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Single Valued Neutrosophic Sub Implicative Ideals of KU-Algebras

Year 2018, Issue: 25, 72 - 83, 06.10.2018

Abstract

We consider the concepts single valued neutrosophic of sub-implicative ideals in KU-algebras, and investigate some related properties. We give conditions for a single valued neutrosophic ideal to be a single valued neutrosophic sub-implicative ideal. We show that any single valued neutrosophic sub-implicative ideal is a single valued neutrosophic ideal, but the converse is not true. Using a level set of a single valued neutrosophic set in a KU-algebra, we give a characterization of single valued neutrosophic sub-implicative ideal.

References

  • [1] A. A. A. Agboola and B. Davvaz, Introduction to Neutrosophic BCI/BCK-Algebras, Int. J. Math. Math. Sci., (2015), 6 pages, Article ID 370267.
  • [2] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20(1), 1986,87-96.
  • [3] B. Davvaz , S. M. Mostafa and F.Kareem. Neutrosophic ideals of neutrosophic KUalgebras Gazi University Journal of Science 30(4): 463-472 (2017)
  • [4] S. M. Mostafa, M. A. Abdel Naby and O. R. Elgendy. Intuitionistic fuzzy KU-ideals in KU-algebras Int. J. of Mathematical Sciences and Applications,Vol. 1, No. 3, September 2011
  • [5] S. M. Mostafa, M. A. Abd-Elnaby and M. M. M. Yousef. Fuzzy Ideals of KUAlgebras, Int. Math. Forum, 6(63)(2011), 3139-3149.
  • [6] S. M. Mostafa, R. A. K. Omar , O. W. Abd El- Baseer, Sub implicative ideals of KUAlgebras, International Journal of Modern Science and Technology Vol. 2, No. 5, 2017. Page 223-227.
  • [7] F. Smarandache, Neutrosophy and Neutrosophic Logic, First International Conference on Neutrosophy ,Neutrosophic Logic , Set, Probability, and Statistics University of New Mexico, Gallup, NM 87301, USA(2002) .
  • [8] F. Smarandache, Neutrosophic set, a generalization of the intuitionistic fuzzy sets,Inter.J.PureAppl.Math., 24,2005,287-297 .
  • [9] F.Smarandache, A Unifying Field in Logics: Neutrosophic Logic,Neutrosophy, Neutrosophic Set, Neutrosophic Probability,American Research Press, Rehoboth, NM, USA, 2003.
  • [10] C. Prabpayak and U. Leerawat, On ideals and congruence in KU-algebras, scientia Magna Journal, Vol. 5(2009), No.1, 54-57.
  • [11] C. Prabpayak and U. Leerawat, On isomorphisms of KU-algebras, scientiamagna journal, 5(2009), no .3, 25-31.
  • [12] H. Wang, F. Smarandache, Y. Zhang, R. Sunderraman, Single valued neutrosophic sets. Technical sciences and applied Mathematics, 2012, 10-14.
  • [13] N. Yaqoob, S. M. Mostafa and M. A. Ansari, On cubic KU-ideals of KU-algebras, ISRN Algebra, (2013) Article ID935905, 10 pages.
  • [14] Zadeh L.A., 1965, Fuzzy sets, Inform. Control, 8, pp. 338–353.
Year 2018, Issue: 25, 72 - 83, 06.10.2018

Abstract

References

  • [1] A. A. A. Agboola and B. Davvaz, Introduction to Neutrosophic BCI/BCK-Algebras, Int. J. Math. Math. Sci., (2015), 6 pages, Article ID 370267.
  • [2] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20(1), 1986,87-96.
  • [3] B. Davvaz , S. M. Mostafa and F.Kareem. Neutrosophic ideals of neutrosophic KUalgebras Gazi University Journal of Science 30(4): 463-472 (2017)
  • [4] S. M. Mostafa, M. A. Abdel Naby and O. R. Elgendy. Intuitionistic fuzzy KU-ideals in KU-algebras Int. J. of Mathematical Sciences and Applications,Vol. 1, No. 3, September 2011
  • [5] S. M. Mostafa, M. A. Abd-Elnaby and M. M. M. Yousef. Fuzzy Ideals of KUAlgebras, Int. Math. Forum, 6(63)(2011), 3139-3149.
  • [6] S. M. Mostafa, R. A. K. Omar , O. W. Abd El- Baseer, Sub implicative ideals of KUAlgebras, International Journal of Modern Science and Technology Vol. 2, No. 5, 2017. Page 223-227.
  • [7] F. Smarandache, Neutrosophy and Neutrosophic Logic, First International Conference on Neutrosophy ,Neutrosophic Logic , Set, Probability, and Statistics University of New Mexico, Gallup, NM 87301, USA(2002) .
  • [8] F. Smarandache, Neutrosophic set, a generalization of the intuitionistic fuzzy sets,Inter.J.PureAppl.Math., 24,2005,287-297 .
  • [9] F.Smarandache, A Unifying Field in Logics: Neutrosophic Logic,Neutrosophy, Neutrosophic Set, Neutrosophic Probability,American Research Press, Rehoboth, NM, USA, 2003.
  • [10] C. Prabpayak and U. Leerawat, On ideals and congruence in KU-algebras, scientia Magna Journal, Vol. 5(2009), No.1, 54-57.
  • [11] C. Prabpayak and U. Leerawat, On isomorphisms of KU-algebras, scientiamagna journal, 5(2009), no .3, 25-31.
  • [12] H. Wang, F. Smarandache, Y. Zhang, R. Sunderraman, Single valued neutrosophic sets. Technical sciences and applied Mathematics, 2012, 10-14.
  • [13] N. Yaqoob, S. M. Mostafa and M. A. Ansari, On cubic KU-ideals of KU-algebras, ISRN Algebra, (2013) Article ID935905, 10 pages.
  • [14] Zadeh L.A., 1965, Fuzzy sets, Inform. Control, 8, pp. 338–353.
There are 14 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Ola Wageeh El–baseer This is me

Samy Mohamed Mostafa

Publication Date October 6, 2018
Submission Date May 15, 2018
Published in Issue Year 2018 Issue: 25

Cite

APA El–baseer, O. W., & Mostafa, S. M. (2018). Single Valued Neutrosophic Sub Implicative Ideals of KU-Algebras. Journal of New Theory(25), 72-83.
AMA El–baseer OW, Mostafa SM. Single Valued Neutrosophic Sub Implicative Ideals of KU-Algebras. JNT. October 2018;(25):72-83.
Chicago El–baseer, Ola Wageeh, and Samy Mohamed Mostafa. “Single Valued Neutrosophic Sub Implicative Ideals of KU-Algebras”. Journal of New Theory, no. 25 (October 2018): 72-83.
EndNote El–baseer OW, Mostafa SM (October 1, 2018) Single Valued Neutrosophic Sub Implicative Ideals of KU-Algebras. Journal of New Theory 25 72–83.
IEEE O. W. El–baseer and S. M. Mostafa, “Single Valued Neutrosophic Sub Implicative Ideals of KU-Algebras”, JNT, no. 25, pp. 72–83, October 2018.
ISNAD El–baseer, Ola Wageeh - Mostafa, Samy Mohamed. “Single Valued Neutrosophic Sub Implicative Ideals of KU-Algebras”. Journal of New Theory 25 (October 2018), 72-83.
JAMA El–baseer OW, Mostafa SM. Single Valued Neutrosophic Sub Implicative Ideals of KU-Algebras. JNT. 2018;:72–83.
MLA El–baseer, Ola Wageeh and Samy Mohamed Mostafa. “Single Valued Neutrosophic Sub Implicative Ideals of KU-Algebras”. Journal of New Theory, no. 25, 2018, pp. 72-83.
Vancouver El–baseer OW, Mostafa SM. Single Valued Neutrosophic Sub Implicative Ideals of KU-Algebras. JNT. 2018(25):72-83.


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