so forth on. To solve this subject, we propose a method to improve the multiplicative inconsistency preserving the preference information of every element of an initial IFPR. For this, we formulate a formula that straightforwardly calculates the multiplicative consistent IFPR preserving the preference information of every element of the IFPR. Based on it, the necessary and sufficient results for the IFPR to be multiplicatively consistent are derived. By using the results, a consistency testing matrix and a consistency index that can select the most inconsistent elements in the IFPR are constructed and a method that revises them by a proper intuitionitic fuzzy numbers for improving inconsistency as well as preserving the initial preference information is proposed. Then, it is proved that the consistency index converges into zero. As a result, an acceptable consistent IFPR that preserves the preference information of every element and saves a lot of elements of the initial IFPR is constructed. In addition, this method needs a few calculations in comparison with previous methods to improve multiplicative inconsistency of IFPRs, because they calculate a multiplicative consisten IFPR by solving the optimal models constructed based on sufficient conditions for IFPRs to be mltiplicatively consistent. Finally, illustrative examples and comparative analysis are given to demonstrate the efficiency of the proposed method.