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Topology vs generalized rough sets
Authors:Zhi PeiDaowu Pei  Li Zheng
Institution:a Department of Industrial Engineering, Tsinghua University, Beijing 100084, China
b Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, China
Abstract:This paper investigates the relationship between topology and generalized rough sets induced by binary relations. Some known results regarding the relation based rough sets are reviewed, and some new results are given. Particularly, the relationship between different topologies corresponding to the same rough set model is examined. These generalized rough sets are induced by inverse serial relations, reflexive relations and pre-order relations, respectively. We point that inverse serial relations are weakest relations which can induce topological spaces, and that different relation based generalized rough set models will induce different topological spaces. We proved that two known topologies corresponding to reflexive relation based rough set model given recently are different, and gave a condition under which the both are the same topology.
Keywords:Rough set theory  Generalized rough set  Relation based rough set  Topology
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