On definable concepts of rough set models

In various generalized rough set models, definable concepts are used to approximate other concepts. Based on a unified abstract rough set theory, this paper investigates the mathematical structure of the set of definable concepts in several generalized rough set models such as relation based models, covering based models, and fuzzy based models. It is shown that there exist two kinds of interesting structures for the set of definable concepts, which are often used in rough set models: the complementary structure and the equational structure. In addition, relations between different rough set models are discussed.