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

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.