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Aggregate, Arithmetic, and Geometric Operators of Octagonal Neutrosophic Numbers and Its Application in Multi-Criteria Decision-Making Problems

In: Neutrosophic Operational Research

Author

Listed:
  • Muhammad Saqlain

    (Lahore Garrison University, DHA Phase-VI, Sector C)

  • Muhammad Saeed

    (University of Management and Technology)

  • Rana Muhammad Zulqarnain

    (School of Mathematics, Northwest University Xi’an)

  • Ali Hamza

    (Lahore Garrison University)

Abstract

The validity and soundness of any theory cannot be proved without the fundamentals. The theory of octagonal neutrosophic numbers (ONNs) was proposed by Saqlain, Hamza, & Farooq ( , International Journal of Neutrosophic Science 3:29-43, 2020a). The aim of this paper is to propose the mathematical operators, like sum, difference, product, power rules, and relations—secondly, to propose the weighted arithmetic averaging operator and weighted geometric averaging operator. Furthermore, the application of the proposed methods in decision-making is illustrated in detail. Finally, the present work concludes with the future directions, where decision-making can be done.

Suggested Citation

  • Muhammad Saqlain & Muhammad Saeed & Rana Muhammad Zulqarnain & Ali Hamza, 2021. "Aggregate, Arithmetic, and Geometric Operators of Octagonal Neutrosophic Numbers and Its Application in Multi-Criteria Decision-Making Problems," Springer Books, in: Florentin Smarandache & Mohamed Abdel-Basset (ed.), Neutrosophic Operational Research, pages 493-518, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-57197-9_23
    DOI: 10.1007/978-3-030-57197-9_23
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