A Novel Group Decision-Making Method Based on Extended VIKOR and Interval-Valued Intuitionistic Fuzzy

Researchers have increasingly turned their attention to the interval-valued intuitionistic fuzzy-based group decision-making (GDM) method due to the vagueness and uncertainty that characterize decision-making problems in today’s complex social environments. In the GDM process, determining the weights of experts and measuring the proximity of two decision matrices are two important aspects. In recent years, researchers have enriched and improved the study of GDM methods by using projection measures. However, existing normalized projection measures still have flaws and lack specific regret matrices for GDM methods where the evaluation information is interval-valued intuitionistic fuzzy. To address these problems, this study first develops a new normalized vector projection measure formula that can be used to directly measure the proximity of two interval-valued intuitionistic fuzzy matrices. The study then provides an objective method for determining the weights of experts based on the evaluation matrix of the experts, using the weighted geometric mean operator and the normalized projection measure formula developed in this study. Finally, the study extends the ViseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method using the normalized projection measure formula it developed, constructing a new GDM method integrating group utility, regret, and satisfaction measures for the problem of evaluating the evaluation information as interval-valued intuitionistic fuzzy numbers. This study improves the classical VIKOR method by adding the measure of the group satisfaction matrix and giving specific group regret and satisfaction matrices. It investigated the feasibility and validity of the method in this study through three applied practical cases. Experimental comparative analysis with methods in the existing literature, it confirms that the GDM method it constructed is feasible and shows that the method can continuously promote group consensus and obtaining stable ranking results.