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Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems

Author

Listed:
  • Juan-juan Peng
  • Jian-qiang Wang
  • Jing Wang
  • Hong-yu Zhang
  • Xiao-hong Chen

Abstract

As a variation of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to represent uncertain, imprecise, incomplete and inconsistent information that exists in the real world. Simplified neutrosophic sets (SNSs) have been proposed for the main purpose of addressing issues with a set of specific numbers. However, there are certain problems regarding the existing operations of SNSs, as well as their aggregation operators and the comparison methods. Therefore, this paper defines the novel operations of simplified neutrosophic numbers (SNNs) and develops a comparison method based on the related research of intuitionistic fuzzy numbers. On the basis of these operations and the comparison method, some SNN aggregation operators are proposed. Additionally, an approach for multi-criteria group decision-making (MCGDM) problems is explored by applying these aggregation operators. Finally, an example to illustrate the applicability of the proposed method is provided and a comparison with some other methods is made.

Suggested Citation

  • Juan-juan Peng & Jian-qiang Wang & Jing Wang & Hong-yu Zhang & Xiao-hong Chen, 2016. "Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(10), pages 2342-2358, July.
    • Handle: RePEc:taf:tsysxx:v:47:y:2016:i:10:p:2342-2358
    DOI: 10.1080/00207721.2014.994050
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    Cited by:

    1. Naeem Jan & Kifayat Ullah & Tahir Mahmood & Harish Garg & Bijan Davvaz & Arsham Borumand Saeid & Said Broumi, 2019. "Some Root Level Modifications in Interval Valued Fuzzy Graphs and Their Generalizations Including Neutrosophic Graphs," Mathematics, MDPI, vol. 7(1), pages 1-22, January.
    2. Wendi Chen & Jiaxing Gu & Shouzhen Zeng & Xiaoying Xie, 2023. "Solid Waste Landfill Site Assessment Framework Based on Single-Valued Neutrosophic Hybrid Aggregation and Multi-Criteria Analysis," Sustainability, MDPI, vol. 15(7), pages 1-21, March.
    3. Chao Tian & Wen Yu Zhang & Shuai Zhang & Juan Juan Peng, 2019. "An Extended Single-Valued Neutrosophic Projection-Based Qualitative Flexible Multi-Criteria Decision-Making Method," Mathematics, MDPI, vol. 7(1), pages 1-16, January.
    4. Shengjun Wu & Jie Wang & Guiwu Wei & Yu Wei, 2018. "Research on Construction Engineering Project Risk Assessment with Some 2-Tuple Linguistic Neutrosophic Hamy Mean Operators," Sustainability, MDPI, vol. 10(5), pages 1-26, May.
    5. Chao Tian & Juan Juan Peng, 2020. "A Multi-Criteria Decision-Making Method Based on the Improved Single-Valued Neutrosophic Weighted Geometric Operator," Mathematics, MDPI, vol. 8(7), pages 1-17, June.
    6. Qaisar Khan & Peide Liu & Tahir Mahmood, 2018. "Some Generalized Dice Measures for Double-Valued Neutrosophic Sets and Their Applications," Mathematics, MDPI, vol. 6(7), pages 1-16, July.
    7. Kuei-Hu Chang, 2022. "A novel reliability calculation method under neutrosophic environments," Annals of Operations Research, Springer, vol. 315(2), pages 1599-1615, August.
    8. Chao Tian & Juan Juan Peng & Zhi Qiang Zhang & Mark Goh & Jian Qiang Wang, 2020. "A Multi-Criteria Decision-Making Method Based on Single-Valued Neutrosophic Partitioned Heronian Mean Operator," Mathematics, MDPI, vol. 8(7), pages 1-25, July.
    9. Muhammad Riaz & Hafiz Muhammad Athar Farid & Jurgita Antucheviciene & Gülay Demir, 2023. "Efficient Decision Making for Sustainable Energy Using Single-Valued Neutrosophic Prioritized Interactive Aggregation Operators," Mathematics, MDPI, vol. 11(9), pages 1-29, May.
    10. Juan-juan Peng & Chao Tian & Zhi-qiang Zhang & Hai-yu Song & Jian-qiang Wang, 2019. "Single-Valued Neutrosophic Power Shapley Choquet Average Operators and Their Applications to Multi-Criteria Decision-Making," Mathematics, MDPI, vol. 7(11), pages 1-27, November.
    11. Jie Wang & Jianping Lu & Guiwu Wei & Rui Lin & Cun Wei, 2019. "Models for MADM with Single-Valued Neutrosophic 2-Tuple Linguistic Muirhead Mean Operators," Mathematics, MDPI, vol. 7(5), pages 1-26, May.
    12. Zhang-peng Tian & Jing Wang & Jian-qiang Wang & Hong-yu Zhang, 2017. "Simplified Neutrosophic Linguistic Multi-criteria Group Decision-Making Approach to Green Product Development," Group Decision and Negotiation, Springer, vol. 26(3), pages 597-627, May.
    13. Nuraini Rahim & Lazim Abdullah & Binyamin Yusoff, 2020. "A Border Approximation Area Approach Considering Bipolar Neutrosophic Linguistic Variable for Sustainable Energy Selection," Sustainability, MDPI, vol. 12(10), pages 1-21, May.

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