Textural approach to generalized rough sets based on relations

  • Authors:
  • Murat Diker

  • Affiliations:
  • Hacettepe University, Department of Mathematics, 06532 Beytepe, Ankara, Turkey

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2010

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Abstract

This paper presents a discussion on rough set theory from the textural point of view. A texturing is a family of subsets of a given universal set U satisfying certain conditions which are generally basic properties of the power set. The suitable morphisms between texture spaces are given by direlations defined as pairs (r,R) where r is a relation and R is a corelation. It is observed that the presections are natural generalizations for rough sets; more precisely, if (r,R) is a complemented direlation, then the inverse of the relation r (the corelation R) is actually a lower approximation operator (an upper approximation operator).