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Definition (1.1 ). A BCI-algebra is an algebra (X,*,0) of type (2,0) , where X is nonempty set, * is a binary operation and 0 is a constant , satisfying the following axioms: for all x, y, z X: 1. ((x *y) * (x * z)) * (z * y) = 0,. 2. (x * (x * y)) * y = 0,. 3. x * x = 0,. 4. x * y =0 and y * x = 0 imply x = y,. Definition (1.2 ). 2. A BCK-algebra is a
2478/v10037-007-0001-z. Several Classes of BCI-algebras and their Properties. Yuzhong Ding. Qingdao University of Science and Technology. China. Summary. I have formalized the BCI-algebras closely following the book. [6], sections 1.1 to 1.3, 1.6, 2.1 to 2.3, and 2.7. In this article the general theory of BCI-algebras and
Logic algebras are the algebraic foundation of reasoning mechanism in many fields such as computer sciences, information sciences, cybernetics and artifi- cial intelligence. In 1966, Imai and Iseki [8, 9] introduced the notions, called. BCK-algebras and BCI-algebras. These notions are originated from two dif- ferent ways:
19 Dec 2017 Full-text (PDF) | We introduce the notion of t -derivation of a BCI-algebra and investigate related properties. Moreover, we study t -derivations in a p -semisimple BCI-algebra and establish some results on t -derivations in a p -semisimple BCI-algebra.
20 Apr 2012 The notion of BCK-algebra was proposed by Imai and Iseki in 1966 1 . In the same year,. Iseki introduced the notion of a BCI-algebra 2 , which is a generalization of a BCK-algebra. A series of interesting notions concerning BCI-algebras were introduced and studied, several papers have been written on
20 Dec 2017 Full-text (PDF) | We associate a graph to any subset Y of a BCI-algebra X and denote it by G(Y). Then we find the set of all connected components of G(X) and verify the relation between X and G(X), when X is commutative BCI-algebra or G(X) is complete graph or n-star graph. Finally, we attempt to
15 Dec 2013 Abstract. We introduce more generalizations of BCI, BCK and of Hilbert algebras, with proper examples, and show the hierarchies existing between all these algebras, old and new ones. Namely, we found thirty one new generalizations of BCI and BCK algebras and twenty generalizations of Hilbert
Malaysian Mathematical. Sciences Society math.usm.my/bulletin. Bull. Malays. Math. Sci. Soc. (2) 32(2) (2009), 119–130. Generalized Fuzzy Ideals of BCI-Algebras. 1. Jianming Zhan and. 2. Young Bae Jun. 1Department of Mathematics. Hubei Institute for Nationalities. Enshi, Hubei Province, 445000, P. R. China.
The notion of K-algebras on a group (G, ·) was first introduced by K. H. Dar and M. Akram in [1, 2] as a non-associative and non-commutative algebraic structure. A K-algebra was built on the group G(briefly, K(G)-algebra) by using the induced binary operation ? on (G, ·). Recently, K. H. Dar and M. Akram have proved that a
BCI-algebras with Condition (S) and their Properties. Tao Sun. Qingdao University of Science and Technology. China. Junjie Zhao. Qingdao University of Science and Technology. China. Xiquan Liang. Qingdao University of Science and Technology. China. Summary. In this article we will first investigate the elementary pro-.
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