Volume 25 • Issue 2 • PP: 93-116 • 2025
New approach for subbisemiring of bisemiring is applied to complex cubic anti neutrosophic set and its extension
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© 2025 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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We construct and analyze the concept of complex cubic anti neutrosophic subbisemiring (ComCANSBS). We analyze the important properties and homomorphic aspects of ComCANSBS. For bisemirings, we propose the ComCANSBS level sets. A complex neutrosophic subset of bisemiring Ⓢ is represented by the symbol Γ if and only if each non-empty level set R(℘,κ), where R) = |ℜ⊤Γ ·eiθ z}|{ℑ⊤Γ ,z}|{ℜ גΓ ·eiθz}|{ℑ גΓ ,z}|{ℜΓ ·eiθz}|{ℑΓ ,ℜ⊤Γ ·eiθℑ⊤Γ ,ℜ גΓ · eiθℑ גΓ,ℜΓ · eiθℑΓ ) is a ComCANSBS of Ⓢ. Let Υ be a ComCANSBS of bisemiring Ⓢ. If and only if Υ is a ComCANSBS of Ⓢ × Ⓢ, then Γ is a ComCANSBS of bisemiring Ⓢ. Let Γ be the strongest complex anti neutrosophic relation of bisemiring Ⓢ. We show that homomorphic images of all ComCANSBSs are ComCANSBSs, and homomorphic pre-images of all ComCANSBSs are ComCANSBSs. There are examples given to illustrate our results.
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References
[1] L. A. Zadeh, Fuzzy sets, Information and Control, 8, (1965), 338-353.
[2] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1), (1986) 87-96.
[3] R. R. Yager, Pythagorean membership grades in multi criteria decision-making, IEEE Trans. Fuzzy Systems, 22, (2014), 958-965.
[4] S. Ashraf, S. Abdullah, T. Mahmood, F. Ghani and T. Mahmood, Spherical fuzzy sets and their applications in multi-attribute decision making problems, Journal of Intelligent and Fuzzy Systems, 36, (2019), 2829-284.
[5] B.C. Cuong and V. Kreinovich, Picture fuzzy sets a new concept for computational intelligence problems, in Proceedings of 2013 Third World Congress on Information and Communication Technologies (WICT 2013), IEEE, (2013), 1-6.
[6] F. Smarandache, A unifying field in logics Neutrosophy Neutrosophic Probability, Set and Logic, Rehoboth American Research Press (1999).
[7] Daniel Ramot, Ron Milo, Menahem Friedman, and Abraham Kandel, Complex fuzzy set, IEEE Transactions on Fuzzy System, 10(2), 2002.
[8] S.J Golan, Semirings and their Applications, Kluwer Academic Publishers, London, 1999.
[9] Faward Hussian, Raja Muhammad Hashism, Ajab Khan, Muhammad Naeem, Generalization of bisemirings, International Journal of Computer Science and Information Security, 14(9), (2016), 275-289.
[10] K. M. Lee, Bipolar-valued fuzzy sets and their operations, Proc. Int. Conf. Intelligent Technologies Bangkok, Thailand, (2000) 307-312.
[11] J. Ahsan, K. Saifullah, and F. Khan, Fuzzy semirings, Fuzzy Sets and systems, 60, (1993), 309-320.
[12] M.K Sen, S. Ghosh An introduction to bisemirings, Southeast Asian Bulletin of Mathematics, 28(3), (2001), 547-559.
[13] Hasan, Z. ”Deep Learning for Super Resolution and Applications,” Galoitica: Journal of Mathematical Structures and Applications, vol. 8, no. 2, pp. 34-42, 2023.
[14] Roopadevi1,, P. Karpagadevi, M. Krishnaprakash, S. Broumi, S. Gomathi, S. ”Comprehensive DecisionMaking with Spherical Fermatean Neutrosophic Sets in Structural Engineering,” International Journal of Neutrosophic Science, vol. 24, no. 4, pp. 432-450, 2024.
[15] SG Quek, H Garg, G Selvachandran,MPalanikumar, K Arulmozhi,VIKOR and TOPSIS framework with a truthful-distance measure for the (t, s)-regulated interval-valued neutrosophic soft set, Soft Computing, 1–27, 2023.
[16] Mahmoud, H. Abdelhafeez, A. ”Spherical Fuzzy Multi-Criteria Decision-Making Approach for Risk Assessment of Natech,” Journal of Neutrosophic and Information Fusion, vol. 2, no. 1, pp. 59-68, 2023.
[17] M Palanikumar, K Arulmozhi, MCGDM based on TOPSIS and VIKOR using Pythagorean neutrosophic soft with aggregation operators, Neutrosophic Sets and Systems, (2022), 538–555.
[18] M Palanikumar, S Broumi, Square root (l1, l2)phantine neutrosophic normal interval-valued sets and their aggregated operators in application to multiple attribute decision making, International Journal of Neutrosophic Science, 4, (2022).
[19] Ozcek, M. ”A Review on the Structure of Fuzzy Regular Proper Mappings in Fuzzy Topological Spaces and Their Properties,” Journal of Pure Mathematics for Theoretical Computer Science, vol. 3, no. 2, pp. 60-71, 2023.
[20] Ali, O. Mashhadani, S. Alhakam, I. M., S. ”A New Paradigm for Decision Making under Uncertainty in Signature Forensics Applications based on Neutrosophic Rule Engine,” International Journal of Neutrosophic Science, vol. 24, no. 2, pp. 268-282, 2024.
[21] M Palanikumar, N Kausar, H Garg, A Iampan, S Kadry, M Sharaf, Medical robotic engineering selection based on square root neutrosophic normal interval-valued sets and their aggregated operators, AIMS Mathematics, 8(8), (2023), 17402–17432.
[22] A. Al Quran, A. G. Ahmad, F. Al-Sharqi, A. Lutfi, Q-Complex Neutrosophic Set, International Journal of Neutrosophic Science, 20(2), (2023), 08–19.
[23] 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, 45, (2023), 305– 321.
[24] F. Al-Sharqi, Y. Al-Qudah and N. Alotaibi, Decision-making techniques based on similarity measures of possibility neutrosophic soft expert sets. Neutrosophic Sets and Systems, 55(1), (2023), 358–382.
[25] F. Al-Sharqi, A. G. Ahmad, A. Al Quran, Mapping on interval complex neutrosophic soft sets, International Journal of Neutrosophic Science, 19(4), (2022), 77–85.
[26] 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, 20(4), (2023), 65–77.
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