More on fuzzy lattices

In this paper, the concept of an (∈,∈∨qk)(∈,∈∨qk)-fuzzy sublattice (ideal, filter) and (∈¯,∈¯∨q¯k)-fuzzy sublattice (ideal, filter) in a lattice is introduced, which is a generalization of the concept as given by Davvaz and Kazancı(2011) [18]. Characterizations for an (∈,∈∨qk)(∈,∈∨qk)-fuzzy sublattice (ideal, filter) and (∈¯,∈¯∨q¯k)-fuzzy sublattice (ideal, filter) are provided. Different classes of lattices are characterized by the properties of these fuzzy sublattices (ideals, filters). Using the notions of a fuzzy sublattice (ideal, filter) with thresholds, characterization of a fuzzy sublattice (ideal, filter), an (∈,∈∨qk)(∈,∈∨qk)-fuzzy sublattice (ideal, filter) and (∈¯,∈¯∨q¯k)-fuzzy sublattice (ideal, filter) are discussed.