Samy M. MOSTAFA, NAİM ÇAĞMAN

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

In this paper, the concepts of (σ, τ)- 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.

PDF

___

[1] 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.

[2] 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.

[3] Jun Y.B., Xin, X.L., Fuzzy hyper BCK-ideals of hyper BCK -algebras, Scientiae Mathematicae Japonicae Online, 4(2001), 415–422.

[4] 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.

[5] 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.

[6] Jun, Y.B., Xin, X.L., Fuzzy hyper BCK-ideals of hyper BCK -algebras, Sci. Math. Jpn., 53(2)(2001), 353–360.

[7] 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.

[8] Lee, K.M., Bipolar-valued fuzzy sets and their operations, Proc. Int. Conf. on Intelligent Technologies, Bangkok, Thailand, (2000), 307–312.

[9] 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.

[10] 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. [11] Marty, F., Sur une generalization de la notion de groupe, 8th Congress Math. Scandinaves, Stockholm, (1934), 45–49.

[12] Mostafa, S.M., Abd-Elnaby, M.A., Yousef, M.M.M., Fuzzy ideals of KU-algebras, Int. Math. Forum, 63(6)(2011), 3139–3149.

[13] Mostafa, S.M., Kareem, F., Davvaz, B., Hyper structure theory applied to KU-algebras, Journal of Hyper Structures, 6(2)(2017), 82–95.

[14] Mostafa, S.M., Hameed, A.T., Ghanem, R.A., Hyper structures of KU-algebras: Theorems & fuzzy Applications, submitted.

[15] Prabpayak, C., Leerawat, U., On ideals and congruence in KU-algebras, Scientia Magna Journal, 5(1)(2009), 54–57.

[16] Prabpayak, C., Leerawat, U., On isomorphisms of KU-algebras, Scientia Magna Journal, 5(3)(2009), 25–31.

[17] Yaqoob, N., Mostafa, S.M., Ansari, M. A., On cubic KU-ideals of KU-algebras, ISRN Algebra, (2013) Article ID935905, 10 pages.

[18] Zadeh, L.A., Fuzzy sets, Inform. And Control, 8(1965), 338–353.