HESITANT FUZZY SETS APPROACH TO IDEAL
THEORY IN TERNARY SEMIGROUPS
A. Fairooze Talee1, M. Yahya Abbasi2, S. Ali Khan3
1,2,3Department of Mathematics
Jamia Millia Islamia
New Delhi - 110 025, INDIA

Abstract

In this paper, we introduce hesitant fuzzy ideals on ternary semigroups and define hesitant fuzzy left (resp. lateral, right)ideals on ternary semigroups. Here we define hesitant fuzzy point on ternary semigroups and prove some interesting results on them. We also characterize regular ternary semigroups in terms of hesitant fuzzy left, hesitant fuzzy lateral and hesitant fuzzy right ideals using hesitant fuzzy points.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 31
Issue: 4
Year: 2018

DOI: 10.12732/ijam.v31i4.2

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References

  1. [1] B. Davvaz, A. Zeb and A. Khan, On (α,β)-fuzzy ideals of ternary semigroups, J. Indones. Math. Soc., 19, No 2 (2013), 123138.
  2. [2] Y.B. Jun, K.J. Lee and S.Z. Song, Hesitant fuzzy bi-ideals in semigroups, Commun. Korean Math. Soc., 30, No 3 (2015), 143154.
  3. [3] S. Kar and P. Sarkar, Fuzzy ideals of ternary semigroups, Fuzzy Inf. Eng., 2 (2012), 181-193.
  4. [4] E. Kasner, An extension of the group concept, Bull. Amer. Math. Soc., 10 (1904), 290-291.
  5. [5] D.H. Lehmer, A ternary analogue of abelian groups, AMS J. Math., 59 (1932), 329-338.
  6. [6] M.Y. Abbasi, A.F. Talee, X.Y. Xie and S.A. Khan, Hesitant fuzzy ideal extension in po-semigroups, TWMS J. App. Eng. Math., (2017), Accepted.
  7. [7] F.M. Sioson, Ideal theory in ternary semigroups, Math. Japan., 10 (1965), 63-84.
  8. [8] V. Torra and Y. Narukawa, On HFSs and decision, in: The 18th IEEE International Conference on Fuzzy Systems, Jeju Island, Korea (2009), 13781382.
  9. [9] V. Torra, Hesitant fuzzy sets, Int. J. Intell. Syst., 25 (2010), 529539.
  10. [10] X.Y. Xie and J. Tang, Fuzzy radicals and prime fuzzy ideals of ordered semigroups, Information Sciences, 178 (2008), 43574374.
  11. [11] L.A. Zadeh, Fuzzy sets, Inform. Control., 8 (1965), 338-353.