Multi-attribute group decision-making method using single-valued neutrosophic credibility numbers with fairly variable extended power average operators and GRA-MARCOS

Data trading platform (DTP) selection is a classic multi-attribute group decision-making (MAGDM) problem. As an extension of intuitionistic fuzzy sets (IFSs), single-valued neutrosophic credibility numbers (SvNCNs) can express both fuzzy evaluation information and the credibility level of the information, offering better expressiveness in describing fuzzy decision-making information. However, existing studies on aggregation operators and decision-making methods in the SvNCN environment are inadequate. Therefore, this paper proposes a MAGDM technique based on the fairly weighted variable extended power average (SvNCNFWVEPA) operators of SvNCNs and grey relational analysis (GRA)-Measurement of Alternatives and Ranking according to Compromise Solution (MARCOS) method. The main contributions are as follows: (1) we propose fairly operation rules for aggregating SvNCNs in an unbiased manner; (2) addressing the lack of SvNCN measurement research, we introduce preference distance and entropy measures for SvNCNs, then utilize the entropy measure to compute the objective weights of the attributes; (3) to effectively aggregate SvNCN information, inspired by the variable power geometric (VPG) operators and the extended power average (EPA) operators, we propose the variable extended power average (VEPA) operator for scientifically handling extreme values, extending it to SvNCNs with the SvNCNs fairly variable extended power average (SvNCNFVEPA) operators and their extended form; (4) we introduce the GRA method to calculate the degree of utility of alternatives relative to ideal and anti-ideal alternatives, forming the GRA-MARCOS method. This method can reflect both indicator differences and the similarity of alternatives, thereby rendering the evaluation results more scientific and objective; (5) to illustrate the application of the method to the MAGDM problem, we apply it to the example of DTP selection. Parameter sensitivity analysis and comparative analysis with other existing methods demonstrate that our proposed method is more scientific and flexible.