International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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Volume 22 , Issue 1 , PP: 86-103, 2023 | Cite this article as | XML | Html | PDF | Full Length Article

A Normalized Weighted Bonferroni Mean Aggregation Operator in Neutrosophic Vague Multi-Criteria Decision- Making

Hazwani Hashim 1 * , Noor Azzah Awang 2 , Lazim Abdullah 3

  • 1 School of Mathematical Sciences, College of Computing, Informatics and Mathematics, Universiti Teknologi MARA (UiTM) Kelantan Branch, Bukit Ilmu, 18500 Machang Kelantan Darul Naim, Malaysia - (hazwanihashim@uitm.edu.my)
  • 2 School of Mathematical Sciences, College of Computing, Informatics and Mathematics, Universiti Teknologi MARA (UiTM), 40450 Shah Alam, Selangor Darul Ehsan, Malaysia - (azzahawang@uitm.edu.my)
  • 3 Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu (UMT) Kuala Nerus, 21030, Malaysia - (lazim_m@umt.edu.my)
  • Doi: https://doi.org/10.54216/IJNS.220107

    Received: March 22, 2023 Revised: June 27, 2023 Accepted: September 03, 2023
    Abstract

    Decision-making problems involve uncertain and incomplete information, which can be well represented by the Neutrosophic set (NS). Various extensions of NS are available in the literature for solving such problems. However, the published extensions of NS have some restrictions such as single based membership degree. Neutrosophic vague set (NVS) is a newly developed theory to address the shortcomings of previous set theory. NVS is structured based on interval membership in the context of dependent membership functions. Beside uncertainty information, aggregation operators (AOs) are critical components in real-world decision-making issues. As a generalization to the conventional aggregation functions defined on the set of real numbers, numerous AOs have been presented in the literature. Each AO provides a distinct purpose in effectively resolving decision-making problems. Recently, Bonferroni meant (BM) operator has received great attention among scholars because of its ability to consider interrelationship among criteria available in decision-making problems. Based on the advantages of the NV and BM operator, we would like to fill in the gaps by developing a Neutrosophic vague normalized weighted Bonferroni mean (NV-NWBM). In addition, five mathematical properties related to proposed AO are also examined. Besides that, a three-phase decision-making framework is presented to clarify that the proposed AO can be applied to real world decision-making issues. The NV-NWBM operator along with decision-making framework is applied to the example of investment selection under NV environment. The finding shows a computer company is the best alternative for investment. Finally, influence of parameter is performed to validate the effect of parameter towards ranking order.

    Keywords :

    Neutrosophic Vague , Aggregation Operator , Bonferroni mean.

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    Cite This Article As :
    Hashim, Hazwani. , Azzah, Noor. , Abdullah, Lazim. A Normalized Weighted Bonferroni Mean Aggregation Operator in Neutrosophic Vague Multi-Criteria Decision- Making. Journal of International Journal of Neutrosophic Science, vol. 22, no. 1, 2023, pp. 86-103. DOI: https://doi.org/10.54216/IJNS.220107
    Hashim, H. Azzah, N. Abdullah, L. (2023). A Normalized Weighted Bonferroni Mean Aggregation Operator in Neutrosophic Vague Multi-Criteria Decision- Making. Journal of International Journal of Neutrosophic Science, 22( 1), 86-103. DOI: https://doi.org/10.54216/IJNS.220107
    Hashim, Hazwani. Azzah, Noor. Abdullah, Lazim. A Normalized Weighted Bonferroni Mean Aggregation Operator in Neutrosophic Vague Multi-Criteria Decision- Making. Journal of International Journal of Neutrosophic Science 22, no. 1 (2023): 86-103. DOI: https://doi.org/10.54216/IJNS.220107
    Hashim, H. , Azzah, N. , Abdullah, L. (2023) . A Normalized Weighted Bonferroni Mean Aggregation Operator in Neutrosophic Vague Multi-Criteria Decision- Making. Journal of International Journal of Neutrosophic Science , 22( 1) , 86-103 . DOI: https://doi.org/10.54216/IJNS.220107
    Hashim H. , Azzah N. , Abdullah L. [2023]. A Normalized Weighted Bonferroni Mean Aggregation Operator in Neutrosophic Vague Multi-Criteria Decision- Making. Journal of International Journal of Neutrosophic Science. 22( 1): 86-103. DOI: https://doi.org/10.54216/IJNS.220107
    Hashim, H. Azzah, N. Abdullah, L. "A Normalized Weighted Bonferroni Mean Aggregation Operator in Neutrosophic Vague Multi-Criteria Decision- Making," Journal of International Journal of Neutrosophic Science, vol. 22, no. 1, pp. 86-103, 2023. DOI: https://doi.org/10.54216/IJNS.220107