Some properties of fuzzy positive implicative ideal in BCK-algebras
by
Lele Celestin
Harbin Institute of Technology (China)
Coauthors: Wu Congxing (Harbin Institute of Technology)

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 approach.

In this paper, we use the notion of fuzzy point to study ideal and positive implicative ideal in BCK-algebras, then we clarify the links between the fuzzy point approach, the classical fuzzy approach and the ordinary case.

Clearly, given an ordinary BCK-algebras (X, +, 0) and a classical fuzzy subset A of X, we construct the set (X', +) of all fuzzy points of X and the subset A' of X' and establish the similarity between some properties of A and A'.

Through this similarity, many concepts and conclusion for the ordinary BCK-algebras theory can be directly transfer to those for fuzzy BCK-algebras. Clearly, we give the definition of weak ideal, positive implicative weak ideal and analyze the relation between weak ideal, fuzzy ideal and ordinary ideal in BCK-algebras.

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Date received: February 26, 2000

Copyright © 2000 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 # caee-06.