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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

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

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 Articles
Authors

Samy M. Mostafa

Naim Cagman

Publication Date June 30, 2019
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.
AMA Mostafa SM, Cagman N. Bipolar Fuzzy (T,S)-Norm Hyper KU–Ideals (Sub Algebras). TJMCS. June 2019;11(1):29-39.
Chicago Mostafa, Samy M., and Naim Cagman. “Bipolar Fuzzy (T,S)-Norm Hyper KU–Ideals (Sub Algebras)”. Turkish Journal of Mathematics and Computer Science 11, no. 1 (June 2019): 29-39.
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 S. M. Mostafa and N. Cagman, “Bipolar Fuzzy (T,S)-Norm Hyper KU–Ideals (Sub Algebras)”, TJMCS, vol. 11, no. 1, pp. 29–39, 2019.
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 2019), 29-39.
JAMA 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, 2019, pp. 29-39.
Vancouver Mostafa SM, Cagman N. Bipolar Fuzzy (T,S)-Norm Hyper KU–Ideals (Sub Algebras). TJMCS. 2019;11(1):29-3.