Some Characterization of Fermatean Fuzzy L-ring Ideals

Authors

  • Amal Kumar Adak Department of Mathematics, Ganesh Dutt College, Begusarai, India. https://orcid.org/0000-0002-3644-782X
  • Nil Kamal * Department of Mathematics, Lalit Narayan Mithila University, Darbhanga, India.
  • Wajid Ali Department of Mathematics, Air University, Islamabad, Pakisthan.

https://doi.org/10.22105/scfa.v1i2.31

Abstract

The Fermatean fuzzy set (FFS) represents a robust approach for addressing ambiguity, effectively managing issues that remain unresolved by Intuitionistic fuzzy set and Pythagorean fuzzy set concepts. Due to its practical utility and significant impact on tackling real-world challenges across various domains, FFS has spurred extensive research. This study defines Fermatean fuzzy sublattice and Fermatean fuzzy lattice. Additionally, it introduces Fermatean fuzzy L-ring ideals. The paper explores the concept of homomorphism within Fermatean fuzzy sets. Furthermore, it investigates important findings concerning the image and pre-image of Fermatean fuzzy L-ring ideals, utilizing properties of infimum and supremum. The results are illustrated through pertinent numerical examples.
    

Keywords:

Intuitionistic fuzzy sets, Pythagorean fuzzy sets, Fermatean fuzzy sets, Fermatean fuzzy lattice, Fermatean fuzzy L-ring ideal

References

  1. [1] Adak, A. K. (2020). Interval-valued intuitionistic fuzzy subnear rings. In Handbook of research on emerging applications of fuzzy algebraic structures (pp. 213-224). IGI Global Scientific Publishing. https://doi.org/10.4018/978-1-7998-0190-0.ch013
  2. [2] Ajmal, N., & Thomas, K. V. (1995). The lattices of fuzzy ideals of a ring. Fuzzy sets and Systems, 74(3), 371-379. https://doi.org/10.1016/0165-0114(94)00313-V
  3. [3] Ajmal, N. (1994). Homomorphism of fuzzy groups, correspondence theorem and fuzzy quotient groups. Fuzzy sets and systems, 61(3), 329-339. https://doi.org/10.1016/0165-0114(94)90175-9
  4. [4] Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy sets and systems, 20(1), 87-96. https://doi.org/10.1016/S0165-0114(86)80034-3
  5. [5] Atanassov, K. T. (1994). New operations defined over the intuitionistic fuzzy sets. Fuzzy sets and Systems, 61(2), 137-142. https://doi.org/10.1016/0165-0114(94)90229-1
  6. [6] Brikhoff, G. (1967). Lattice theory. American mathematical theory providence, Rhode, Island. https://B2n.ir/pj7540
  7. [7] Burillo López, P., & Bustince Sola, H. N. (1995). Intuitionistic fuzzy relations:(Part I). Mathware & soft computing. 2(1), 5-38. https://B2n.ir/mg5547
  8. [8] Burrillo, P. J., & Bustince, H. (1995). Intuitionistic fuzzy relations (Part II). Effect of Atanassov's operators on the properties of the intuitionistic fuzzy relations. Mathware and soft computing, 2(2), 117-148. https://eudml.org/doc/39052
  9. [9] Chandrasekharan Rao, K., & Swaminathan, V. (2008). Anti-homomorphism in near rings. Journal of the institute of mathematics and computer sciences (Mathematical series), 21(2), 83-88. https://www.researchgate.net/publication/267430650
  10. [10] Jin-Xuan, F. (1994). Fuzzy homomorphism and fuzzy isomorphism. Fuzzy sets and systems, 63(2), 237-242. https://doi.org/10.1016/0165-0114(94)90354-9
  11. [11] Hassan, A. A. M. (1999). On fuzzy rings and fuzzy homomorphisms. Journal of fuzzy mathematics, 7, 291-304.
  12. [12] Ahn, Y. S., Hur, K., & Kim, D. S. (2005). The lattice of intuitionistic fuzzy ideals of a ring. Journal of applied mathematics & informatics, 19(1), 551-572. https://www.koreascience.kr/article/JAKO200504840588221.pub?&lang=en
  13. [13] Hur, K., Jang, S. Y., & Kang, H. W. (2005). Intuitionistic fuzzy ideals of a ring. Theoretical mathematics and pedagogical mathematics, 12(3), 193-209. https://koreascience.kr/article/JAKO200507521979074.page
  14. [14] Hur, K., Kang, H. W., & Song, H. K. (2003). Intuitionistic fuzzy subgroups and subrings. Honam mathematical journal, 25(1), 19-41. https://koreascience.kr/article/JAKO200310102424449.page
  15. [15] Kim, K. H., & Jun, Y. B. (2002). Intuitionistic fuzzy ideals of semigroups. Indian journal of pure and applied mathematics, 33(4), 443-449. https://www.researchgate.net/publication/292636449
  16. [16] Kim, K. H., & Jun, Y. B. (2001). Intuitionistic fuzzy interior ideals of semigroups. International journal of mathematics and mathematical sciences, 27(5), 261-267. https://doi.org/10.1155/S0161171201010778
  17. [17] Kim, K. H., & Lee, J. G. (2005). On intuitionistic fuzzy bi-ideals of semigroups. Turkish journal of mathematics, 29(2), 201-210. https://journals.tubitak.gov.tr/math/vol29/iss2/9
  18. [18] Kuncham, S. P., & Bhavanari, S. (2005). Fuzzy prime ideal of a gamma near ring. Soochow journal of mathematics, 31(1), 121-129. https://www.researchgate.net/publication/267027652
  19. [19] Meena, K., & Thomas, K. V. (2011). Intuitionistic L-fuzzy subrings. International mathematical forum, 6(52), 2561-2572. https://www.researchgate.net/publication/268435419
  20. [20] Natrajan, R., & Moganavalli, S. (2012). Fuzzy sublattice ordered rings. International journals of contemporary mathematical sciences, 7(13), 625-630. https://B2n.ir/yn8147
  21. [21] Olson, D. M. (1978). A note on the homomorphism theorem for hemirings. International journal of mathematics and mathematical sciences, 1(4), 439-445. 10.1155/S0161171278000447
  22. [22] Palaniappan, N., & Arjunan, K. (2006). The homomorphism, anti-homomorphism of a fuzzy and anti fuzzy ideals. Varahmihir journal of mathematical sciences, 6(1), 181-188. https://www.researchgate.net/publication/265700351
  23. [23] S. K. Sardar, S. K. Majumder., & M. Mandal. (2011). Atanassov’s intuitionistic fuzzy ideals of Γ-semigroups. International journal of algebra, 5(7), 335-353. https://B2n.ir/gf6464
  24. [24] Sasireka, K. R., Sathappan, K. E., & Chellappa, B. (2016). Intuitionistic fuzzy L-filters. International journal of mathematics and its applications, 4(2), 171-178.
  25. [25] Senapati, T., & Yager, R. R. (2019). Some new operations over Fermatean fuzzy numbers and application of Fermatean fuzzy WPM in multiple criteria decision making. Informatica, 30(2), 391-412. https://doi.org/10.3233/INF-2019-1216
  26. [26] Sheikabdullah, A., & Jeyaraman, K. (2010). Anti-homomorphisms in fuzzy ideals of rings. International journal of contemporary mathematical sciences, 5(55), 2717-2721. https://www.researchgate.net/publication/228738949
  27. [27] Thomas, K. V., & Nair, L. S. (2011). Intuitionistic fuzzy sublattices and ideals. Fuzzy information and engineering, 3(3), 321-331. https://doi.org/10.1007/s12543-011-0086-5
  28. [28] Thomas, K. V., & Nair, L. S. (2011). Rough intuitionistic fuzzy sets in a lattice. International mathematics forum, 6(27), 1327-1335. https://www.researchgate.net/publication/265893265
  29. [29] Tripathy, B. K., Satapathy, M. K., & Choudhury, P. K. (2013). Intuitionistic fuzzy lattices and intuitionistic fuzzy Boolean algebras. International journal of engineering and technology, 5(3), 2352-2361. https://www.researchgate.net/profile/Bk-Tripathy/publication/274255232
  30. [30] Yager, R. R., & Abbasov, A. M. (2013). Pythagorean membership grades, complex numbers, and decision making. International journal of intelligent systems, 28(5), 436-452. https://doi.org/10.1002/int.21584
  31. [31] Yager, R. R. (2013). Pythagorean fuzzy subsets. 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS) (pp. 57-61). IEEE. https://doi.org/10.1109/IFSA-NAFIPS.2013.6608375
  32. [32] Wang, G. J. (1984). Order-homomorphisms on fuzzes. Fuzzy sets and Systems, 12(3), 281-288. https://doi.org/10.1016/0165-0114(84)90074-5
  33. [33] Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X

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Published

2024-05-10

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Vol. 1 No. 2 (2024): Soft Computing Fusion with Applications

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How to Cite

Some Characterization of Fermatean Fuzzy L-ring Ideals. (2024). Soft Computing Fusion With Applications , 1(2), 80-90. https://doi.org/10.22105/scfa.v1i2.31

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