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Multi-criteria decision-making method based on a cross-entropy with interval neutrosophic sets

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  • Zhang-peng Tian
  • Hong-yu Zhang
  • Jing Wang
  • Jian-qiang Wang
  • Xiao-hong Chen

Abstract

In this paper, two optimisation models are established to determine the criterion weights in multi-criteria decision-making situations where knowledge regarding the weight information is incomplete and the criterion values are interval neutrosophic numbers. The proposed approach combines interval neutrosophic sets and TOPSIS, and the closeness coefficients are expressed as interval numbers. Furthermore, the relative likelihood-based comparison relations are constructed to determine the ranking of alternatives. A fuzzy cross-entropy approach is proposed to calculate the discrimination measure between alternatives and the absolute ideal solutions, after a transformation operator has been developed to convert interval neutrosophic numbers into simplified neutrosophic numbers. Finally, an illustrative example is provided, and a comparative analysis is conducted between the approach developed in this paper and other existing methods, to verify the feasibility and effectiveness of the proposed approach.

Suggested Citation

  • Zhang-peng Tian & Hong-yu Zhang & Jing Wang & Jian-qiang Wang & Xiao-hong Chen, 2016. "Multi-criteria decision-making method based on a cross-entropy with interval neutrosophic sets," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(15), pages 3598-3608, November.
    • Handle: RePEc:taf:tsysxx:v:47:y:2016:i:15:p:3598-3608
    DOI: 10.1080/00207721.2015.1102359
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    References listed on IDEAS

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    2. Sengupta, Atanu & Pal, Tapan Kumar, 2000. "On comparing interval numbers," European Journal of Operational Research, Elsevier, vol. 127(1), pages 28-43, November.
    3. Caballero, Rafael & Hernández-Díaz, Alfredo G. & Laguna, Manuel & Molina, Julián, 2015. "Cross entropy for multiobjective combinatorial optimization problems with linear relaxations," European Journal of Operational Research, Elsevier, vol. 243(2), pages 362-368.
    4. Liu, Bingsheng & Shen, Yinghua & Zhang, Wei & Chen, Xiaohong & Wang, Xueqing, 2015. "An interval-valued intuitionistic fuzzy principal component analysis model-based method for complex multi-attribute large-group decision-making," European Journal of Operational Research, Elsevier, vol. 245(1), pages 209-225.
    5. Macedo, Pedro & Scotto, Manuel, 2014. "Cross-entropy estimation in technical efficiency analysis," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 124-130.
    6. Editors, 2014. "International Journal of Systems Science," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(12), pages 1-1, December.
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    Cited by:

    1. Xiao-Wen Qi & Jun-Ling Zhang & Shu-Ping Zhao & Chang-Yong Liang, 2017. "Tackling Complex Emergency Response Solutions Evaluation Problems in Sustainable Development by Fuzzy Group Decision Making Approaches with Considering Decision Hesitancy and Prioritization among Asse," IJERPH, MDPI, vol. 14(10), pages 1-35, October.
    2. Juan-juan Peng & Jian-qiang Wang & Wu-E Yang, 2017. "A multi-valued neutrosophic qualitative flexible approach based on likelihood for multi-criteria decision-making problems," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(2), pages 425-435, January.
    3. Surapati Pramanik & Shyamal Dalapati & Shariful Alam & Florentin Smarandache & Tapan Kumar Roy, 2018. "NC-Cross Entropy Based MADM Strategy in Neutrosophic Cubic Set Environment," Mathematics, MDPI, vol. 6(5), pages 1-26, April.

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