Rough approximations on a complete completely distributive lattice with applications to generalized rough sets

  • Authors:

  • Chen Degang;Zhang Wenxiu;Daniel Yeung;E. C. C. Tsang

  • Affiliations:

  • Department of Mathematics and Physics, North China Electric Power University, 102206 Beijing, China;Institute for Information and System Science,Xi'an Jiaotong University, Xi'an 710049, China;Department of Computing, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong 852, China;Department of Computing, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong 852, China

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

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Abstract

The generalizations of rough sets considered with respect to similarity relation, covers and fuzzy relations, are main research topics of rough set theory. However, these generalizations have shown less connection among each other and have not been brought into a unified framework, which has limited the in-depth research and application of rough set theory. In this paper the complete completely distributive (CCD) lattice is selected as the mathematical foundation on which definitions of lower and upper approximations that form the basic concepts of rough set theory are proposed. These definitions result from the concept of cover introduced on a CCD lattice and improve the approximations of the existing crisp generalizations of rough sets with respect to similarity relation and covers. When T-similarity relation is considered, the existing fuzzy rough sets are the special cases of our proposed approximations on a CCD lattice. Thus these generalizations of rough sets are brought into a unified framework, and a wider mathematical foundation for rough set theory is established.