The Construction of Fuzzy Concept Lattices Based on (&thgr;, σ)-Fuzzy Rough Approximation Operators

  • Authors:

  • Yanqing Yao;Jusheng Mi;Zhoujun Li;Bin Xie

  • Affiliations:

  • (Correspd.) (Also working: School of Computer Science and Engineering, Beihang University, Beijing, China and College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, ...;College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, Hebei, China. mijsh@263.net;(Also working: School of Computer Science and Engineering, Beihang University, Beijing, China and Beijing Key Laboratory of Network Technology, Beihang University, Beijing, China) State Key Labora ...;College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, Hebei, China. happyxiebin@126.com

  • Venue:
  • Fundamenta Informaticae - Knowledge Technology
  • Year:
  • 2011

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Abstract

Formal concept analysis and rough set analysis are two complementary approaches for analyzing data. This paper studies approaches to constructing fuzzy concept lattices based on generalized fuzzy rough approximation operators. For a residual implicator &thgr; satisfying &thgr;(a, b) = &thgr;(1 − b, 1 − a) and its dual σ, a pair of (&thgr;, σ)-fuzzy rough approximation operators is defined. We then propose three kinds of fuzzy operators, and examine some of their basic properties. Thus, three complete fuzzy concept lattices can be produced, for which the properties are analogous to those of the classical concept lattices.