DOI QR코드

DOI QR Code

MS-FUZZY IDEALS OF MS-ALGEBRAS

  • Received : 2020.09.09
  • Accepted : 2021.02.22
  • Published : 2021.05.30

Abstract

In this paper, we introduce concepts of MS-fuzzy ideals of MS-algebras. We reveal the connections between MS-fuzzy ideals and several kinds of fuzzy ideals as fuzzy prime ideals, kernel fuzzy ideals, e-fuzzy ideals and closure fuzzy ideals. We show that many of these classes are proper subclasses of the class of MS-fuzzy ideals. Finally some properties of the homomorphic images, inverse homomorphic images of MS-fuzzy ideals are studied.

Keywords

References

  1. B.A. Alaba, T.G. Alemayehu, Clousure fuzzy ideals of MS-algebras, Ann. Fuzzy Math. Inform. 16 (2018), 247-260. https://doi.org/10.30948/afmi.2018.16.2.247
  2. B.A. Alaba, M.A. Taye and T.G. Alemayehu, Fuzzy Congruences on MS-algebras, Journal of Mathematics and Informatics 15 (2019), 49-57 https://doi.org/10.22457/jmi.130av15a5
  3. B.A. Alaba, M.A. Taye, T.G. Alemayehu, δ-fuzzy ideals in MS-algebras, IJMAA 6 (2018), 273-280.
  4. N. Ajmal, Fuzzy lattice, Inform. Sci. 79 (1994), 271-291. https://doi.org/10.1016/0020-0255(94)90124-4
  5. M. Attallah, Completely fuzzy prime ideals of distributive lattices, J. Fuzzy Math. 8 (2000), 151-156.
  6. E. Badawy and M. Sambasiva Rao, Closure ideals of MS-algebras, Chamchuri Journal of Mathematics 6 (2014), 31-46.
  7. E. Badawy, E. Seid, A. Geber, MS-ideals of MS-Algebras, Applied Mathematical Sciences 13 (2019), 347-357. https://doi.org/10.12988/ams.2019.9231
  8. E. Badawy, δ-ideals in MS-algebras, J. Compu. Sci. Syst. Bio. 9 (2016), 28-32.
  9. J. Berman, Distributive lattices with an additional unary operation, Aequationes Math. 16 (1977), 165-171. https://doi.org/10.1007/BF01836429
  10. T.S. Blyth and J.C. Varlet, Ockham Algebras, Oxford University Press, 1994.
  11. T.S. Blyth and J.C. Varlet, On a common abstraction of de Morgan and Stone algebras, Proc. Roy. Soc. Edinburgh Sect. A 94 (1983), 301-308. https://doi.org/10.1017/S0308210500015663
  12. T.S. Blyth and J.C. Varlet, Subvarieties of the class of MS-algebras, Proc. Roy. Soc. Edinburgh Sect. A 95 (1983), 157-169. https://doi.org/10.1017/S0308210500015869
  13. G. Gratzer, General lattice theory, New york, San Francisco, U.S.A Academic Press, 1978.
  14. B.B.N. Koguep, C. Nkuimi and C. Lele, On Fuzzy prime ideals of lattice, Samsa Journal of Pure and Applied Mathematics 3 (2008), 1-11.
  15. C. Luo and Y. Zheng, MS-algebras whose e-Ideals are Kernel ideals, Studia Logica 95 (2018), 157-169.
  16. A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35 (1971), 512-517. https://doi.org/10.1016/0022-247X(71)90199-5
  17. U.M. Swamy and D.V. Raju, Fuzzy ideals and congruences of lattices, Fuzzy sets and systems 95 (1998), 249-253. https://doi.org/10.1016/S0165-0114(96)00310-7
  18. U.M. Swamy and D.V. Raju, Irreducibility in algebraic fuzzy systems, Fuzzy Sets and Systems 41 (1991), 233-241. https://doi.org/10.1016/0165-0114(91)90227-H
  19. Bo. Yuan and W. Wu, Fuzzy ideals on a distributive lattice, Fuzzy Sets and Systems 35 (1990), 231-240. https://doi.org/10.1016/0165-0114(90)90196-D
  20. L.A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X