Volume 25 , Issue 4 , PP: 01-09, 2025 | Cite this article as | XML | Html | PDF | Full Length Article
Nader Mahmoud Taffach 1 , Mohammad Alsheikh 2 , Ahmed Hatip 3
Doi: https://doi.org/10.54216/IJNS.250401
This paper introduces a novel approach to the concept of neutrosophic Lie algebra by leveraging the AH isometry framework. We establish foundational properties of neutrosophic Lie algebra, demonstrating that each neutrosophic algebra inherently fulfills the criteria of a Lie algebra. Moreover, we introduce distinct neutrosophic Lie algebraic structures, providing illustrative examples to support these constructs. By integrating neutrosophic logic, our approach effectively addresses indeterminacy, ambiguity, and imprecision, enhancing the classical algebraic structures with new dimensions of flexibility. The potential applications of neutrosophic Lie algebra are vast, particularly in fields requiring nuanced treatments of uncertainty.
Neutrosophic rings , Neutrosophic algebra, AH Isometry , Neutrosophic Lie Algebra , Neutrosophic Lie Subalgebra
[1] B. C. Hall and B. C. Hall, Lie Groups, Lie Algebras, and Representations. Springer New York, 2013.
[2] A. A. Kirillov, An Introduction to Lie Groups and Lie Algebras, vol. 113. Cambridge University Press, 2008.
[3] K. Erdmann and M. J. Wildon, Introduction to Lie Algebras, vol. 122. London: Springer, 2006.
[4] R. Carter, "Lie Algebras of Finite and Affine Type," Cambridge University Press, 2005.
[5] J. Humphreys, "Introduction to Lie Algebras and Representation Theory," Springer, 1997.
[6] F. Smarandache, Introduction to Neutrosophic Statistics. USA: Sitech & Education Publishing, 2014, vol. 3, pp. 31–55.
[7] Z. Yang, "Applications of Neutrosophic Measures in Decision Sciences," Journal of Decision Analytics, vol. 12, pp. 102–115, 2020.
[8] H. Kamaci, “Neutrosophic Cubic Hamacher Aggregation Operators and Their Applications in Decision Making,” Neutrosophic Sets and Systems, vol. 33, pp. 234–255, 2020.
[9] 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.
[10] J. Anuradha, “Neutrosophic Fuzzy Hierarchical Clustering for Dengue Analysis in Sri Lanka,” Neutrosophic Sets and Systems, vol. 31, pp. 179–199, 2020.
[11] R. Sahin, “Neutrosophic Hierarchical Clustering Algorithms,” Neutrosophic Sets and Systems, vol. 2, pp. 19–24, 2014.
[12] 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.
[13] 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.
[14] 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.
[15] M. Sahin, N. Olgun, V. Uluçay, 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.
[16] 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.
[17] F. Yuhua, “Neutrosophic Examples in Physics,” Neutrosophic Sets and Systems, vol. 1, pp. 26–33, 2013.
[18] J. P. Dix, “Mathematical Foundations of Neutrosophic Logic,” Neutrosophic Systems and Applications, vol. 10, pp. 15–30, 2015.
[19] L. Guo, "Extensions of Fuzzy Measures and Their Applications in Data Science," Data-Driven Mathematics, vol. 8, pp. 77–88, 2019.
[20] M. Akram and G. Shahzadi, “Decision-Making Based on Neutrosophic Graphs,” Neutrosophic Sets and Systems, vol. 22, pp. 67–83, 2019.
[21] M. Ali, F. Smarandache, M. Shabir, and L. Vladareanu, “Generalization of Neutrosophic Rings and Neutrosophic Fields,” Neutrosophic Sets and Systems, vol. 5, pp. 9–14, 2014.
[22] J. Ye, “Improved Correlation Coefficient of Single-Valued Neutrosophic Sets and Its Application to Decision Making,” Applied Mathematical Modelling, vol. 38, no. 3, pp. 1170–1182, 2014.
[23] M. Abobala and A. Hatip, “An Algebraic Approach to Neutrosophic Euclidean Geometry,” Neutrosophic Sets and Systems, vol. 43, 2021.
[24] H. Liu, "Decision-Making Methods Based on Neutrosophic Sets," Neutrosophic Sets and Systems, vol. 8, pp. 13–22, 2014.
[25] G. Deli and S. Subashini, "Multi-Attribute Decision Making Using Interval Neutrosophic Sets," International Journal of Systems Science and Engineering, vol. 1, pp. 32–41, 2015.
[26] D. Lhiani, K. Zayood, N. Taffach, and A. Katy, “On the Roots of Unity in Several Complex Neutrosophic Rings,” Neutrosophic Sets and Systems, vol. 54, 2023.
[27] P. Wang and C. Peng, “Multi-Criteria Decision-Making Method Based on Neutrosophic Sets and the Weighted Aggregation Operator,” Symmetry, vol. 12, no. 3, pp. 485, 2020.
[28] R. Yager and L. Liu, "Decision-Making with a Neutrosophic Set-Based Aggregation Model," Information Sciences, vol. 39, no. 2, pp. 56–68, 2015.
[29] A. Broumi, "Single-Valued Neutrosophic Decision-Making Approach for Solving Multi-Objective Programming Problems," Symmetry, vol. 13, no. 3, pp. 101–110, 2021.
[30] A. Hatip, “On Intuitionistic Fuzzy Subgroups of (M-N) Type and Their Algebraic Properties,” Galoitica: Journal of Mathematical Structures and Applications, vol. 4, no. 1, pp. 15–20, Mar. 2023. doi: 10.54216/GJMSA.040102.
[31] H. Wang and Z. Qin, "Symbolic and Algebraic Manipulations in Multi-Valued Logic," Journal of Applied Algebra, vol. 45, pp. 150–161, 2023.
[32] M. Khatib and Y. Abbas, “Refined Neutrosophic Structures and Applications in Decision Analysis,” Journal of Neutrosophic Applications, vol. 10, pp. 123–135, 2024.
[33] L. A. Zadeh, “Fuzzy Sets,” Information and Control, vol. 8, pp. 338–353, 1965.
[34] K. Atanassov, “Intuitionistic Fuzzy Sets,” Fuzzy Sets and Systems, vol. 20, pp. 87–96, 1986.
[35] R. Sahin, “Neutrosophic Hierarchical Clustering Algorithms,” Neutrosophic Sets and Systems, vol. 2, pp. 19–24, 2014
[36] F. Smarandache, A Unifying Field in Logics Neutrosophy: Neutrosophic Probability, Set and Logic. 1998.
[37] J. Yager, "Refined Fuzzy Set-Based Decision Models for Complex Data," Applied Soft Computing, vol. 15, pp. 20–30, 2024.
[38] A. Chakraborty and S. Mondal, "Exploration of Refined Aggregation Operators for Multi-Criteria Decision Making," Soft Computing, vol. 25, pp. 45–60, 2023.
[39] K. Liu and P. Zhang, "Advanced Topics in Neutrosophic Rings and Modules," International Journal of Mathematics and Statistics, vol. 19, pp. 33–47, 2023.
