Computer Science ›› 2022, Vol. 49 ›› Issue (3): 263-268.doi: 10.11896/jsjkx.210100204

• Artificial Intelligence • Previous Articles     Next Articles

On Topological Properties of Generalized Rough Approximation Operators

LI Yan-yan, QIN Ke-yun   

  1. College of Mathematics,Southwest Jiaotong University,Chengdu 611756,China
  • Received:2021-01-26 Revised:2021-06-10 Online:2022-03-15 Published:2022-03-15
  • About author:LI Yan-yan,born in 1995,postgra-duate.Her main research interests include rough set theory and formal concept analysis.
    QIN Ke-yun,born in 1962,Ph.D,professor,Ph.D supervisor.His main research interests include rough set theory,formal concept analysis and fuzzy logic.
  • Supported by:
    National Natural Science Foundation of China(61976130).

Abstract: Rough set theory is a mathematical tool for dealing with uncertain information.The core notions of rough set theory is approximation operators of approximation spaces.Pawlak approximation operators are established by using equivalence relations on the universe.They are extended to generalized rough approximation operators based on arbitrary binary relations.The topolo-gical structures of approximation operators are important topics in rough set theory.This paper is devoted to the study of topological properties of generalized rough approximation operators induced by arbitrary binary relations.Four types of topologies induced by generalized approximation operators based on granules and subsystems are presented and the relationships among these four types of topologies are discussed.The bases of the topologies induced by generalized approximation operators based on granules are presented by the right-neighborhood systems for objects,and the normality and regularity for related topologies are investigated.By analyzing the properties of the generalized upper approximation operators based on the subsystem,it is proved that the topologies induced by the subsystem-based generalized upper approximation operators can be transformed into the topologies induced by the generalized lower approximation operators based on the objects.

Key words: Generalized rough approximation operator, Granules, Subsystems, Topology

CLC Number: 

  • TP182
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