Q-Fuzzy Implementations of N- Lie Ideals Structures Over Lie Subalgebas -A New Approach

In this paper, we study the concept of q-fuzzy n-lie sub algebras (ideals) of lie algebras and investigate some of their properties. We discuss the relationship between q-fuzzy lie sub algebra (respectively ideals) and Lie sub algebras (respectively ideals). For a finite number of q-fuzzy n-lie sub algebras, we construct new q-fuzzy n-lie sub algebras on their direct sum. Finally, we analyze the homomorphism concept of q-fuzzy n-lie sub algebra over ideals.

Q-fuzzy set, sub algebra, q-fuzzy n-ideal, direct sum, homomorphism, Lie algebra, vector space.

1. Xu, X. Representations of Lie algebras and coding theory. arXiv 2009, arXiv:0902.2837. [Google Scholar] [Google Scholar] [Crossref]

2. Akram, M. New fuzzy lie subalgebras over a fuzzy field. World Appl. Sci. J. 2009, 7, 33–38. [Google Scholar] [Google Scholar] [Crossref]

3. Fritzsche, B. Sophus Lie—A Sketch of His Life and Work. J. Lie Theory 1991, 9, 1–38. [Google Scholar] 13. [Google Scholar] [Crossref]

4. Helgason, S. Sophus Lie, the mathematician. In Proceedings of the Sophus Lie Memorial Conference, Oslo, Norway, 17–21 August 1992; pp. 3–21. [Google Scholar] 14 [Google Scholar] [Crossref]

5. Hartwig, J.T.; Larsson, D.; Silvestrov, D.S. Deformations of Lie Algebras Using σ-Derivations. J. Algebr. 2006, 295, 314–361. [Google Scholar] [CrossRef]15 [Google Scholar] [Crossref]

6. Casas, J.M.; Insua, M.A.; Pacheco, N. On Universal Central Extensions of Hom-Lie Algebras. Hacet. J. Math. Stat. 2015, 44, 277–288. [Google Scholar] [CrossRef]16 [Google Scholar] [Crossref]

7. Makhlouf, A.; Silvestrov, S. Notes on 1-parameter Formal Deformations of Hom-associative and Hom-Lie Algebras. Gruyter 2010, 22, 715–739. [Google Scholar] [CrossRef]17 [Google Scholar] [Crossref]

8. Mikhalouf, M.; Silvestrov, S. Hom-algebra structures. J. Gen. Lie Theory Appl. 2008, 2, 51–64. [Google Scholar] [CrossRef] 18 [Google Scholar] [Crossref]

9. Shaqaqha, S. Fuzzy Hom-Lie Ideals of Hom-Lie Algebras. arXiv 2023, arXiv:2210.08932. [Google Scholar]19 [Google Scholar] [Crossref]

10. Kdaisat, N. On Hom-Lie Algebras; Yarmouk University: Irbid, Jordan, 2021. [Google Scholar]20 [Google Scholar] [Crossref]

11. Shaqaqha, S. Restricted Hom-Lie Superalgebras. Jordan J. Math. Stat. 2019, 12, 233–255. [Google Scholar]21 [Google Scholar] [Crossref]

12. Zadeh, L.A. Fuzzy Sets. Inf. Control 1965, 8, 338–353. [Google Scholar] [CrossRef]22 [Google Scholar] [Crossref]

13. Li, D.-F. Multiattribute decision making models and methods using intuitionistic fuzzy sets. J. Comput. Syst. Sci. 2005, 70, 73–85. [Google Scholar] [CrossRef]23 [Google Scholar] [Crossref]

14. Capocelli, R.M.; De Luca, A. Fuzzy sets and decision theory. Inf. Control 1973, 23, 446–473. [Google Scholar] [CrossRef]24 [Google Scholar] [Crossref]

15. Zadeh, L.A.; Klir, G.J.; Yuan, B. Fuzzy sets. In Fuzzy Logic, and Fuzzy Systems: Selected Papers; World Scientific: Singapore, 1996. [Google Scholar]25 [Google Scholar] [Crossref]

16. McBratney, A.B.; Odeh, I.O.A. Application of fuzzy sets in soil science: Fuzzy logic, fuzzy measurements and fuzzy decisions. Geoderma 1997, 77, 85–113. [Google Scholar] [CrossRef]26 [Google Scholar] [Crossref]

17. Zadeh, L.A. Making computers think like people [fuzzy set theory]. IEEE Spectr. 1984, 21, 26–32. [Google Scholar] [CrossRef] [Google Scholar] [Crossref]

18. Smithson, M.; Verkuilen, J. Fuzzy Set Theory: Applications in the Social Sciences; Sage: Newcastle upon Tyne, UK, 2006. [Google Scholar] [Google Scholar] [Crossref]

19. Treadwell, W.A. Fuzzy Set Theory Movement in the Social Sciences. Public Adm. Rev. 1995, 55, 91–98. [Google Scholar] [CrossRef] [Google Scholar] [Crossref]

20. Dubois, D.; Prade, H. Fuzzy set and possibility theory-based methods in artificial intelligence. Artif. Intell. 2003, 148, 1–9. [Google Scholar] [CrossRef] [Google Scholar] [Crossref]

21. Henkind, S.J.; Yager, R.R.; Benis, A.M.; Harrison, M.C. A clinical alarm system using techniques from artificial intelligence and fuzzy set theory. In Approximate Reasoning in Intelligent Systems, Decision and Control; Elsevier: Amsterdam, The Netherlands, 1987; pp. 91–104. [Google Scholar] [CrossRef] [Google Scholar] [Crossref]

22. Kandel, A.; Schneider, M. Fuzzy Sets and Their Applications to Artificial Intelligence. Adv. Comput. 1989, 28, 69–105. [Google Scholar] [CrossRef] [Google Scholar] [Crossref]

23. Guiffrida, A.L.; Nagi, R. Fuzzy set theory applications in production management research: A literature survey. J. Intell. Manuf. 1998, 9, 39–56. [Google Scholar] [CrossRef] [Google Scholar] [Crossref]

24. Zopounidis, C.; Pardalos, P.M.; Baourakis, G. Fuzzy Sets in Management, Economics, and Marketing; World Scientific: Singapore, 2001. [Google Scholar] [Google Scholar] [Crossref]

25. Yehia, S.E.-B. Fuzzy Ideals and Fuzzy Subalgebras of Lie Algebras. Fuzzy Sets Syst. 1996, 80, 237–244. [Google Scholar] [CrossRef] [Google Scholar] [Crossref]

26. Akram, M. Fuzzy Lie Algebras; Springer Nature Singapore Pte Ltd.: Singapore, 2018. [Google Scholar] [CrossRef] [Google Scholar] [Crossref]

27. Akram, M.; Shum, K.P. Intuitionistic Fuzzy Lie Algebras. Southeast Asian Bull. Math. 2007, 31, 843–855. [Google Scholar] [Google Scholar] [Crossref]

28. Akram, M. Intuitionistic (S,T)-fuzzy Lie Ideals of Lie Algebras. Quasigroups Relat. Syst. 2007, 15, 201–218. [Google Scholar] [Google Scholar] [Crossref]

29. Akram, M. Intuitionistic fuzzy Lie ideals of Lie algebras. Int. J. Fuzzy Math. 2008, 6, 991–1008. [Google Scholar] [Google Scholar] [Crossref]

30. Davvaz, B.; Dudek, W.A. Fuzzy n-Lie Algebras. J. Gen. Lie Theory Appl. 2017, 11, 1000268. [Google Scholar] [CrossRef] [Google Scholar] [Crossref]

31. Shaqaqha, S. On Fuzzification of n-Lie Algebras. Jordan J. Math. Stat. 2022, 15, 523–540. [Google Scholar] [Google Scholar] [Crossref]

32. Shaqaqha, S. Complex Fuzzy Lie Algebras. Jordan J. Math. Stat. 2020, 13, 231–247. [Google Scholar] [Google Scholar] [Crossref]

33. Sheng, Y. Representations of Hom-Lie Algebras. Algebr. Represent. Theory 2012, 15, 1081–1098. [Google Scholar] [CrossRef] [Google Scholar] [Crossref]

34. Huang, C.E.; Shi, F.G. On the Fuzzy Dimensions of Fuzzy Vector Spaces. Iran. J. Fuzzy Syst. 1012, 9, 141–150. [Google Scholar] [Google Scholar] [Crossref]

35. Parimala, M.; Smarandache, F.; Tahan, M.A.; Ozel, C. On Complex Neutrosophic Lie Algebras. Palest. J. Math. 2022, 11, 235–242. [Google Scholar] [Google Scholar] [Crossref]

36. Shaqaqha, S.; Kdaisat, N. More properties of (multiplicative)-Hom-Lie Algebras. Palest. J. Math. 2024; accepted. [Google Scholar] [Google Scholar] [Crossref]

37. Kim, C.G.; Lee, D.S. Fuzzy Lie Ideals and Fuzzy Lie Subalgebras. Fuzzy Sets Syst. 1998, 94, 101–107. [Google Scholar] [CrossRef] [Google Scholar] [Crossref]

38. Shaqaqha, S. Isomorphism Theorems of Complex Fuzzy Γ-Rings. Mo. J. Math. Sci. 2022, 34, 196–207. [Google Scholar] [CrossRef] [Google Scholar] [Crossref]

39. Atanassov, K.T. Intuitionistic fuzzy sets. Fuzzy Sets Syst. 1986, 20, 87–96. [Google Scholar] [CrossRef] [Google Scholar] [Crossref]

40. Alkouri, A.S.; Salleh, A. Complex intuitionistic fuzzy sets. In Proceedings of the International Conference on Fundamental and Applied Sciences (ICFAS’12), Kuala Lumpur, Malaysia, 12–14 June 2012; pp. 464–470. [Google Scholar] [Google Scholar] [Crossref]

41. 70102/e6t1ve40 [Google Scholar] [Crossref]

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