1
Basic Sciences Department, Preparatory Year Deanship, King Faisal University, Al-Ahsa 31982, Saudi Arabia
(aalquran@kfu.edu.sa)
2
Department of Mathematics, Faculty of Education for Pure Sciences, University Of Anbar, Ramadi, Anbar, Iraq; College of Pharmacy, National University of Science and Technology, Dhi Qar, Iraq
(faisal.ghazi@uoanbar.edu.iq)
3
Department of Mathematics, College of Science and Arts, Qassim University, Al- Badaya 51951, Saudi Arabia; Department of Operations and Management Research, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt
(Ha.Ahmed@qu.edu.sa)
4
Department of Statistics and Business Analytics, United Arab Emirates University, UAE
(h.alqahtani@uaeu.ac.ae)
5
Deanship of Development and Quality Assurance, King Faisal University, Al-Ahsa 31982, Saudi Arabia
(abanyawad@kfu.edu.sa)
Abstract :
From fuzzy to neutrosophy, multiple hybrid models have been innovated, with each introduced model surpassing its predecessor. Due to the inherent indeterminacy in the world, a more precise form of imprecision is required. As a result, more sophisticated variants of the neutrosophic set have been created. Examples of these amalgamations include fuzzy neutrosophic sets, intuitionistic fuzzy neutrosophic sets, Pythagorean fuzzy neutrosophic sets, neutrosophic vague sets, and neutrosophic rough sets. The main objective of this paper is to present another variant of the neutrosophic set called T-spherical fuzzy-valued neutrosophic set (T-SFVNS). Serving as a generalization of the aforementioned combinations, T-SFVNS allows for the representation of indeterminacy and inconsistency in a more nuanced manner. In this paper, we define the T-SFVNS and Tspherical fuzzy-valued neutrosophic numbers (T-SFVNNs). Additionally, we propose several types of score and accuracy functions to compare the T-SFVNNs. We also present the basic operations of T-SFVNSs and the algebraic operations of T-SFVNNs, supported by proofs and illustrative examples..
Keywords :
Decision Making; Neutrosophic set; Optimization; Simplified neutrosophic set; T-spherical fuzzy sets.
References :
[1] B.C. Cuong, Picture fuzzy sets, Journal of Computer Science and Cybernetics., 30 ( 2014), 409-420.
[2] L. A. Zadeh, Fuzzy sets, Inform. Contr., 8 (1965), 338-353.
[3] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Set. Syst., 20 (1986), 87-96.
[4] R. Wang and Y. Li, Picture hesitant fuzzy set and its application to multiple criteria decision-making, Symmetry., 10 (2018) p. 295.
[5] S. Ashraf, S. Abdullah, T. Mahmood, F. Ghani, T. Mahmood, Spherical fuzzy sets and their applications in multi-attribute decision making problems, J. Intell. Fuzzy Syst., 36 ( 2019), 2829-2844.
[6] T. Mahmood, K. Ullah, Q. Khan, N. Jan, An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets, Neural Comput. Appl., 31 (2019), 7041-7053.
[7] F. Smarandache, Neutrosophic set- a generalisation of the intuitionistic fuzzy sets, International Journal
of Pure and Applied Mathematics, 24 (2005), 287-297.
[8] J. Ye, A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets, Journal of Intelligent & Fuzzy Systems, 26 (2014), 2459–2466.
[9] A. Al-Quran, N. Hassan, E. Marei, A novel approach to neutrosophic soft rough set under uncertainty, Symmetry., 11 (2019) p. 384.
[10] A. Al-Quran, H. Hashim, L. Abdullah, A hybrid approach of interval neutrosophic vague sets and DEMATEL with new linguistic variable, Symmetry., 12 (2020) p. 275.
[11] M. Ali, F. Smarandache, Complex neutrosophic set, Neural Computing and Applications, 28 (2017) 1817-1834.
[12] A. Al-Quran, A. Ahmad, F. Al-Sharqi, A. Lutfi, Q-complex neutrosophic set, Int. j. neutrosophic sci., 20 (2023), 8-19.
[13] F. Al-Sharqi, A. Ahmad, A. Al-Quran, Fuzzy parameterized-interval complex neutrosophic soft sets and their applications under uncertainty, J. Intell. Fuzzy Syst., 44 (2023), 1453–1477.
[14] R. R. Yager, Pythagorean fuzzy subsets, In: 2013 Joint IFSA World Congress NAFIPS Annual Meeting (IFSA/NAFIPS), 2013, 57–61. https://doi.org/10.1109/IFSA-NAFIPS.2013.6608375
[15] M. Bhowmik, M. Pal, Intuitionistic neutrosophic set, Journal of Information and Computing Science, 4 (2009),142-152.
[16] M. Unver, E. Turkarslan, N. Celik, M. Olgun, J. Ye, Intuitionistic fuzzy-valued neutrosophic multi-sets and numerical applications to classification, Complex Intell. Syst., 8 (2022), 1703-1721.
[17] M. Palanikumar, K. Arulmozhi, C. Jana, Multiple attribute decision-making approach for Pythagorean neutrosophic normal interval-valued fuzzy aggregation operators, Comput. Appl. Math., 41 (2022), 90.
[18] P. Chellamani, D. Ajay, Pythagorean neutrosophic Dombi fuzzy graphs with an application to MCDM. Neutrosophic Sets Syst., 47 (2021), 411–431. https://doi.org/10.5281/zenodo.5775162
[19] M. Palanikumar, K. Arulmozhi, MCGDMbased on TOPSIS and VIKOR using Pythagorean neutrosophic soft with aggregation operators, Neutrosophic Sets Syst., 51 (2022), 538–555.
[20] M.C. Bozyigit, M. Olgun, M. Unver, A new type of neutrosophic set in Pythagorean fuzzy environment and applications to multi-criteria decision making, Int. j. neutrosophic sci., 20 (2023), 107-134.https://doi.org/10.54216/IJNS.200208
[21] Jamiatun Nadwa Ismail et al. The Integrated Novel Framework: Linguistic Variables in Pythagorean Neutrosophic Set with DEMATEL for Enhanced Decision Support. Int. J. Neutrosophic Sci., vol. 21, no. 2, pp. 129-141, 2023.
[22] F. Al-Sharqi, A. Al-Quran, M. U. Romdhini, Decision-making techniques based on similarity measures of possibility interval fuzzy soft environment, Iraqi Journal for Computer Science and Mathematics, vol. 4, pp.18–29, 2023.
[23] Z. bin M. Rodzi et al., “Integrated Single-Valued Neutrosophic Normalized Weighted Bonferroni Mean (SVNNWBM)-DEMATEL for Analyzing the Key Barriers to Halal Certification Adoption in Malaysia,” Int. J. Neutrosophic Sci., vol. 21, no. 3, pp. 106–114, 2023.
[24] A. Al-Quran, F. Al-Sharqi, K. Ullah, M. U. Romdhini, M. Balti and M. Alomai, Bipolar fuzzy hypersoft set and its application in decision making, International Journal of Neutrosophic Science, vol. 20, no. 4, pp. 65-77, 2023.
[25] S. H. Zail et al., Neutrosophic BCK-algebra and Ω-BCK-algebra. International Journal of Neutrosophic Science, vol. 19, no. 3, pp. 8-15, 2022.
[26] F. Al-Sharqi, M. U. Romdhini, A. Al-Quran, Group decision-making based on aggregation operator and score function of Q-neutrosophic soft matrix, Journal of Intelligent and Fuzzy Systems, vol. 45, pp.305–321, 2023.
[27] M Palanikumar, K Arulmozhi, A Iampan, S Broumi, Medical diagnosis decision making using type- II generalized Pythagorean neutrosophic interval valued soft sets.International Journal of Neutrosophic Science (IJNS) 20 (1), 2023.
| Style | # |
|---|---|
| MLA | Ashraf Al-Quran, Faisal Al-Sharqi, Hamiden Abd El- Wahed Khalifa, Haifa Alqahtani, Ali M. A. Bany Awad. "T-Spherical Fuzzy-Valued Neutrosophic Set Theory." International Journal of Neutrosophic Science, Vol. 23, No. 2, 2024 ,PP. 104-115 (Doi : https://doi.org/10.54216/IJNS.230209) |
| APA | Ashraf Al-Quran, Faisal Al-Sharqi, Hamiden Abd El- Wahed Khalifa, Haifa Alqahtani, Ali M. A. Bany Awad. (2024). T-Spherical Fuzzy-Valued Neutrosophic Set Theory. Journal of International Journal of Neutrosophic Science, 23 ( 2 ), 104-115 (Doi : https://doi.org/10.54216/IJNS.230209) |
| Chicago | Ashraf Al-Quran, Faisal Al-Sharqi, Hamiden Abd El- Wahed Khalifa, Haifa Alqahtani, Ali M. A. Bany Awad. "T-Spherical Fuzzy-Valued Neutrosophic Set Theory." Journal of International Journal of Neutrosophic Science, 23 no. 2 (2024): 104-115 (Doi : https://doi.org/10.54216/IJNS.230209) |
| Harvard | Ashraf Al-Quran, Faisal Al-Sharqi, Hamiden Abd El- Wahed Khalifa, Haifa Alqahtani, Ali M. A. Bany Awad. (2024). T-Spherical Fuzzy-Valued Neutrosophic Set Theory. Journal of International Journal of Neutrosophic Science, 23 ( 2 ), 104-115 (Doi : https://doi.org/10.54216/IJNS.230209) |
| Vancouver | Ashraf Al-Quran, Faisal Al-Sharqi, Hamiden Abd El- Wahed Khalifa, Haifa Alqahtani, Ali M. A. Bany Awad. T-Spherical Fuzzy-Valued Neutrosophic Set Theory. Journal of International Journal of Neutrosophic Science, (2024); 23 ( 2 ): 104-115 (Doi : https://doi.org/10.54216/IJNS.230209) |
| IEEE | Ashraf Al-Quran, Faisal Al-Sharqi, Hamiden Abd El- Wahed Khalifa, Haifa Alqahtani, Ali M. A. Bany Awad, T-Spherical Fuzzy-Valued Neutrosophic Set Theory, Journal of International Journal of Neutrosophic Science, Vol. 23 , No. 2 , (2024) : 104-115 (Doi : https://doi.org/10.54216/IJNS.230209) |