Abstract
The intuitionistic fuzzy preference relation (IFPR), whose elements are intuitionistic fuzzy values, is a powerful structure in expressing the comprehensive preference information of a person. In this paper, after reviewing different kinds of consistency for IFPR, we construct a mathematical model to derive the underlying crisp weighting vector from a multiplicative consistent IFPR. Such method is very easy to be understood. As to multiplicative inconsistent IFPR, we claim that there are two ways to repair it, which are interactive method and automatic method. When the expert does not want to interact with the analyst, or if the analyst cannot find the initial expert to re-evaluate and alter his/her preferences, or if consistency must be urgently obtained, the proposed automatic algorithm is efficient and useful. Finally, we propose a procedure for group decision making with IFPRs based on the multiplicative consistency of IFPRs. It is proven that if all individual IFPRs are multiplicative consistent, their overall IFPR fused by IFWG operator is also multiplicative consistent. Some numerical examples are given to illustrate the validity and applicability of the proposed methods.