Science China Information Sciences

, Volume 53, Issue 7, pp 1397–1408 | Cite as

A mathematical model for concept granular computing systems

  • GuoFang Qiu
  • JianMin Ma
  • HongZhi Yang
  • WenXiu Zhang
Research Papers

Abstract

Extent-intent and intent-extent operators are introduced between two complete lattices in this paper and a mathematical model for concept granular computing system is established. We proved that the set of all concepts in this system is a lattice with the greatest element and the least element. This framework includes formal concept lattices from formal contexts, L fuzzy concept lattices from L fuzzy formal contexts and three kinds of variable threshold concept lattices, i.e. the extension and the intension of a concept are a crisp set and a crisp set, a crisp set and a fuzzy set, a fuzzy set and a crisp set, respectively. Finally, some iterative algorithms for constructing concepts are proposed and they are proved to be optimal concepts under some conditions in this system.

Keywords

granular computing formal concept analysis concept lattice mathematical model 

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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • GuoFang Qiu
    • 1
  • JianMin Ma
    • 2
  • HongZhi Yang
    • 3
  • WenXiu Zhang
    • 3
  1. 1.School of ManagementXi’an University of Architecture & TechnologyXi’anChina
  2. 2.Faculty of ScienceChang’an UniversityXi’anChina
  3. 3.Faculty of ScienceXi’an Jiaotong UniversityXi’anChina

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