Generalized infinitive rough sets based on reflexive relations

We associate a binary neighborhood system with a given binary relation, and then re-examine the structure of binary relational rough set model from the viewpoint of binary neighborhood systems. Based on the associated binary neighborhood system, we define an equivalence relation on the universe of discourse by regarding objects of the universe as equivalent if their associated binary neighborhood systems are identical. The induced equivalence relation is interpreted as the indiscernibility relation on the universe. From this view, we propose equivalent form of lower and upper approximations in binary relational rough set model in ways paralleling the corresponding definitions for Pawlak´s lower and upper approximations. In addition, we extend variable precision rough set model to variable precision binary relational rough set model.