Abstract
In this paper, we propose a method that improves multiplicative consistency based on a fractional programming model to derive the normalized intuitionistic fuzzy priority weight vector from an intuitionistic fuzzy preference relation. To do so, a new definition is formulated that captures previous definitions for multiplicative consistency of intuitionistic fuzzy preference relations. A transformation formula is proposed to convert the normalized intuitionistic fuzzy priority weight vector into a multiplicative consistent intuitionistic fuzzy preference relation. By using the properties of some function, we construct a deviation matrix and prove that the elements in the intuitionistic fuzzy preference relation corresponding to the largest value in the deviation matrix is the most inconsistent. This method not only preserves a lot of the original preference judgments, but also reduce many operations in comparison with previous methods to improve multiplicative inconsistency. Several numerical examples are given to convince the proposed model and method.
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