Research Article
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Bipolar Fuzzy (T,S)-Norm Hyper KU–Ideals (Sub Algebras)

Year 2019, Volume: 11 Issue: 1, 29 - 39, 30.06.2019
https://izlik.org/JA84DD38KR

Abstract

In this paper, the concepts of $(\sigma,\tau)$- bipolar fuzzy $(T,S)$- norm of the notions (strong, weak, $s$-weak) hyper  $KU$-ideals in hyper $KU$-algebras are introduced and some properties are discussed.

References

  • Jun, Y.B., Xin, X.L., Roh, E.H., Zahedi, M.M., Strong hyper BCK-ideals of hyper BCK-algebra, Math. Jap., 51(3)(2000), 493--498.
  • Jun, Y.B., Zahedi, M.M., Xin, X.L., Borzooei, R.A., On hyper BCK-algebra, Italian J. Pure App. Math., Oxford Ser., 10(2000), 127--136.
  • Jun Y.B., Xin, X.L., Fuzzy hyper BCK-ideals of hyper BCK-algebras, Scientiae Mathematicae Japonicae Online, 4(2001), 415--422.
  • Jun, Y.B., Kang, M.S., Kim, H.S., Bipolar fuzzy hyper BCK-ideals in hyper BCK-algebras, Iranian Journal of Fuzzy Systems, 8(2)(2011), 105--120.
  • Jun, Y.B., Shim, W.H., Fuzzy implicative hyper BCK-ideals of hyper BCK-algebras, Internat. J. Math. Math. Sci., 29(2)(2002), 63--70.
  • Jun, Y.B., Xin, X.L., Fuzzy hyper BCK-ideals of hyper BCK-algebras, Sci. Math. Jpn., 53(2)(2001), 353--360.
  • Jun, Y.B., Zahedi, M.M., Xinand, X.L., Borzooei, R.A., On hyper BCK-algebras, Italian J. of Pure and Appl. Math., 8(2000), 127--136.
  • Lee, K.M., Bipolar-valued fuzzy sets and their operations, Proc. Int. Conf. on Intelligent Technologies, Bangkok, Thailand, (2000), 307--312.
  • Li, X., Zheng, C., {The direct product characteristics of the intuitionistic fuzzy groups with respect to t-s norms", Mathematics in Practice and Theory, 38(2008), 109--114.
  • Lin, M.L., Some properties on the intuitionistic fuzzy group with respect to trigonal norms, Journal of Zhangzhou Normal University (Nat. Sci.), 2(2007), 1--5.
  • Marty, F., Sur une generalization de la notion de groupe, 8th Congress Math. Scandinaves, Stockholm, (1934), 45--49.
  • Mostafa, S.M., Abd-Elnaby, M.A., Yousef, M.M.M., Fuzzy ideals of KU-algebras, Int. Math. Forum, 63(6)(2011), 3139--3149.
  • Mostafa, S.M., Kareem, F., Davvaz, B., Hyper structure theory applied to KU-algebras, Journal of Hyper Structures, 6(2)(2017), 82--95.
  • Mostafa, S.M., Hameed, A.T., Ghanem, R.A., Hyper structures of KU-algebras: Theorems & fuzzy Applications, submitted.
  • Prabpayak, C., Leerawat, U., On ideals and congruence in KU-algebras, Scientia Magna Journal, 5(1)(2009), 54--57.
  • Prabpayak, C., Leerawat, U., On isomorphisms of KU-algebras, Scientia Magna Journal, 5(3)(2009), 25--31.
  • Yaqoob, N., Mostafa, S.M., Ansari, M. A., On cubic KU-ideals of KU-algebras, ISRN Algebra, (2013) Article ID935905, 10 pages.
  • Zadeh, L.A., Fuzzy sets, Inform. And Control, 8(1965), 338--353.

Year 2019, Volume: 11 Issue: 1, 29 - 39, 30.06.2019
https://izlik.org/JA84DD38KR

Abstract

References

  • Jun, Y.B., Xin, X.L., Roh, E.H., Zahedi, M.M., Strong hyper BCK-ideals of hyper BCK-algebra, Math. Jap., 51(3)(2000), 493--498.
  • Jun, Y.B., Zahedi, M.M., Xin, X.L., Borzooei, R.A., On hyper BCK-algebra, Italian J. Pure App. Math., Oxford Ser., 10(2000), 127--136.
  • Jun Y.B., Xin, X.L., Fuzzy hyper BCK-ideals of hyper BCK-algebras, Scientiae Mathematicae Japonicae Online, 4(2001), 415--422.
  • Jun, Y.B., Kang, M.S., Kim, H.S., Bipolar fuzzy hyper BCK-ideals in hyper BCK-algebras, Iranian Journal of Fuzzy Systems, 8(2)(2011), 105--120.
  • Jun, Y.B., Shim, W.H., Fuzzy implicative hyper BCK-ideals of hyper BCK-algebras, Internat. J. Math. Math. Sci., 29(2)(2002), 63--70.
  • Jun, Y.B., Xin, X.L., Fuzzy hyper BCK-ideals of hyper BCK-algebras, Sci. Math. Jpn., 53(2)(2001), 353--360.
  • Jun, Y.B., Zahedi, M.M., Xinand, X.L., Borzooei, R.A., On hyper BCK-algebras, Italian J. of Pure and Appl. Math., 8(2000), 127--136.
  • Lee, K.M., Bipolar-valued fuzzy sets and their operations, Proc. Int. Conf. on Intelligent Technologies, Bangkok, Thailand, (2000), 307--312.
  • Li, X., Zheng, C., {The direct product characteristics of the intuitionistic fuzzy groups with respect to t-s norms", Mathematics in Practice and Theory, 38(2008), 109--114.
  • Lin, M.L., Some properties on the intuitionistic fuzzy group with respect to trigonal norms, Journal of Zhangzhou Normal University (Nat. Sci.), 2(2007), 1--5.
  • Marty, F., Sur une generalization de la notion de groupe, 8th Congress Math. Scandinaves, Stockholm, (1934), 45--49.
  • Mostafa, S.M., Abd-Elnaby, M.A., Yousef, M.M.M., Fuzzy ideals of KU-algebras, Int. Math. Forum, 63(6)(2011), 3139--3149.
  • Mostafa, S.M., Kareem, F., Davvaz, B., Hyper structure theory applied to KU-algebras, Journal of Hyper Structures, 6(2)(2017), 82--95.
  • Mostafa, S.M., Hameed, A.T., Ghanem, R.A., Hyper structures of KU-algebras: Theorems & fuzzy Applications, submitted.
  • Prabpayak, C., Leerawat, U., On ideals and congruence in KU-algebras, Scientia Magna Journal, 5(1)(2009), 54--57.
  • Prabpayak, C., Leerawat, U., On isomorphisms of KU-algebras, Scientia Magna Journal, 5(3)(2009), 25--31.
  • Yaqoob, N., Mostafa, S.M., Ansari, M. A., On cubic KU-ideals of KU-algebras, ISRN Algebra, (2013) Article ID935905, 10 pages.
  • Zadeh, L.A., Fuzzy sets, Inform. And Control, 8(1965), 338--353.
There are 18 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Samy M. Mostafa

Naim Cagman

Publication Date June 30, 2019
IZ https://izlik.org/JA84DD38KR
Published in Issue Year 2019 Volume: 11 Issue: 1

Cite

APA Mostafa, S. M., & Cagman, N. (2019). Bipolar Fuzzy (T,S)-Norm Hyper KU–Ideals (Sub Algebras). Turkish Journal of Mathematics and Computer Science, 11(1), 29-39. https://izlik.org/JA84DD38KR
AMA 1.Mostafa SM, Cagman N. Bipolar Fuzzy (T,S)-Norm Hyper KU–Ideals (Sub Algebras). TJMCS. 2019;11(1):29-39. https://izlik.org/JA84DD38KR
Chicago Mostafa, Samy M., and Naim Cagman. 2019. “Bipolar Fuzzy (T,S)-Norm Hyper KU–Ideals (Sub Algebras)”. Turkish Journal of Mathematics and Computer Science 11 (1): 29-39. https://izlik.org/JA84DD38KR.
EndNote Mostafa SM, Cagman N (June 1, 2019) Bipolar Fuzzy (T,S)-Norm Hyper KU–Ideals (Sub Algebras). Turkish Journal of Mathematics and Computer Science 11 1 29–39.
IEEE [1]S. M. Mostafa and N. Cagman, “Bipolar Fuzzy (T,S)-Norm Hyper KU–Ideals (Sub Algebras)”, TJMCS, vol. 11, no. 1, pp. 29–39, June 2019, [Online]. Available: https://izlik.org/JA84DD38KR
ISNAD Mostafa, Samy M. - Cagman, Naim. “Bipolar Fuzzy (T,S)-Norm Hyper KU–Ideals (Sub Algebras)”. Turkish Journal of Mathematics and Computer Science 11/1 (June 1, 2019): 29-39. https://izlik.org/JA84DD38KR.
JAMA 1.Mostafa SM, Cagman N. Bipolar Fuzzy (T,S)-Norm Hyper KU–Ideals (Sub Algebras). TJMCS. 2019;11:29–39.
MLA Mostafa, Samy M., and Naim Cagman. “Bipolar Fuzzy (T,S)-Norm Hyper KU–Ideals (Sub Algebras)”. Turkish Journal of Mathematics and Computer Science, vol. 11, no. 1, June 2019, pp. 29-39, https://izlik.org/JA84DD38KR.
Vancouver 1.Mostafa SM, Cagman N. Bipolar Fuzzy (T,S)-Norm Hyper KU–Ideals (Sub Algebras). TJMCS [Internet]. 2019 June 1;11(1):29-3. Available from: https://izlik.org/JA84DD38KR