International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 5, Pages 269-287
doi:10.1155/S0161171201006408
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
Abstract
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.