Skip Navigation Links
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com


Characterizations of Non-Associative Ordered Semigroups by Their Intuitionistic Fuzzy Bi-Ideals

Discontinuity, Nonlinearity, and Complexity 9(2) (2020) 257--275 | DOI:10.5890/DNC.2020.06.007

Nasreen Kausar$^{1}$, Meshari Alesemi$^{2}$, Salahuddin$^{2}$, Mohammad Munir$^{3}$

$^{1}$ Department of Mathematics, University of Agriculture FSD Pakistan

$^{2}$ Department of Mathematics, Jazan University, Jazan, Kingdom of Saudi Arabia

$^{3}$ Department of Mathematics, Government Postgraduate College, Abbottabad, Pakistan

Download Full Text PDF

 

Abstract

The aim of this paper is to investigate, the characterizations of different classes of non-associative and non-commutative ordered semigroups in terms of intuitionistic fuzzy left (right, bi-, generalized bi-, (1,2)-) ideals.

References

  1. [1]  Atanassov, K.T. (1986), Intuitionistic fuzzy sets, Fuzzy sets and systems, 20, 87-96.
  2. [2]  Atanassov, K.T. (1994), New operations defined over the intuitionistic fuzzy sets, Fuzzy sets and systems, 61, 137-142.
  3. [3]  Biswas, R. (1989), Intuitionistic fuzzy subgroups, Math. forum, x, 37-46.
  4. [4]  Cho, R.J., Jezek, J., and Kepka, T. (1999), Paramedial groupoids, Czechoslovak Math. J., 49, 277-290.
  5. [5]  Das, P.S. (1981), Fuzzy groups and level subgroups, J. Math. Anal. Appli., 84, 264-269.
  6. [6]  Jezek, J. and Kepka, T. (1983),Medial groupoids, Rozpravy CSAV Rada Mat. a Prir. Ved., 93/2, 93 pp.
  7. [7]  Jun, Y.B. (2005), Intuitionistic fuzzy bi-ideals of ordered semigroups, KyungpookMath. J., 45, 527-537.
  8. [8]  Kazim, M.A. and Naseeruddin,M. (1972), On almost semigroups, Alig. Bull. Math., 2, 1-7.
  9. [9]  Kausar, N. and Waqar, M. (2019), Characterizations of non-associative rings by their intuitionistic fuzzy bi-ideals, European Journal of Pure and Applied Mathematics, 12, 1226-250.
  10. [10]  Kausar, N. (2019), Characterizations of non-associative ordered semigroups by the properties of their fuzzy ideals with thresholds (α,β], Prikladnaya Diskretnaya Matematika, 43, 37-59.
  11. [11]  Kausar, N. (2019), Direct product of finite intuitionistic fuzzy normal subrings over non-associative rings, European Journal of Pure and Applied Mathematics, 12(2), 622-648.
  12. [12]  Kausar, N., Islam, B., Javaid, M., Amjad, S., and Ijaz, U. (2019), Characterizations of non-associative rings by the properties of their fuzzy ideals, Journal of Taibah University for Science, 13(1), 820-833.
  13. [13]  Kausar, N., Islam, B., Amjad, S., andWaqar, M. (2019), Intuitionistics fuzzy ideals with thresholds (α,β] in LA-rings, European Journal of Pure and Applied Mathematics, 12(3), 906-943.
  14. [14]  Kausar, N. and Waqar, M. (2019), Direct product of finite fuzzy normal subrings over non-associative rings, International Journal of Analysis and Applications, 17(5), 752-770.
  15. [15]  Kausar, N., Alesemi, M., and Salahuddin (2020), "Anti fuzzy interior ideals on Ordered AG-groupoids", European Journal of Pure and Applied Mathematics, 13(1), 113-129.
  16. [16]  Kehayopulu, N. (1990), On left regular ordered semigroups, Math Japon., 35, 1057-1060.
  17. [17]  Kehayopulu, N. (1993), On intra-regular ordered semigroups, Semigroup Forum, 46, 271-278.
  18. [18]  Kehayopulu, N. and Tsingelis, M. (2002), Fuzzy sets in ordered groupoids, Semigroup Forum, 65, 128-132.
  19. [19]  Kim, K.H. and Jun, Y.B. (2002), Intuitionistic fuzzy ideals of semigroups, Indian J. Pure Appl Math., 33, 443-449.
  20. [20]  Kuroki, N. (1979), Fuzzy bi-ideals in semigroups, Comment. Math. Univ. St. Pauli, 28, 17-21.
  21. [21]  Mushtaq, Q. and Yusuf, S.M. (1978), On LA-semigroups, Alig. Bull. Math., 8, 65-70.
  22. [22]  Protic, P.V. and Stevanovic, N. (1995), AG-test and some general properties of Abel-Grassmann’s groupoids, Pure Math. Appl., 6, 371-383.
  23. [23]  Rosenfeld, A. (1971), Fuzzy groups, J. Math. Anal. Appl., 35, 512-517.
  24. [24]  Shah, T., Kausar, N., and Rehman, I. (2012), Intuitionistic fuzzy normal subrings over a non-associative ring, An. St. Univ. Ovidius Constanta, 20, 369-386.
  25. [25]  Shah, T. and Kausar, N. (2014), Characterizations of non-associative ordered semigroups by their fuzzy bi-ideals, Theoretical Computer Science, 529, 96-110.
  26. [26]  Shah, T., Rehman, I., and Ali, A. (2010), On ordering of AG-groupoids, Int. Elect. J. Pure Appl. Math., 2219-224.
  27. [27]  Shah, T., Rehman, I., and Chinram, R. (2010), On M-systems in ordered AG-groupoids, Far East J. Math. Sci., 47, 13-21.
  28. [28]  Zadeh, L.A. (1965), Fuzzy sets, Inform and control, 8, 338-353.