On the structure of generalized rough sets

  • Authors:

  • Michiro Kondo

  • Affiliations:

  • School of Information Environment, Tokyo Denki University, Inzai 270-1382, Japan

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2006

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Abstract

In this paper we consider some fundamental properties of generalized rough sets induced by binary relations on algebras and show that 1.Any reflexive binary relation determines a topology. 2.If @q is a reflexive and symmetric relation on a set X, then O={A@?X|@q"-(A)=A} is a topology such that A is open if and only if it is closed. 3.Conversely, for every topological space (X,O) satisfying the condition that A is open if and only if it is closed, there exists a reflexive and symmetric relation R such that O={A@?X|R"-(A)=A}. 4.Let @q be an equivalence relation on X. For any pseudo @w-closed subset A of X,@q"-(A) is an @w-closed set if and only if @w(x,x,...,x)@?@q"-(A) for any x@?X. Moreover we consider properties of generalized rough sets.