Journal
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
Volume 52, Issue 2, Pages 231-239Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.ijar.2010.07.010
Keywords
Rough set theory; Generalized rough set; Relation based rough set; Topology
Categories
Funding
- NSF of China [10871229]
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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. (C) 2010 Elsevier Inc. All rights reserved.
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