Sub - implicative ideals in KU - algebras and their applications in fuzzy theory
OlA WAGIH ABD EL-BASEER;
Abstract
Y. Imai and K. Iseki introduced two classes of abstract algebras: BCK- algebras and BCIalgebras
[18-22]. It is known that the class of BCK-algebras is a proper subclass of the
class of BCI -algebras. In [3, 11, 16, and 17] Q. P. Hu and X. Li introduced a wide class
of abstract algebras: BCH - algebras. They have shown that the class of BCI- algebras is
a proper subclass of the class of BCH- algebras. In[58 ] the authors introduced the notion
of d-algebras, which is another useful generalization of BCK- algebras, and then they
investigated several relations between d-algebras and BCK- algebras as well as some
other interesting relations between d-algebras and oriented digraphs. Y.B. Jun, E. H. Roh
and H. S. Kim[26 ] introduce a new notion, called BH-algebras, which is a generalization
of BCH/ BCI /BCK-algebras. They also defined the notions of ideals in BH-algebras.
Recently J. Neggers and H. S. Kim[ 61 ] introduced the notion of B-algebra, and studied
some of its properties. In 1983, (Y. Komori) [39 ] introduced a notion of BCC-algebras,
and (W. A. Dudek) [15 ] redefined the notion of BCC-algebras by using a dual form of
the ordinary definition in the sense of Y. Komori. In [15 ], (W. A. Dudek and X. H.
Zhang) introduced a notion of BCC-ideals in BCC algebras and described connections
between such ideals and congruences. In 2001, (J.Neggers, S.S.Ahn and H.S.Kim) [ 59]
introduced a new notion, called a Q-algebra and generalized some theorems discussed in
BCI/BCK-algebras. Prabpayak and Leerawat [62, 63] introduced a new algebraic
structure which is called KU-algebra. They gave the concept of homomorphisms of KUalgebras
and investigated some related properties. The concept of a fuzzy set, was
introduced in [74]. O. Xi [72] applied the concept of fuzzy to BCK-algebras. In
[45,47,52 ], studied the fuzzification of BCK-algebra and BCI-algebra. In 2002, Mostafa
Abd-Elnaby and Yousef [55] introduced the notion of fuzzy ideals of KU-algebras and
then they investigated several basic properties which are related to fuzzy KU-ideals. They
described how to deal with the homomorphic image and inverse image of fuzzy KUideals.
They have also proved that the Cartesian product of fuzzy KU-ideals in Cartesian
[18-22]. It is known that the class of BCK-algebras is a proper subclass of the
class of BCI -algebras. In [3, 11, 16, and 17] Q. P. Hu and X. Li introduced a wide class
of abstract algebras: BCH - algebras. They have shown that the class of BCI- algebras is
a proper subclass of the class of BCH- algebras. In[58 ] the authors introduced the notion
of d-algebras, which is another useful generalization of BCK- algebras, and then they
investigated several relations between d-algebras and BCK- algebras as well as some
other interesting relations between d-algebras and oriented digraphs. Y.B. Jun, E. H. Roh
and H. S. Kim[26 ] introduce a new notion, called BH-algebras, which is a generalization
of BCH/ BCI /BCK-algebras. They also defined the notions of ideals in BH-algebras.
Recently J. Neggers and H. S. Kim[ 61 ] introduced the notion of B-algebra, and studied
some of its properties. In 1983, (Y. Komori) [39 ] introduced a notion of BCC-algebras,
and (W. A. Dudek) [15 ] redefined the notion of BCC-algebras by using a dual form of
the ordinary definition in the sense of Y. Komori. In [15 ], (W. A. Dudek and X. H.
Zhang) introduced a notion of BCC-ideals in BCC algebras and described connections
between such ideals and congruences. In 2001, (J.Neggers, S.S.Ahn and H.S.Kim) [ 59]
introduced a new notion, called a Q-algebra and generalized some theorems discussed in
BCI/BCK-algebras. Prabpayak and Leerawat [62, 63] introduced a new algebraic
structure which is called KU-algebra. They gave the concept of homomorphisms of KUalgebras
and investigated some related properties. The concept of a fuzzy set, was
introduced in [74]. O. Xi [72] applied the concept of fuzzy to BCK-algebras. In
[45,47,52 ], studied the fuzzification of BCK-algebra and BCI-algebra. In 2002, Mostafa
Abd-Elnaby and Yousef [55] introduced the notion of fuzzy ideals of KU-algebras and
then they investigated several basic properties which are related to fuzzy KU-ideals. They
described how to deal with the homomorphic image and inverse image of fuzzy KUideals.
They have also proved that the Cartesian product of fuzzy KU-ideals in Cartesian
Other data
| Title | Sub - implicative ideals in KU - algebras and their applications in fuzzy theory | Other Titles | المثاليات المطلقة الجزئية في الجبر كيو و تطبيقاتها في النظريات الفازية . | Authors | OlA WAGIH ABD EL-BASEER | Issue Date | 2018 |
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