“…The mathematical object L can be selected such as distributive lattices, Boolean algebras and residuated lattices to the purposes. Research on L-fuzzy approximation spaces is one of the hot fields of rough set theory, and many papers have been published so far [3,7,8,13]. Since most of the proofs in such papers are element-based, it is a tedious work to check the conditions of the definitions one by one, and they are relatively long proofs.…”