The Multiplicative Consistency Index of Hesitant Fuzzy Preference Relation

Hesitant fuzzy preference relation (HFPR) shows to be a unique and suitable technique to integrate all the values of decision makers when comparing pairwise alternatives (or criteria), while the consistency index of a HFPR determines the accuracy and reliability. In order to improve the accuracy in checking the multiplicative consistency of a HFPR, this paper aims to provide a new method to determine the value of the consistency index for a HFPR. First of all, we point out the weaknesses of the existing method in checking the multiplicative consistency of a HFPR. As there is no any theoretical evidence to support the given consistency threshold, to determine the value of such consistency index, we investigate the density function of the consistency index of a HFPR. After making some theoretical discussions on three methods, an algorithm is then proposed to determine the value of the multiplicative consistency index of a HFPR. Based on some simulations, a value table of critical values of the multiplicative consistency index of a HFPR is determined, whose elements vary with respect to the order of the HFPR and the measure used on distance calculations. Finally, some illustrative examples are given to show the applicability and efficiency of the determined critical value table of multiplicative consistency index in the process of consistency checking over a HFPR.