International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 5, Pages 269-287

On imaginable T-fuzzy subalgebras and imaginable T-fuzzy closed ideals in BCH-algebras

Young Bae Jun1 and Sung Min Hong2

1Department of Mathematics Education, Gyeongsang National University, Chinju 660-701, Korea
2Department of Mathematics, Gyeongsang National University, Chinju 660-701, Korea

Received 9 December 2000

Copyright © 2001 Young Bae Jun and Sung Min Hong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We inquire further into the properties on fuzzy closed ideals. We give a characterization of a fuzzy closed ideal using its level set, and establish some conditions for a fuzzy set to be a fuzzy closed ideal. We describe the fuzzy closed ideal generated by a fuzzy set, and give a characterization of a finite-valued fuzzy closed ideal. Using a t-norm T, we introduce the notion of (imaginable) T-fuzzy subalgebras and (imaginable) T-fuzzy closed ideals, and obtain some related results. We give relations between an imaginable T-fuzzy subalgebra and an imaginable T-fuzzy closed ideal. We discuss the direct product and T-product of T-fuzzy subalgebras. We show that the family of T-fuzzy closed ideals is a completely distributive lattice.