An Extension of ARAS Methodology for Multi-criteria Group Decision-Making Problems within Probability Multi-valued Neutrosophic Sets

Probability multi-valued neutrosophic sets (PMVNSs) can depict the preference and hesitancy of decision makers (DMs) simultaneously, and utility-based additive ratio assessment (ARAS) can effectively evaluate and rank feasible alternatives. In order to make optimal decision making under the environment of the PMVNSs, in this paper, an extended ARAS methodology for multi-criteria group decision making (MCGDM) is developed. Firstly, we propose probability multi-valued neutrosophic normalized weighted Bonferroni distance (PMVNNWBD) to measure the closeness of weighted probability multi-valued neutrosophic numbers (PMVNNs). Then, an entropy measure for PMVNSs is proposed to describe the inaccuracy degree of PMVNSs and to derive the weights of DMs. Further, considering the relationship between criteria, we construct a modified maximizing deviation model based on PMVNNWBD to obtain criteria weights. Moreover, an extended ARAS method for MCGDM is established to handle PMVNSs based on the obtained weight information of DMs and criteria. Finally, the feasibility and superiority of the proposed approach are verified by a case study concerning third-party logistics (3PLs) supplier selection, and sensitive analysis of different parameters shows our proposed approach is flexible.