Probability multi-valued neutrosophic sets and its application in multi-criteria group decision-making problems

This paper introduces probability multi-valued neutrosophic sets (PMVNSs) based on multi-valued neutrosophic sets and probability distribution. PMVNS can serve as a reliable tool to depict uncertain, incomplete, inconsistent and hesitant decision-making information and reflect the distribution characteristics of all provided evaluation values. This paper focuses on developing an innovative method to address multi-criteria group decision-making (MCGDM) problems in which the weight information is completely unknown and the evaluation values taking the form of probability multi-valued neutrosophic numbers (PMVNNs). First, the definition of PMVNSs is described. Second, an extended convex combination operation of PMVNNs is defined, and the probability multi-valued neutrosophic number weighted average operator is proposed. Moreover, two cross-entropy measures for PMVNNs are presented, and a novel qualitative flexible multiple criteria method (QUALIFLEX) is developed. Subsequently, an innovative MCGDM approach is established by incorporating the proposed aggregation operator and the developed QUALIFLEX method. Finally, an illustrative example concerning logistics outsourcing is provided to demonstrate the proposed method, and its feasibility and validity are further verified by comparison with other existing methods.