PT-TOPSIS methods for multi-attribute group decision making under single-valued neutrosophic sets

Multi-attribute group decision making (MAGDM) is a flexible and complex problem due to multiple factors. Decision makers have different preferences in the face of different risks and benefits. In this paper, it proposed that the extended single-valued neutrosophic TOPSIS method based on the prospect theory (SVN-PT-TOPSIS) can be widely applied to MAGDM. It provides decision-makers with more rigorous decision-making methods. The purpose is to make the results more objective and fair and to reduce subjective errors. This paper is applied in a single-value neutrosophic sets (SVNSs) environment, which contains membership value, uncertainty value and non-membership value, and can effectively reflect the fuzzy decision state of decision makers. It also combines the CRITIC method to determine the weights and considers the psychological state of decision makers according to the prospect theory, which can effectively reduce the influence of subjective preferences on decision making. The innovations of this paper are mainly as follows. Firstly, after the score function determines the positive and negative ideal values, using the distance formula reflects the distance between each single-value neutrosophic number (SVNN) and the positive and negative ideal values. We will feel the overall quality of each scheme more directly. Secondly determine the weights using the CRITIC method based on the distance matrix of each SVNN from the negative ideal. This is not a subjective decision weight, so the influence of personal preferences on the decision can be avoided. Thirdly, the composite profit value and the composite loss value are confirmed based on the prospect theory (PT), taking into account the decision maker’s risk preferences. Finally, use the relative profit loss ratio to rank the programs. After case analysis, other classical decisionmaking methods are selected for comparative analysis of the extended TOPSIS It is confirmed that the SVN-PT-TOPSIS method is reasonable and effective, which is suitable for MAGDM problems.