Abstract: In this paper, the author propose a unique multi-attribute group decision making(MAGDM) method SVN-CPT-GRA. The method takes the single-value neutrosophic environment as the decision-making environment and uses the entropy weighted-grey relational analysis method under cumulative prospect theory. First, based on the evaluation of decision-makers, the single-value neutrosophic decision matrix was obtained. The entropy weight method was used to calculate the attribute weights. Next, according to the distance between each SVNN and the negative ideal value, combining the gray relation analysis and the cumulative prospect theory, the correlation between each solution and the attribute is compared to determine the advantages and disadvantages of each solution. Finally, the extended gray relational analysis method is demonstrated to be effectively applied to the decision-making process through a case study of investment choices in new energy vehicles and a comparison with other methods. The main innovations in this paper can be summarized as follows. Firstly, combining the cumulative prospect theory with the gray relational analysis for decision making can better reflect and represent the psychological changes and risk sensitivity of decision makers. Secondly, the entropy weight method is used to determine the attribute weights according to the distance between SVNN and the negative ideal value, which makes the attribute weights more objective and ensures the scientificity and reasonableness of the attribute weights. Thirdly, applying GRA method to the single-value neutrosophic environment, the original simple and practical GRA method to be more widely applied to the fuzzy environment, expanding the scope of application. Overall, the extended GRA method proposed in this paper can be more efficiently and scientifically adapted to MAGDM in fuzzy environments, providing more choices for decision-makers.
Keywords: Single-valued neutrosophic sets (SVNSs), grey relational analysis (GRA), multi-attribute group decision making (MAGDM), CRITIC, cumulative prospect theory (CPT)
