The algebraic structures of generalized rough set theory

  • Authors:

  • Guilong Liu;William Zhu

  • Affiliations:

  • School of Information Science, Beijing Language and Culture University, Beijing 100083, China;College of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2008

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Abstract

Rough set theory is an important technique for knowledge discovery in databases, and its algebraic structure is part of the foundation of rough set theory. In this paper, we present the structures of the lower and upper approximations based on arbitrary binary relations. Some existing results concerning the interpretation of belief functions in rough set backgrounds are also extended. Based on the concepts of definable sets in rough set theory, two important Boolean subalgebras in the generalized rough sets are investigated. An algorithm to compute atoms for these two Boolean algebras is presented.