On the topological properties of generalized rough sets

  • Authors:

  • Hai Yu;Wan-Rong Zhan

  • Affiliations:

  • -;-

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2014

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Abstract

In this paper, we consider some topological properties of generalized rough sets induced by binary relations and show that1.Any serial binary relation can induce a topology. 2.Let R be a binary relation on a universe U. t(R) and e(R) denote the transitive closure and the equivalence closure of R, respectively. If R is a reflexive relation on U, then R and t(R) induce the same topology, i.e. T(R)=T(t(R)). The interior and closure operators of the topology T(R) induced by R are the lower and upper approximation operators t(R) and t(R)@?, respectively. Moreover, R(T(R))=t(R), where R(T(R)) is the relation induced by the topology T(R). 3.When R is a reflexive and symmetric relation, R and e(R) induce the same topology, i.e. T(R)=T(e(R)). The interior and closure operators of the topology T(R) induced by R are the lower and upper approximation operators e(R) and e(R)@?, respectively. Moreover, R(T(R))=e(R). 4.Based on the above conclusions, the notion of topological reduction of incomplete information systems is proposed, and characterizations of reduction of consistent incomplete decision tables are obtained.