Multigranulation rough set theory over two universes

摘要: Recently, a multigranulation rough set MGRS has become new direction in theory, which is based on multiple binary relations the universe of discourse. The existing literature about assumption same universe. In reality, however, good deal practical decision making may relate to possibility two or more different universes. this paper, we consider approximation given concept over universes with respect space formed by mappings universes, i.e., model. We respectively define optimistic set, pessimistic and variable precision each can be appropriate real-world decision-making problem management science. Then several important properties these models are discussed detail. Also, relationship between investigated. At last, entropy granularity mapping defined, then give an approach uncertainty measurement for model provides new, effective problems