Multiplicative consistency of interval-valued intuitionistic fuzzy preference relation

Interval-valued intuitionistic fuzzy preference relation (IVIFPR) is an important structure in representing fuzzy information comprehensively. This paper focuses on the multiplicative consistency of the IVIFPR. Some concepts, such as the approximate multiplicative consistent IVIFPR, the perfect multiplicative consistent IVIFPR and the acceptable multiplicative consistent IVIFPR are defined. Then, a desirable property of multiplicative consistent IVIFPR is investigated. Two algorithms are developed to construct the approximate/perfect multiplicative consistent IVIFPR. Since inconsistent IVIFPR is common but unreasonable in deriving the priorities of an IVIFPR, an iterative procedure is proposed to improve the consistency of an inconsistent IVIFPR. Furthermore, a convergent approach is developed for group decision making with IVIFPRs. Several numerical examples are given to illustrate the validity and applicability of the algorithms and procedures.