Rough approximations via ideal on a complete completely distributive lattice

The rough approximations on a complete completely distributive lattice L based on binary relation were introduced by Zhou and Hu (Inf Sci 269:378–387, 2014 ), where the binary relation was defined on the set of non-zero join-irreducible elements. This paper extends Zhou and Hu’s rough set model by defining new approximation operators via ideal. When I is the least ideal of L and R is a reflexive binary relation, these two approximations coincide. We present the essential properties of new approximations and also discuss how the new one relates to the old one. Finally, the topological and lattice structures of the approximations are given.