First,we reviewed the definitions of lattice implication algebras,lattice implication subalgebras,and LI-ideals,and provided an equivalent definition of LI-ideal. Then we investigated some properties of lattice implication subalgebra and LI-ideal,and found the least lattice implication subalgebra. Finally,the relation between lattice implication subalgebra and LI-ideal is presented. It is proved that no LI-ideals are non-trivial lattice implication subalgebras.
The concepts of interval valued (∈,∈∨q)-fuzzy Boolean, MV - and G- filters in a MTL-algebra are introduced. The properties of these generalized fuzzy filters are studied and in particular, the relationships between these fuzzy filters in an MTL-algebra are investigated.
