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A novel group decision-making model based on triangular neutrosophic numbers

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Abstract

In group decision-making (GDM) model, experts often evaluate their opinion by using triangular fuzzy numbers. The preference relations with triangular fuzzy numbers are in consistent in nature, so we turned to neutrosophic in this paper. It is very important to take into account consistency of expert opinion and consensus degree in GDM. In order to distinguish the typical consistency, the concept of additive approximation consistency is proposed for triangular neutrosophic additive reciprocal matrices. The properties of triangular neutrosophic additive reciprocal matrices with additive approximation consistency are studied in detail. Second, by using \((n-1)\) restricted preference values, a triangular neutrosophic additive reciprocal preference relation with additive approximation consistency is constructed. The differences among expert’s opinions are measured using consensus degree. For generating a collective triangular neutrosophic additive reciprocal matrix with additive approximation consistency, the neutrosophic triangular weighted aggregation operator is used. Finally, a novel algorithm for the group decision-making problem with triangular neutrosophic additive reciprocal preference relations is presented. A numerical example is carried out to illustrate the proposed definitions and algorithm.

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Acknowledgements

We all want to thank anonymous for the constructive suggestions that improved both the quality and clarity of the research.

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Authors and Affiliations

  1. Department of Operations Research, Faculty of Computers and Informatics, Zagazig University, Sharqiyah, Egypt

    Mohamed Abdel-Basset & Mai Mohamed

  2. Department of Information System, Faculty of Computers and Informatics, Zagazig University, Sharqiyah, Egypt

    Abdel-Nasser Hussien

  3. School of Computing Science and Engineering, VIT University, Vellore, Tamil Nadu, 632014, India

    Arun Kumar Sangaiah

Authors
  1. Mohamed Abdel-Basset
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  2. Mai Mohamed
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  3. Abdel-Nasser Hussien
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  4. Arun Kumar Sangaiah
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Correspondence to Arun Kumar Sangaiah.

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This article does not contain any studies with human participants or animals performed by any of the authors.

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Communicated by G. Yi.

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Abdel-Basset, M., Mohamed, M., Hussien, AN. et al. A novel group decision-making model based on triangular neutrosophic numbers. Soft Comput 22, 6629–6643 (2018). https://doi.org/10.1007/s00500-017-2758-5

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  • DOI: https://doi.org/10.1007/s00500-017-2758-5

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