An Extended Multi-criteria Group Decision-Making PROMETHEE Method Based on Probability Multi-valued Neutrosophic Sets

The PROMETHEE method, one of the most widely used and best known methods, takes advantage of the outranking principle to rank potential alternatives. The probability multi-valued neutrosophic sets (PMVNSs) have the power to describe complex uncertain information more comprehensively. Thus, in order to integrate the merits of PROMETHEE method and PMVNSs, this paper extends the PROMETHEE method to PMVNSs environment. Firstly, some basic preliminaries are reviewed, such as multi-valued neutrosophic sets (MVNSs), PMVNSs and classical PROMETHEE method. Then, we propose the operational laws of PMVNSs based on the operational rules of the MVNSs and probability distribution. Meanwhile, the score function and accuracy function of PMVNSs are given to simplify the comparison of any two probability multi-valued neutrosophic numbers (PMVNNs). Further, we develop a new distance measure for PMVNNs with unequal length, and then based on the distance measure and deviation maximization method, the attribute weights are determined; an extended PROMETHEE method for multi-criteria group decision-making with the information of PMVNSs is established to achieve the process for optimal alternative selection. In the end, a practical example concerning third party logistics providers is used to highlight the feasibility and superiority of the proposed approach.