Spatial Bounded Consistency of Intuitionistic Fuzzy Preference Relations

The consistency of intuitionistic fuzzy preference relations (IFPRs) is an important requirement in handling the decision-making problems modeled with IFPRs. Multiplicative consistency and additive consistency are two common types of consistency of IFPRs. These types of consistency of IFPRs are developed in the form of mathematical formulas to satisfy the perfect rationality of decision makers. In real decision-making, the decision makers are generally of bounded rationality rather than perfect rationality due to their own preferences. In consideration of the decision-makers' preferences, this article proposes a new type of consistency of IFPRs, which is named spatial bounded consistency. A spatial framework is constructed to characterize the relations of three IFPRs among three alternatives. The spatial transitivity of IFPRs is defined based on the restricted max-max transitivity of IFPRs. By following the spatial transitivity of IFPRs, the preferences of decision makers contained in IFPRs are described in two situations. Under the assumption that the preferences of a decision maker are according in handling similar decision-making problems, the historical IFPRs satisfying spatial transitivity are collected to represent decision-makers' preferences. On this basis, the spatial bounded consistency of IFPRs is then developed. A multicriteria group decision-making (MCGDM) method is designed based on the spatial bounded consistency. A problem of selecting the supplier of breast puncture needle is analyzed to demonstrate the applicability and effectiveness of the developed MCGDM method.