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N-fuzzy ideals of lattices

Year 2017, Volume: 66 Issue: 2, 340 - 348, 01.08.2017
https://doi.org/10.1501/Commua1_0000000824

Abstract

In this paper, the new concepts of N -fuzzy ideals and N -fuzzyprime ideals of lattices have been introduced. Also, some of theirs basic properties are investigated. Hence, some results about the homomorphic N -imageand pre-image of N -fuzzy ideals of lattices are established

References

  • Biswas, R., Fuzzy subgroups and anti fuzzy subgroups, Fuzzy Sets and Systems 35 (1990), 124.
  • Datta, S. K., On anti fuzzy bi-ideals in rings, International Journal of Pure and Applied Mathematics 51 (2009), 375-382.
  • Dheena P. and Mohanraaj G., On Intuitionistic Fuzzy K-ideals of Semiring, International Journal of Computational Cognition 9(2) (2011), 45-50.
  • Gratzer, G., Lattice theory - First concepts and Distributive lattices, Freeman Company, San Francisco, 1971.
  • Hong, S. M. and Jun, Y. B., Anti fuzzy ideals in BCK-algebras, Kyungpook Mathematical Journal 38 (1998), 145-150.
  • Khan, M. and Asif, T., Characterizations of semigroups by their anti Fuzzy ideals, Journal of Mathematics Research 2(3) (2010), 134-143.
  • Kim, K. H. and Jun, Y. B., Anti fuzzy R-subgroups of near-rings, Scientiae Mathematicae 2 (1999), 147-153.
  • Klir, G. J. and Yuan, B., Fuzzy Sets and Fuzzy Logic: Theory and Applications, New Delhi, Koguep, B. B. N., Nkuimi, C. and Lele, C., On Fuzzy Prime Ideals of Lattices, SAMSA Journal of Pure and Applied Mathematics 3 (2008), 1-11.
  • Lekkoksung, S. and Lekkoksung, N., On Generalized Anti Fuzzy Bi-Ideals in Ordered Semigroups, International Journal of Contemporary Mathematical Sciences 7(16) (2012), 764.
  • Mordeson, J. N. and Malik, D. S., Fuzzy Commutative Algebra, World Scienti…c Publishing Company, Singapure, 1998.
  • Rosenfeld, A., Fuzzy Groups, Journal of Mathematical Analysis and Applications 35 (1971), 517.
  • Shabir, M. and Nawaz, Y., Semigroups characterized by the properties of their anti fuzzy ideals, Journal of Advanced Research in Pure Mathematics 3 (2009), 42-59.
  • Srinivas, T., Nagaiah, T. and Swamy, P. N., Anti fuzzy ideals of near rings, Annals of Fuzzy Mathematics and Informatics 3(2) (2012), 255-266.
  • Yuan, B. and Wu, W., Fuzzy ideals on a distributive lattice, Fuzzy Sets and Systems 35 (1990), 231-240.
  • Zadeh, L. A., Fuzzy sets, Information and Control 8 (1965), 338-353.
  • Zhou, M., Xiang, D. and Zhan, J., On anti fuzzy ideals of rings, Annals of Fuzzy Mathe- matics and Informatics 1 (2011), 197–205.
  • Current address : Yıldıray Çelik: Department of Mathematics, Ordu University, 52200, Ordu, TURKEY.
  • E-mail address : ycelik61@gmail.com
Year 2017, Volume: 66 Issue: 2, 340 - 348, 01.08.2017
https://doi.org/10.1501/Commua1_0000000824

Abstract

References

  • Biswas, R., Fuzzy subgroups and anti fuzzy subgroups, Fuzzy Sets and Systems 35 (1990), 124.
  • Datta, S. K., On anti fuzzy bi-ideals in rings, International Journal of Pure and Applied Mathematics 51 (2009), 375-382.
  • Dheena P. and Mohanraaj G., On Intuitionistic Fuzzy K-ideals of Semiring, International Journal of Computational Cognition 9(2) (2011), 45-50.
  • Gratzer, G., Lattice theory - First concepts and Distributive lattices, Freeman Company, San Francisco, 1971.
  • Hong, S. M. and Jun, Y. B., Anti fuzzy ideals in BCK-algebras, Kyungpook Mathematical Journal 38 (1998), 145-150.
  • Khan, M. and Asif, T., Characterizations of semigroups by their anti Fuzzy ideals, Journal of Mathematics Research 2(3) (2010), 134-143.
  • Kim, K. H. and Jun, Y. B., Anti fuzzy R-subgroups of near-rings, Scientiae Mathematicae 2 (1999), 147-153.
  • Klir, G. J. and Yuan, B., Fuzzy Sets and Fuzzy Logic: Theory and Applications, New Delhi, Koguep, B. B. N., Nkuimi, C. and Lele, C., On Fuzzy Prime Ideals of Lattices, SAMSA Journal of Pure and Applied Mathematics 3 (2008), 1-11.
  • Lekkoksung, S. and Lekkoksung, N., On Generalized Anti Fuzzy Bi-Ideals in Ordered Semigroups, International Journal of Contemporary Mathematical Sciences 7(16) (2012), 764.
  • Mordeson, J. N. and Malik, D. S., Fuzzy Commutative Algebra, World Scienti…c Publishing Company, Singapure, 1998.
  • Rosenfeld, A., Fuzzy Groups, Journal of Mathematical Analysis and Applications 35 (1971), 517.
  • Shabir, M. and Nawaz, Y., Semigroups characterized by the properties of their anti fuzzy ideals, Journal of Advanced Research in Pure Mathematics 3 (2009), 42-59.
  • Srinivas, T., Nagaiah, T. and Swamy, P. N., Anti fuzzy ideals of near rings, Annals of Fuzzy Mathematics and Informatics 3(2) (2012), 255-266.
  • Yuan, B. and Wu, W., Fuzzy ideals on a distributive lattice, Fuzzy Sets and Systems 35 (1990), 231-240.
  • Zadeh, L. A., Fuzzy sets, Information and Control 8 (1965), 338-353.
  • Zhou, M., Xiang, D. and Zhan, J., On anti fuzzy ideals of rings, Annals of Fuzzy Mathe- matics and Informatics 1 (2011), 197–205.
  • Current address : Yıldıray Çelik: Department of Mathematics, Ordu University, 52200, Ordu, TURKEY.
  • E-mail address : ycelik61@gmail.com
There are 18 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Yıldıray Çelık This is me

Publication Date August 1, 2017
Published in Issue Year 2017 Volume: 66 Issue: 2

Cite

APA Çelık, Y. (2017). N-fuzzy ideals of lattices. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 66(2), 340-348. https://doi.org/10.1501/Commua1_0000000824
AMA Çelık Y. N-fuzzy ideals of lattices. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2017;66(2):340-348. doi:10.1501/Commua1_0000000824
Chicago Çelık, Yıldıray. “N-Fuzzy Ideals of Lattices”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66, no. 2 (August 2017): 340-48. https://doi.org/10.1501/Commua1_0000000824.
EndNote Çelık Y (August 1, 2017) N-fuzzy ideals of lattices. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66 2 340–348.
IEEE Y. Çelık, “N-fuzzy ideals of lattices”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 66, no. 2, pp. 340–348, 2017, doi: 10.1501/Commua1_0000000824.
ISNAD Çelık, Yıldıray. “N-Fuzzy Ideals of Lattices”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66/2 (August 2017), 340-348. https://doi.org/10.1501/Commua1_0000000824.
JAMA Çelık Y. N-fuzzy ideals of lattices. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66:340–348.
MLA Çelık, Yıldıray. “N-Fuzzy Ideals of Lattices”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 66, no. 2, 2017, pp. 340-8, doi:10.1501/Commua1_0000000824.
Vancouver Çelık Y. N-fuzzy ideals of lattices. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66(2):340-8.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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