Complex Intuitionistic Fuzzy Neutrosophic Structures in Lie Algebras: Subalgebras, Ideals, and Homomorphisms
Resumo
This paper introduces the notions of complex intuitionistic fuzzy neutrosophic Lie subalgebras and ideals, formulated in the context of neutrosophic norms, specifically, the t-norm(T) and s-norm(S) applied to Lie subalgebras. It further explores how these structures relate to classical Lie subalgebras and ideals. Additionally, the study defines operations such as intersection, sum, and homomorphism on these structures and examines several fundamental and key properties associated with them.
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References
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Neutrosophic-Based Neural Network, Neutrosophic Sets and Systems, vol. 16, pp. 28–34, (2017).
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[37] M. Sahin, N. Olgun, V. Ulu，cay, A. Kargın, and F. Smarandache, A New Similarity Measure Based on Falsity Value between Single-Valued Neutrosophic Sets Based on the Centroid Points of Transformed Single-Valued Neutrosophic Numbers with Applications to Pattern Recognition, Neutrosophic Sets and Systems, vol. 15, pp. 31–48, (2017).
[38] M. M. Lotfy, S. ELhafeez, M. Eisa, and A. Salama, A Review of Recommender Systems Algorithms Utilized in Social Networks-Based E-Learning Systems & Neutrosophic System, Neutrosophic Sets and Systems, vol. 8, pp. 32–41, (2015).
[39] F. Yuhua, Neutrosophic Examples in Physics, Neutrosophic Sets and Systems, vol. 1, pp. 26–33, (2013). [40] J. P. Dix, Mathematical Foundations of Neutrosophic Logic, Neutrosophic Systems and Applications, vol.10, pp. 15–30, (2015).
[41] L. Guo, Extensions of Fuzzy Measures and Their Applications in Data Science, Data-Driven Mathematics, vol. 8, pp. 77–88, (2019).
[42] M. Abobala and A. Hatip, An Algebraic Approach to Neutrosophic Euclidean Geometry, Neutrosophic Sets and Systems, vol. 43, (2021).
[43] H. Liu, Decision-Making Methods Based on Neutrosophic Sets, Neutrosophic Sets and Systems, vol. 8, pp. 13–22, (2014).
[44] R. Rasuli, Complex intuitionistic fuzzy Lie subalgebras under norms, (2025).
[1] M. T. Abu Osman, On some products of fuzzy subgroups, Fuzzy Sets and Systems, vol. 24, pp. 79–86,(1987).
[2] A. Alkouri and A. R. Salleh, Complex Atanassov’s intuitionistic fuzzy sets, International Conference on Fundamental and Applied Sciences, AIP Conference Proceedings, vol. 1482, pp. 464–470, (2012).
[3] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87–96, (1986).
[4] K. T. Atanassov, New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol.61, pp. 137–142, (1994).
[5] K. T. Atanassov, Intuitionistic Fuzzy Sets Theory and Applications, Physica-Verlag, Heidelberg, (1999).
[6] J. J. Buckley and E. Eslami, An Introduction to Fuzzy Logic and Fuzzy Sets, Springer-Verlag, Berlin
Heidelberg GmbH, (2002).
[7] T. Hungerford, Algebra, Graduate Texts in Mathematics, Springer, (2003). [8] K. C. Kim and D. S. Lee, Fuzzy Lie ideals and fuzzy Lie subalgebras, Fuzzy Sets and Systems, vol. 94, pp. 101–107, (1998).
[9] D. S. Malik and J. N. Mordeson, Fuzzy Commutative Algebra, World Science Publishing Co. Pte. Ltd., (1995).
[10] D. Ramot, M. Friedman, G. Langholz, and A. Kandel, Complex fuzzy logic, IEEE Transactions on Fuzzy Systems, vol. 11, no. 4, pp. 450–461, (2003).
[11] D. Ramot, R. Milo, M. Friedman, and A. Kandel, Complex fuzzy sets, IEEE Transactions on Fuzzy
Systems, vol. 10, no. 2, pp. 171–186, (2002).
[12] R. Rasuli, Norms over intuitionistic fuzzy subgroups on direct product of groups, Communications in Combinatorics, Cryptography & Computer Science, vol. 1, pp. 39–54, (2023).
[13] R. Rasuli, T-norms over complex fuzzy subgroups, Mathematical Analysis and Its Contemporary Applications, vol. 5, no. 1, pp. 33–49, (2023).
[14] R. Rasuli, T-Fuzzy subalgebras of BCI-algebras, International Journal of Open Problems in Computer Science and Mathematics, vol. 16, no. 1, pp. 55–72, (2023).
[15] R. Rasuli, Norms over Q-intuitionistic fuzzy subgroups of a group, Notes on Intuitionistic Fuzzy Sets, vol. 29, no. 1, pp. 30–45, (2023).
[16] R. Rasuli, Fuzzy ideals of BCI-algebras with respect to t-norm, Mathematical Analysis and Its Contemporary Applications, vol. 5, no. 5, pp. 39–50, (2023).
[17] R. Rasuli, Intuitionistic fuzzy complex subgroups with respect to norms (T and S), Journal of Fuzzy
Extension and Applications, vol. 4, no. 5, pp. 92–114, (2023).
[18] R. Rasuli, Normalization, commutativity and centralization of TFSM(G), Journal of Discrete Mathematical Sciences & Cryptography, vol. 26, no. 4, pp. 1027–1050, (2023).
[19] R. Rasuli, Complex fuzzy Lie subalgebras and complex fuzzy ideals under t-norms, Journal of Fuzzy Extension and Applications, vol. 4, no. 3, pp. 173–187, (2023).
[20] R. Rasuli, Anti fuzzy B-subalgebras under S-norms, Communications in Combinatorics, Cryptography & Computer Science, vol. 1, pp. 61–74, (2023).
[21] R. Rasuli, Normality and translation of IFS(G Ö Q) under norms, Notes on Intuitionistic Fuzzy Sets, vol. 29, no. 2, pp. 114–132, (2023).
[22] R. Rasuli, Anti fuzzy multigroups and t-conorms, Proc. of 2nd Nat. Conf. on Soft Computing and Cognitive Science, Conbad Kavous Univ., Minudasht, Iran, April 18–19, (2023).
[23] R. Rasuli, Anti fuzzy d-algebras and t-conorms, Proc. of 2nd Nat. Conf. on Soft Computing and Cognitive Science, Conbad Kavous Univ., Minudasht, Iran, April 18–19, (2023).
[24] R. Rasuli, Some properties of fuzzy algebraic structures of QIFSN(G), Proc. of 4th Int. Conf. on Computational Algebra, Computational Number Theory and Applications (CACNA’2023), Univ. of Kashan, Iran, July 4–6, (2023).
[25] S. E. Yehia, Fuzzy ideals and fuzzy subalgebras of Lie algebras, Fuzzy Sets and Systems, vol. 80, pp. 237–244, (1996).
[26] S. E. Yehia, The adjoint representation of fuzzy Lie algebras, Fuzzy Sets and Systems, vol. 119, pp. 409–417, (2001).
[27] L. A. Zadeh, Fuzzy sets, Information and Control, vol. 8, pp. 338–353, (1965).
[28] F. Smarandache, Introduction to Neutrosophic Statistics, Sitech & Education Publishing, USA, vol. 3, pp. 31–55, (2014).
[29] Z. Yang, Applications of Neutrosophic Measures in Decision Sciences, Journal of Decision Analytics, vol. 12, pp. 102–115, (2020).
[30] H. Kamaci, Neutrosophic Cubic Hamacher Aggregation Operators and Their Applications in Decision Making, Neutrosophic Sets and Systems, vol. 33, pp. 234–255, (2020).
[31] A. Salama, A. Sharaf Al-Din, I. Abu Al-Qasim, R. Alhabib, and M. Badran, Introduction to Decision
Making for Neutrosophic Environment Study on the Suez Canal Port, Neutrosophic Sets and Systems, vol. 35, pp. 22–44, (2020).
[32] J. Anuradha, Neutrosophic Fuzzy Hierarchical Clustering for Dengue Analysis in Sri Lanka, Neutrosophic Sets and Systems, vol. 31, pp. 179–199, (2020).
[33] R. Sahin, Neutrosophic Hierarchical Clustering Algorithms, Neutrosophic Sets and Systems, vol. 2, pp.19–24, (2014).
[34] G. Shahzadi, M. Akram, and A. B. Saeid, An Application of Single-Valued Neutrosophic Sets in Medical Diagnosis, Neutrosophic Sets and Systems, vol. 18, no. 3, pp. 80–88, (2017).
[35] O. A. Ejaita and P. Asagba, An Improved Framework for Diagnosing Confusable Diseases Using
Neutrosophic-Based Neural Network, Neutrosophic Sets and Systems, vol. 16, pp. 28–34, (2017).
[36] A. Chakraborty, B. Banik, S. P. Mondal, and S. Alam, Arithmetic and Geometric Operators of Pentagonal Neutrosophic Number and its Application in Mobile Communication Service-Based MCGDM Problem, Neutrosophic Sets and Systems, vol. 32, pp. 61–79, (2020).
[37] M. Sahin, N. Olgun, V. Ulu，cay, A. Kargın, and F. Smarandache, A New Similarity Measure Based on Falsity Value between Single-Valued Neutrosophic Sets Based on the Centroid Points of Transformed Single-Valued Neutrosophic Numbers with Applications to Pattern Recognition, Neutrosophic Sets and Systems, vol. 15, pp. 31–48, (2017).
[38] M. M. Lotfy, S. ELhafeez, M. Eisa, and A. Salama, A Review of Recommender Systems Algorithms Utilized in Social Networks-Based E-Learning Systems & Neutrosophic System, Neutrosophic Sets and Systems, vol. 8, pp. 32–41, (2015).
[39] F. Yuhua, Neutrosophic Examples in Physics, Neutrosophic Sets and Systems, vol. 1, pp. 26–33, (2013). [40] J. P. Dix, Mathematical Foundations of Neutrosophic Logic, Neutrosophic Systems and Applications, vol.10, pp. 15–30, (2015).
[41] L. Guo, Extensions of Fuzzy Measures and Their Applications in Data Science, Data-Driven Mathematics, vol. 8, pp. 77–88, (2019).
[42] M. Abobala and A. Hatip, An Algebraic Approach to Neutrosophic Euclidean Geometry, Neutrosophic Sets and Systems, vol. 43, (2021).
[43] H. Liu, Decision-Making Methods Based on Neutrosophic Sets, Neutrosophic Sets and Systems, vol. 8, pp. 13–22, (2014).
[44] R. Rasuli, Complex intuitionistic fuzzy Lie subalgebras under norms, (2025).
Publicado
2026-04-17
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Special Issue: Global Assembly for Mathematical Modeling and Analysis
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