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

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Abstract

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.

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Acknowledgements

The authors would like to thank the associate editor and anonymous reviewers for their helpful comments that improved the paper. This work was supported by the National Natural Science Foundation of China (Nos. 71571193 and 71271218).

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  1. School of Business, Central South University, Changsha, 410083, People’s Republic of China

    Hong-gang Peng, Hong-yu Zhang & Jian-qiang Wang

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  1. Hong-gang Peng
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Correspondence to Jian-qiang Wang.

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Peng, Hg., Zhang, Hy. & Wang, Jq. Probability multi-valued neutrosophic sets and its application in multi-criteria group decision-making problems. Neural Comput & Applic 30, 563–583 (2018). https://doi.org/10.1007/s00521-016-2702-0

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