Probability multi-valued neutrosophic sets (PMVNSs) can better describe the incomplete and indeterminate evaluation information, and the ELECTRE method can rank the alternatives in the light of the outranking relations among criteria. To combine their advantages, this paper introduces an extended ELECTRE method to address multi-criteria group decision-making (MCGDM) problems with the information of PMVNSs. Firstly, we introduce the definitions of PMVNSs and the classical ELECTRE method, discuss the ELECTRE-based outranking relations for PMVNSs and analyze some properties of them. Furthermore, the probability multi-valued neutrosophic ELECTRE method is developed to address MCGDM problems based on the proposed distance measure and outranking relations for PMVNSs. Finally, a typical example for logistics outsourcing provider selection is devoted to demonstrate the feasibility of the proposed approach. Moreover, the same example-based comparisons with other existing methods are carried out, the results show our proposed approach outperforms the existing methods in solving the MCGDM problems with PMVNSs.
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