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Cross-Entropy and Prioritized Aggregation Operator with Simplified Neutrosophic Sets and Their Application in Multi-Criteria Decision-Making Problems

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Abstract

Simplified neutrosophic sets (SNSs) can effectively solve the uncertainty problems, especially those involving the indeterminate and inconsistent information. Considering the advantages of SNSs, a new approach for multi-criteria decision-making (MCDM) problems is developed under the simplified neutrosophic environment. First, the prioritized weighted average operator and prioritized weighted geometric operator for simplified neutrosophic numbers (SNNs) are defined, and the related theorems are also proved. Then two novel effective cross-entropy measures for SNSs are proposed, and their properties are proved as well. Furthermore, based on the proposed prioritized aggregation operators and cross-entropy measures, the ranking methods for SNSs are established in order to solve MCDM problems. Finally, a practical MCDM example for coping with supplier selection of an automotive company is used to demonstrate the effectiveness of the developed methods. Moreover, the same example-based comparison analysis of between the proposed methods and other existing methods is carried out.

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Acknowledgments

The author would like to thank the editors and the anonymous referees for their valuable and constructive comments and suggestions that greatly help the improvement of this paper. This work is supported by the National Natural Science Foundation of China (Nos 71571193, 71271218, and 71431006).

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Correspondence to Jian-qiang Wang.

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Wu, Xh., Wang, Jq., Peng, Jj. et al. Cross-Entropy and Prioritized Aggregation Operator with Simplified Neutrosophic Sets and Their Application in Multi-Criteria Decision-Making Problems. Int. J. Fuzzy Syst. 18, 1104–1116 (2016). https://doi.org/10.1007/s40815-016-0180-2

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  • DOI: https://doi.org/10.1007/s40815-016-0180-2

Keywords

  • Simplified neutrosophic sets
  • Prioritized aggregation operator
  • Cross-entropy
  • Multi-criteria decision-making