International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 1, Pages 45-52
doi:10.1155/S0161171201006214

Some operations on lattice implication algebras

E. H. Roh,1 S. Y. Kim,1 Y. Xu,2 and Young Bae Jun3

1Department of Mathematics Education, Chinju National University of Education, Chinju 660-756, Korea
2Department of Applied Mathematics, Southwest Jiaotong University, Sichuan, Chengdu 610031, China
3Department of Mathematics Education, Gyeongsang National University, Chinju 660-701, Korea

Received 16 November 2000

Copyright © 2001 E. H. Roh et al. 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.

Abstract

We introduce the concept of a ⊗-closed set and a ⊗-homomorphism in lattice implication algebras, and we discuss some of their properties. Next, we introduce the fuzzy implicative filter and obtain equivalent conditions. Finally, we discuss the operation ⊗, fuzzy filters and fuzzy implicative filters.