Computer Science

Computer Science ›› 2023, Vol. 50 ›› Issue (2): 173-177.doi: 10.11896/jsjkx.211100054

• Database & Big Data & Data Science • Previous Articles     Next Articles

Topological Properties of Generalized Rough Approximation Operators Based on Objects

LI Yanyan, QIN Keyun   

  1. College of Mathematics,Southwest Jiaotong University,Chengdu 611756,China
  • Received:2021-11-04 Revised:2022-04-01 Online:2023-02-15 Published:2023-02-22
  • Supported by:
    National Natural Science Foundation of China(61976130)

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Abstract: Rough set theory is a mathematical tool to deal with uncertain problems.The core notion of rough set theory is appro-ximation operators.Pawlak approximation operators based on equivalence relations cab be extended to generalized rough approximation operators based on arbitrary binary relations.The topological structures of approximation operators are important topics in rough set theory.This paper is devoted to the study of topological properties of object-based generalized rough approximation operators.It is proved that the sufficient condition for all definable subsets in a generalized approximation space to form a topology is also its necessary condition.The regularity and normality of this topology are studied.The equivalent conditions for the same topology generated by the serial binary relation and its transitive closure are given.The relationship between this topology and the topology induced by the object-based generalized rough approximation operator under any binary relation is discussed.

Key words: Serial binary relation, Object-based generalized rough approximation operator, Topology

CLC Number: 

  • TP182
[1]PAWLAK Z.Rough sets[J].International Journal of Computer &Information Sciences,1982,11:341-356.
[2]PAWLAK Z.Rough Sets:Theoretical Aspects of Reasoningabout Data [M].Kluwer Academic Publishers,Dordrecht & Boston,1991.
[3]POLKOWSKI L.Rough Sets[M].Heidelberg:Springer,Physica-Verlag,2002.
[4]YAO Y Y.Constructive and algebraic methods of the theory of rough sets [J].Information Sciences,1998,109(1):21-47.
[5]MI J S,ZHANG W X.An axiomatic characterization of a fuzzy generalization of rough sets [J].Information Sciences,2003,160(1):235-249.
[6]PAWLAK Z.Rough set approach to Knowledge-based decision [J].European Journal of Operational Research,1997,99:48-57.
[7]POMEROL J C.Artificial intelligence and human decision ma-king [J].European Journal of Operational Research,1997,99(1):3-25.
[8]WANG G Y.Rough set theory and knowledge acquisition [M].Xi'an:Xi'an Jiaotong University Press,2001.
[9]LIANG J Y,WANG J H,QIAN Y H.A new measure of uncertainty based on knowledge granulation for rough sets [J].Information Sciences,2008,179(4):458-470.
[10]YAO Y Y.Relational interpretations of neighborhood operators and rough set approximation operators[J].Information Sciences,1998,111(1):239-259.
[11]ZHANG W X,WU W Z,LIANG J Y,et al.Rough set theory and method [M].Beijing:Science Press,2001.
[12]LIU G L,ZHU K.The relationship among three types of rough approximation pairs [J].Knowledge-Based Systems,2014,60:28-34.
[13]KELLY J L.General Topology [M].Graduate Texts in Mathematics.New York:Springer-Verlag,1955:0072-5285.
[14]KONDO M.On the structure of generalizeed rough sets [J].Information Science,2006,176(5):589-600.
[15]QIN K Y,YANG J L,ZHENG P.Generalized rough sets based on reflexive and transitive relations [J].Information Sciences,2008,178(21):4138-4141.
[16]YAO Y Y.Two views of the theory of rough sets in finite universes [J].International Journal of Approximate Reasoning,1996,15:291-317.
[17]ZHANG Y L,LI J J,LI C Q.Topological structure of relation-based generalized rough sets [J].Fundamenta Informaticae,2016,147(4):477-491.
[18]WU H S,LIU G L.The relationships between topologies and generalized rough sets [J].International Journal of Approximate Reasoning,2020,119:313-324.
[19]YU H,ZHAN W R.On the topological properties of generalized rough sets [J].Information Sciences,2014,263:141-152.
[20]ZHANG H P,YAO O Y,WANG Z D.Note on “generalized rough sets based on reflexive and transitive relations” [J].Information Sciences,2009,179(4):471-473.
[21]YANG L Y,XU L S.Topological properties of generalized approximation spaces [J].Information Sciences,2011,181(17):3570-3580.
[22]LIU G L.The Axiomization of the Rough Sets Upper Approximation Operations [J].Fundamenta Informaticae,2006,69:331-342.
[23]GALTON A.A generalized topological view of motion in discrete space [J].Theoretical Computer Science,2003,305:111-134.
[24]ALLAM A,BAKEIR M,TABL E.Some methods for generating topologies by relations[J].Bulletin of the Malaysian Mathematical Sciences Society,2008,31(1):35-45.
[25]LI Z W,XIE T S,LI Q G.Topological structure of generalized rough sets[J].Computers and Mathematics with Applications,2012,63:1066-1071.
[26]PEI Z,PEI D W,ZHENG L.Topology vs generalized rough sets [J].International Journal of Approximate Reasoning,2011,52:231-239.
[27]LIU G L.A comparison of two types of generalized rough sets[C]//IEEE International Conference on Granular Computing.IEEE Computer Society,2012:423-426.
[28]GRABOWSKI A.Topological interpretation of rough sets [J].Formalized Mathematics,2014,22(1):89-97.
[29]ZHAO Z G.On some types of covering rough sets from topological points of view [J].International Journal of Approximate Reasoning,2016,68:1-14.
[30]ZHANG Y L,LI C Q.Topological properties of a pair of relation-based approximation operators [J].Filomat,2017,31(19):6175-6183.
[31]LIU G L,ZHENG H,ZOU J Y.Relations arising from coverings and their topological structures [J].International Journal of Approximate Reasoning,2017,80:348-358.
[32]QIU J,LI L,MA Z M,et al.A note on the relationships between generalized rough sets and topologies [J].International Journal of Approximate Reasoning,2021,130:292-296.
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