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Anti Fuzzy BG-ideals in BG-algebra

Year 2019, Issue: 27, 1 - 10, 01.03.2019

Abstract

In this paper, we introduce the concept of anti fuzzy BG-ideals in BG-algebra and we have discussed some of their properties. Relation between anti fuzzy BG-ideal and cartessian product of anti fuzzy BG-ideals is developed.

References

  • [1] S. S. Ahn and H. D. Lee, Fuzzy Subalgebras of Bg-Algebras, Communication of the Korean Mathematical Society 19 (2004) 243-251.
  • [2] K. T. Atanassov , On Intuitionistic Fuzzy Sets Theory, Published by Springer-Verlag Berlin Heidelberg, 2002.
  • [3] K. T. Atanassov, More on intuitionistic Fuzzy Sets, Fuzzy sets and systems 33(1) (1989) 37-45.
  • [4] K. T. Atanassov, Intuitionistic Fuzzy Sets, VII ITKR's Session, Sofia, (Deposed in Central Sci. -Techn. Library of Bulg. Acad. of Sci., 1697/84) (1983)(in Bulg).
  • [5] C. S. Hoo, Fuzzy ideals of BCI and Mv-algebras, fuzzy sets and system 62 (1994) 111-114.
  • [6] Q. P. Hu and X. Li, On proper BCH-algebras, Mathematica Japonica International Society for Mathematical Sciences Japonica 30 (1985) 659{661.
  • [7] Q. P. Hu and X. Li, On BCH-algebras, Mathematics Seminar notes 11 ( 1983) 313-320.
  • [8] K. Iseki, On BCI-algebras, Math. Seminar Notes 8 (1980) 125-130.
  • [9] Y. B. Jun and K. H. Kim, Intuitionistic fuzzy ideals of BCK- algebras, International Journal of Mathematics and Mathematical Sciences 24(12) (2000) 839-849.
  • [10] Y. B. Jun, E. H. Roh and H. S. Kim, On BH-algebras, Scientiae Mathematicae Japonicae Online1 (1998) 347-354.
  • [11] K. H. Kim, Intuitionistic Fuzzy Ideals of Semigroups, Indian Journal of Pure and Appllied Mathematics Math. 33(4) (2002) 443-449.
  • [12] C. B. Kim and H.S. Kim, On BG-algebras, Demonstratio Mathematica 41(3) 497-505.
  • [13] J. Meng and Y. B. Jun, BCK-algebras, Kyung Moon Sa. Co., Seoul, ( 1994).
  • [14] R.Muthuraj, M.Sridharan and P. M. Sitharselvam, Fuzzy BG-Ideals in BG-Algebra, International Journal of Computer Applications 2 (2010) 26-30.
  • [15] Neggers and H. S. Kim, On B-algebras, Mathemati·cki Vensik, 54 (2002) 21-29.
  • [16] Neggers and H. S. Kim, On -d-Algebras, Mathematica Slovaca 49(1999) 19-26.
  • [17] A. Rosenfield, Fuzzy Groups, J. Math. Anal. Appl. 35 (1971) 512-517.
  • [18] M. W. Rysiawa, Anti Fuzzy flters of pseudo-BL-algebras, Commentations Math- ematicae 51(2) (2011) 155-165.
  • [19] T. Senapati, M. Bhowmik, M. Pal, Intuitionistic fuzzifications of ideals in BG- algebras, Mathematical Aeterna 2(9) (2012) 761-778.
  • [20] L. A. Zadeh, Fuzzy sets, Inform. Control. 8 (1965) 338-353.
Year 2019, Issue: 27, 1 - 10, 01.03.2019

Abstract

References

  • [1] S. S. Ahn and H. D. Lee, Fuzzy Subalgebras of Bg-Algebras, Communication of the Korean Mathematical Society 19 (2004) 243-251.
  • [2] K. T. Atanassov , On Intuitionistic Fuzzy Sets Theory, Published by Springer-Verlag Berlin Heidelberg, 2002.
  • [3] K. T. Atanassov, More on intuitionistic Fuzzy Sets, Fuzzy sets and systems 33(1) (1989) 37-45.
  • [4] K. T. Atanassov, Intuitionistic Fuzzy Sets, VII ITKR's Session, Sofia, (Deposed in Central Sci. -Techn. Library of Bulg. Acad. of Sci., 1697/84) (1983)(in Bulg).
  • [5] C. S. Hoo, Fuzzy ideals of BCI and Mv-algebras, fuzzy sets and system 62 (1994) 111-114.
  • [6] Q. P. Hu and X. Li, On proper BCH-algebras, Mathematica Japonica International Society for Mathematical Sciences Japonica 30 (1985) 659{661.
  • [7] Q. P. Hu and X. Li, On BCH-algebras, Mathematics Seminar notes 11 ( 1983) 313-320.
  • [8] K. Iseki, On BCI-algebras, Math. Seminar Notes 8 (1980) 125-130.
  • [9] Y. B. Jun and K. H. Kim, Intuitionistic fuzzy ideals of BCK- algebras, International Journal of Mathematics and Mathematical Sciences 24(12) (2000) 839-849.
  • [10] Y. B. Jun, E. H. Roh and H. S. Kim, On BH-algebras, Scientiae Mathematicae Japonicae Online1 (1998) 347-354.
  • [11] K. H. Kim, Intuitionistic Fuzzy Ideals of Semigroups, Indian Journal of Pure and Appllied Mathematics Math. 33(4) (2002) 443-449.
  • [12] C. B. Kim and H.S. Kim, On BG-algebras, Demonstratio Mathematica 41(3) 497-505.
  • [13] J. Meng and Y. B. Jun, BCK-algebras, Kyung Moon Sa. Co., Seoul, ( 1994).
  • [14] R.Muthuraj, M.Sridharan and P. M. Sitharselvam, Fuzzy BG-Ideals in BG-Algebra, International Journal of Computer Applications 2 (2010) 26-30.
  • [15] Neggers and H. S. Kim, On B-algebras, Mathemati·cki Vensik, 54 (2002) 21-29.
  • [16] Neggers and H. S. Kim, On -d-Algebras, Mathematica Slovaca 49(1999) 19-26.
  • [17] A. Rosenfield, Fuzzy Groups, J. Math. Anal. Appl. 35 (1971) 512-517.
  • [18] M. W. Rysiawa, Anti Fuzzy flters of pseudo-BL-algebras, Commentations Math- ematicae 51(2) (2011) 155-165.
  • [19] T. Senapati, M. Bhowmik, M. Pal, Intuitionistic fuzzifications of ideals in BG- algebras, Mathematical Aeterna 2(9) (2012) 761-778.
  • [20] L. A. Zadeh, Fuzzy sets, Inform. Control. 8 (1965) 338-353.
There are 20 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Muhammad Uzair Khan This is me

Raees Khan This is me

Syed İnayat Ali Shah This is me

Muhammad Luqman This is me

Publication Date March 1, 2019
Submission Date July 3, 2018
Published in Issue Year 2019 Issue: 27

Cite

APA Khan, M. U., Khan, R., Shah, S. İ. A., Luqman, M. (2019). Anti Fuzzy BG-ideals in BG-algebra. Journal of New Theory(27), 1-10.
AMA Khan MU, Khan R, Shah SİA, Luqman M. Anti Fuzzy BG-ideals in BG-algebra. JNT. March 2019;(27):1-10.
Chicago Khan, Muhammad Uzair, Raees Khan, Syed İnayat Ali Shah, and Muhammad Luqman. “Anti Fuzzy BG-Ideals in BG-Algebra”. Journal of New Theory, no. 27 (March 2019): 1-10.
EndNote Khan MU, Khan R, Shah SİA, Luqman M (March 1, 2019) Anti Fuzzy BG-ideals in BG-algebra. Journal of New Theory 27 1–10.
IEEE M. U. Khan, R. Khan, S. İ. A. Shah, and M. Luqman, “Anti Fuzzy BG-ideals in BG-algebra”, JNT, no. 27, pp. 1–10, March 2019.
ISNAD Khan, Muhammad Uzair et al. “Anti Fuzzy BG-Ideals in BG-Algebra”. Journal of New Theory 27 (March 2019), 1-10.
JAMA Khan MU, Khan R, Shah SİA, Luqman M. Anti Fuzzy BG-ideals in BG-algebra. JNT. 2019;:1–10.
MLA Khan, Muhammad Uzair et al. “Anti Fuzzy BG-Ideals in BG-Algebra”. Journal of New Theory, no. 27, 2019, pp. 1-10.
Vancouver Khan MU, Khan R, Shah SİA, Luqman M. Anti Fuzzy BG-ideals in BG-algebra. JNT. 2019(27):1-10.


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