Approaches to group decision making based on interval-valued intuitionistic multiplicative preference relations

In this paper, we introduce a new kind of preference relation called the interval-valued intuitionistic multiplicative preference relation (IVIMPR). Then, we develop two types of operators to aggregate the inter-valvalued intuitionistic multiplicative preference information, including the independent interval-valued intuitionistic multiplicative aggregation operators and the correlative interval-valued intuitionistic multiplicative aggregation operators. The independent interval-valued intuitionistic multiplicative aggregation operators are based on the assumption that the aggregated arguments are independent, and they can be used to deal with the situation that the preferences of decision makers are independent of one another. The correlative interval-valued intuitionistic multiplicative aggregation operators are developed to reflect the correlations of the aggregated arguments based on the Choquet integral and power average, and they can be used to deal with the situation that the preferences of decision makers are dependent with each other. Moreover, we establish various properties and special cases of these operators and then apply them to develop two approaches to group decision making based on IVIMPRs. Finally, an illustrative example is provided to illustrate the effectiveness of the developed operators and approaches.