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)
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.
References :
[1] Smarandache, F., (1998). Neutrosophy: Neutrosophic probability, set, and logic: Analytic synthesis & synthetic analysis. Rehoboth, N. M.: American Research Press.
[2] Wang, H., Smarandache, F., Zhang, Y.-Q and Sunderraman, R. (2010). Single valued neutrosophic sets. In Smarandache, F. (Ed.) Multispace and Multistructure, Vol. IV. (pp.410-413). North-European Scientific Publishers.
[3] Jansi, R., Mohana, K., & Smarandache, F. (2019). Correlation measure for Pythagorean neutrosophic sets with T and F as dependent neutrosophic components. Neutrosophic Set and Systems, 30, 202-212.
[4] Ali, M. and Smarandache, F. (2017). Complex neutrosophic set. Neural Computing and Applications. 28(7), 1817-1834.
[5] Antony Crispin Sweety, C. and Jansi, R. (2021). Fermatean Neutrosophic Sets, International Journal of Advanced Research in Computer and Communication Engineering. 10(6), 24-27.
[6] Deli, I., Ali, M., & Smarandache, F. (2015). Bipolar neutrosophic sets and their application based on multi-criteria decision making problems. In 2015 International conference on advanced mechatronic systems (ICAMechS) (pp. 249-254), Beijing, China, 2015.
[7] Alkhazaleh, S. (2015). Neutrosophic vague set theory. In Wang, P. P., Mordeson, J. N., Wierman, M. J. and Smarandache, F. (Eds.) Critical Review. (pp. 29-39). Omaha, Nebraska: Center for Mathematics of Uncertainty, Creighton University.
[8] Hussain, S. S., Hussain, R. J., & Babu, M. V. (2020). Neutrosophic vague incidence graph. International Journal of Neutrosophic Science, 12(1), 29-38.
[9] Remya, P. B. and Shalini, A. F. (2020). Neutrosophic vague binary G-subalgebra of G-algebra. Neutrosophic Sets and Systems. 38, 576-598
[10] Gayathri, N., Helen, M., & Mounika, P. (2020). On neutrosophic vague measure using python. In AIP Conference Proceedings, 2261(1), AIP Publishing.
[11] Dong, W. M. and Wong, F. S. (1987). Fuzzy weighted averages and implementation of the extension principle. Fuzzy Sets and Systems. 21(2), 183-199.
[12] Chiclana, F., Herrera, F. and Herrera-Viedma, E. (2002). The ordered weighted geometric operator: Properties and application in MCDM problems. In Bouchon-Meunier, B., Gutiérrez-Ríos, J., Magdalena, L. and Yager, R.R. (Eds.) Technologies for Constructing Intelligent Systems 2. (pp. 173-183). Heidelberg: Physica-Verlag.
[13] Bonferroni, C. (1950). Sulle medie multiple di potenze. Bollettino dell'Unione Matematica Italiana. 5(3-4), 267-270.
[14] Liu, P., Zhang, L., Liu, X., & Wang, P. (2016). Multi-valued neutrosophic number Bonferroni mean operators with their applications in multiple attribute group decision making. International Journal of Information Technology & Decision Making, 15(05), 1181-1210.
[15] Ajay, D., Broumi, S., & Aldring, J. (2020). An MCDM method under neutrosophic cubic fuzzy sets with geometric bonferroni mean operator. Neutrosophic Sets and Systems, 32, 187-202.
[16] Awang, A., Aizam, N. A. H., Ab Ghani, A. T., Othman, M. and Abdullah, L. (2020). A normalized weighted Bonferroni mean aggregation operator considering Shapley fuzzy measure under
interval-valued neutrosophic environment for decision-making. International Journal of Fuzzy Systems. 22(1), 321-336.
[17] Nagarajan, D., Kanchana, A., Jacob, K., Kausar, N., Edalatpanah, S. A., & Shah, M. A. (2023). A novel approach based on neutrosophic Bonferroni mean operator of trapezoidal and triangular neutrosophic interval environments in multi-attribute group decision making. Scientific Reports, 13(1), 10455.
[18] Xu ZS, Yager RR (2011) Intuitionistic fuzzy Bonferroni Means, IEEE transactions on systems, man, and cybernetics—part B. Cybernetics 41:568–578.
| Style | # |
|---|---|
| MLA | Hazwani Hashim, Noor Azzah Awang, Lazim Abdullah. "A Normalized Weighted Bonferroni Mean Aggregation Operator in Neutrosophic Vague Multi-Criteria Decision- Making." International Journal of Neutrosophic Science, Vol. 22, No. 1, 2023 ,PP. 86-103 (Doi : https://doi.org/10.54216/IJNS.220107) |
| APA | Hazwani Hashim, Noor Azzah Awang, Lazim Abdullah. (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) |
| Chicago | Hazwani Hashim, Noor Azzah Awang, Lazim Abdullah. "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) |
| Harvard | Hazwani Hashim, Noor Azzah Awang, Lazim Abdullah. (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) |
| Vancouver | Hazwani Hashim, Noor Azzah Awang, Lazim Abdullah. A Normalized Weighted Bonferroni Mean Aggregation Operator in Neutrosophic Vague Multi-Criteria Decision- Making. Journal of International Journal of Neutrosophic Science, (2023); 22 ( 1 ): 86-103 (Doi : https://doi.org/10.54216/IJNS.220107) |
| IEEE | Hazwani Hashim, Noor Azzah Awang, Lazim Abdullah, 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) : 86-103 (Doi : https://doi.org/10.54216/IJNS.220107) |