A comprehensive group decision-making method with interval-valued intuitionistic fuzzy preference relations

This paper investigates the group decision making (GDM) with interval-valued intuitionistic fuzzy (IVIF) preference relations (IVIFPRs). Considering decision maker's (DM's) risk attitude, the new score and accuracy functions for an IVIF value (IVIFV) are defined and a new order relation is proposed to rank IVIFVs. By transforming an IVIFPR into the direct and indirect IFPRs, a new additive consistency of IVIFPR is defined considering the uncertainty and ambiguity. Combining the direct IFPRs and the indirect IFPRs extracted from the IVIFPR, an algorithm is designed to determine the comprehensive IVIF priority weights of IVIFPR. For GDM with IVIFPRs, a multi-objective programming model is constructed to derive DMs' weights by combining TOPSIS and cross entropy, which is solved by Lagrange function method. Based on the determination of DMs' weights, the determination of priority weights and the new order relation of IVIFVs, a comprehensive method is proposed for GDM with IVIFPRs. Finally, a ventilation system selection example is analyzed to verify the effectiveness of the proposed method.