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Multi-Criteria Decision-Making Method Using Heronian Mean Operators under a Bipolar Neutrosophic Environment

Author

Listed:
  • Changxing Fan

    (Department of Computer Science, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, China)

  • Jun Ye

    (Department of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, China)

  • Sheng Feng

    (Department of Computer Science, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, China)

  • En Fan

    (Department of Computer Science, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, China)

  • Keli Hu

    (Department of Computer Science, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, China)

Abstract

In real applications, most decisions are fuzzy decisions, and the decision results mainly depend on the choice of aggregation operators. In order to aggregate information more scientifically and reasonably, the Heronian mean operator was studied in this paper. Considering the advantages and limitations of the Heronian mean (HM) operator, four Heronian mean operators for bipolar neutrosophic number (BNN) are proposed: the BNN generalized weighted HM (BNNGWHM) operator, the BNN improved generalized weighted HM (BNNIGWHM) operator, the BNN generalized weighted geometry HM (BNNGWGHM) operator, and the BNN improved generalized weighted geometry HM (BNNIGWGHM) operator. Then, their propositions were examined. Furthermore, two multi-criteria decision methods based on the proposed BNNIGWHM and BNNIGWGHM operator are introduced under a BNN environment. Lastly, the effectiveness of the new methods was verified with an example.

Suggested Citation

  • Changxing Fan & Jun Ye & Sheng Feng & En Fan & Keli Hu, 2019. "Multi-Criteria Decision-Making Method Using Heronian Mean Operators under a Bipolar Neutrosophic Environment," Mathematics, MDPI, vol. 7(1), pages 1-16, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:1:p:97-:d:198718
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    References listed on IDEAS

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    1. Edmundas Kazimieras Zavadskas & Romualdas Baušys & Marius Lazauskas, 2015. "Sustainable Assessment of Alternative Sites for the Construction of a Waste Incineration Plant by Applying WASPAS Method with Single-Valued Neutrosophic Set," Sustainability, MDPI, vol. 7(12), pages 1-14, December.
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    Cited by:

    1. Chao Zhang & Deyu Li & Xiangping Kang & Yudong Liang & Said Broumi & Arun Kumar Sangaiah, 2020. "Multi-Attribute Group Decision Making Based on Multigranulation Probabilistic Models with Interval-Valued Neutrosophic Information," Mathematics, MDPI, vol. 8(2), pages 1-21, February.
    2. Marcel-Ioan Boloș & Ioana-Alexandra Bradea & Camelia Delcea, 2019. "Neutrosophic Portfolios of Financial Assets. Minimizing the Risk of Neutrosophic Portfolios," Mathematics, MDPI, vol. 7(11), pages 1-27, November.

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