On n-fold ideals in BCK-algebras based on t-norme and fuzzy point
by
Celestin Lele
Dept of Mathematics, Faculty of science, University of Yaounde I, Box 812 Cameroon

The concept of fuzzy sets was first introduced by Zadeh [9] . From that time, the theory of fuzzy sets has been developed in many directions and found applications in a wide variety of fields . It application to various mathematical contexts has given rise to what is now commonly called fuzzy mathematics. Fuzzy algebras is an important branch of fuzzy mathematics, many researchers [6] have studied some algebraic structures such as fuzzy semigroups, fuzzy groups, fuzzy rings, fuzzy ideals, fuzzy modules, fuzzy vectors spaces, fuzzy category and so on. In 1991, Xi [7] applied the concept of fuzzy sets to BCI, BCK, MV-algebras . A BCI-algebra which was introduced by Iseki and Tanaka[2] is an important class of logical algebras which originated from two different ways, One of the motivation is based on the set theory and non -classical prepositional calculus, in other ways, a BCI-algebra arose from algebra of non- classical logic as Boolean algebra arose from classical logic. One of the main problem in fuzzy mathematics is how to carry out the ordinary concepts to the fuzzy case. The difficulty lies in how to pick out the rational generalization from the large number of available approaches. It is worth noting that fuzzy ideal is different from ordinary ideal in the sense that one can not say which BCK-algebra element belongs to the fuzzy ideal under consideration and which one does not.

In this paper, using the concept of fuzzy point, we develop a general theory of fuzzy ideals in BCK-algebra with respect to a t-norm T which includes many known concepts and results as its special cases.

Keywords: BCK-algebra, fuzzy point, fuzzy n-fold ideals,t-norm. REFERENCES 1.J.Meng, Y.B.Jun and H.S.Kim, Fuzzy Implicative Ideals in BCK-Algebras, Fuzzy sets and systems 89(1997)243-24 2. K. Iseki and S. Tanaka , An Introduction to the Theory of BCK -algebra, Math. Japon, 23,(1978) 1-26 3- Y. B. Jun and C-LELE , Fuzzy point BCK/BCI-algebras, The Journal of Algebra and its Application. ( accepted) 4- C.LELE, C.Wu, P. Weke, T . Mamadou and G. Edward Njock, Fuzzy Ideals and Weak Ideals in BCK-algebras Math. Japonica 4(2001) ,599-612 5. C.LELE , Imaginable Weak ideals in BCK –algebras with respect to a t-norm, ( Submitted) 6. J. N. Mordeson and D.S. Malik, Fuzzy Commutative Algebra , Creighton University, World Scientific, Singapore, December 1998 7.O.G Xi, Fuzzy BCK-algebras, Math. Japonica 36, (1991), 935-942 8.Yisheng Huang and Zhaomu, On Ideals in BCK-Algebras , Math. Japonica 50, (1999), 211-226 9. L. A. Zadeh, Fuzzy sets, Inform. And Control, 8,(1965)338-353

Date received: January 28, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cake-23.