Fuzzy Sub Implicative Ideals of KU-Algebras
Yıl 2018,
Sayı: 23, 1 - 12, 01.06.2018
Samy Mohammed Mostafa
,
Ola Wageeh Baseer
Öz
We consider the fuzzification of sub-implicative (sub-commutative) ideals in KU-algebras, and
investigate some related properties. We give conditions for a fuzzy ideal to be a fuzzy sub-implicative (subcommutative)
ideal. We show that any fuzzy sub-implicative (sub-commutative) ideal is a fuzzy ideal, but
the converse is not true. Using a level set of a fuzzy set in a KU-algebra; we give a characterization of a fuzzy
sub-implicative (sub-commutative) ideal.
Kaynakça
- [1] Hong S.M. and Jun Y.B. , Fuzzy and level subalgebras of BCK (BCI) algebras Pusan
Kyongnam Math. J. (Presently , East Asain Math . J.) , 7(2) (1991) , 185-190 .
- [2] Iseki. K. On BCI-algebras. Math. Sem. Notes 8 (1980) 125 – 130
- [3] Jun Y. B., Hong A.M.T, Kim A. T. and Song S. Z., Fuzzy ideals and fuzzy subalgebras
of BCK-algebras , J.fuzzy Math ,7(2) (1999) , 411-418 .
- [4] Liu Y. L, Meng J. and Xu Y., BCI-implicative ideals of BCI-algebras, Information
Sciences (2007) 1 - 10.
- [5] Liu Y. L., S. Y. Liu S. Y., Meng J. FSI-ideals and FSC-ideals of BCl-algebras Bull.
Korean Math. Soc. 41 (2004), No.1, pp. 167-179
- [6] Senapati, T. and Shum K. P., Atanassov’s intuitionistic fuzzy bi-normed KUsubalgebrs
of a KU-algebra, Missouri J. Math. Sci., Volume 29, Issue 1 (2017),
92-112.
- [7] Senapati T.,T-fuzzy KU-ideals of KU-algebras, June 2018, Volume 29, Issue 3–4,
pp 591–600 Afrika Matematika.
- [8] Mostafa S. M., Abd-Elnaby M. and Yousef M. M., Fuzzy ideals of KU-Algebras,
International Math.Forum, Vol.6, (2011), no.63, 3139-3149.
- [9] Mostafa S. M., Kareem F. F., N-Fold Commutative KU-Algebras International Journal
of Algebra, Vol. 8, 2014, no. 6, 267 – 275
- [10] Mostafa S. M., Omar R. A. K, Abd El- Baseer, O. W., Sub implicative ideals of KUAlgebras,
International Journal of Modern Science and Technology Vol. 2, No. 5,
2017. Page 223-227.
- [11] Radwan A. E., Mostafa S. M., Ibrahem F. A. & Kareem F. F., Topology spectrum of
a KU-Algebra. Journal of New Theory 5 (2015) Year: 2015, Number: 8, Pages: 78-91
- [12] Prabpayak C. and Leerawat U., On ideals and congruence in KU-algebras, Scientia
Magna Journal, Vol. 5(2009), No.1, 54-57.
- [13] Prabpayak C. and Leerawat U., On isomorphisms of KU-algebras, Scientia Magna
Journal, 5(2009), no. 3, 25-31
- [14] Xi O. G., Fuzzy BCK-algebras, Math. Japan, 36 (1991) 935-942.
- [15] Zadeh L. A., Fuzzy sets, Inform. and Control, 8 (1965) 338-353.
Yıl 2018,
Sayı: 23, 1 - 12, 01.06.2018
Samy Mohammed Mostafa
,
Ola Wageeh Baseer
Kaynakça
- [1] Hong S.M. and Jun Y.B. , Fuzzy and level subalgebras of BCK (BCI) algebras Pusan
Kyongnam Math. J. (Presently , East Asain Math . J.) , 7(2) (1991) , 185-190 .
- [2] Iseki. K. On BCI-algebras. Math. Sem. Notes 8 (1980) 125 – 130
- [3] Jun Y. B., Hong A.M.T, Kim A. T. and Song S. Z., Fuzzy ideals and fuzzy subalgebras
of BCK-algebras , J.fuzzy Math ,7(2) (1999) , 411-418 .
- [4] Liu Y. L, Meng J. and Xu Y., BCI-implicative ideals of BCI-algebras, Information
Sciences (2007) 1 - 10.
- [5] Liu Y. L., S. Y. Liu S. Y., Meng J. FSI-ideals and FSC-ideals of BCl-algebras Bull.
Korean Math. Soc. 41 (2004), No.1, pp. 167-179
- [6] Senapati, T. and Shum K. P., Atanassov’s intuitionistic fuzzy bi-normed KUsubalgebrs
of a KU-algebra, Missouri J. Math. Sci., Volume 29, Issue 1 (2017),
92-112.
- [7] Senapati T.,T-fuzzy KU-ideals of KU-algebras, June 2018, Volume 29, Issue 3–4,
pp 591–600 Afrika Matematika.
- [8] Mostafa S. M., Abd-Elnaby M. and Yousef M. M., Fuzzy ideals of KU-Algebras,
International Math.Forum, Vol.6, (2011), no.63, 3139-3149.
- [9] Mostafa S. M., Kareem F. F., N-Fold Commutative KU-Algebras International Journal
of Algebra, Vol. 8, 2014, no. 6, 267 – 275
- [10] Mostafa S. M., Omar R. A. K, Abd El- Baseer, O. W., Sub implicative ideals of KUAlgebras,
International Journal of Modern Science and Technology Vol. 2, No. 5,
2017. Page 223-227.
- [11] Radwan A. E., Mostafa S. M., Ibrahem F. A. & Kareem F. F., Topology spectrum of
a KU-Algebra. Journal of New Theory 5 (2015) Year: 2015, Number: 8, Pages: 78-91
- [12] Prabpayak C. and Leerawat U., On ideals and congruence in KU-algebras, Scientia
Magna Journal, Vol. 5(2009), No.1, 54-57.
- [13] Prabpayak C. and Leerawat U., On isomorphisms of KU-algebras, Scientia Magna
Journal, 5(2009), no. 3, 25-31
- [14] Xi O. G., Fuzzy BCK-algebras, Math. Japan, 36 (1991) 935-942.
- [15] Zadeh L. A., Fuzzy sets, Inform. and Control, 8 (1965) 338-353.