Affiliations: State Key Laboratory of Software Development Environment, Beihang University, Beijing, China. yaoyanqing1984@sina.com | College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, Hebei, China. mijsh@263.net | State Key Laboratory of Software Development Environment, Beihang University, Beijing, China. lizj@buaa.edu.cn | College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, Hebei, China. happyxiebin@126.com
Note: [] Address for correspondence: School of Computer Science and Engineering, Beihang University, Beijing 100191, P. R. China and College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, Hebei 050016, P. R. China Also working: School of Computer Science and Engineering, Beihang University, Beijing, China and College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, Hebei, China
Note: [] Also working: School of Computer Science and Engineering, Beihang University, Beijing, China and Beijing Key Laboratory of Network Technology, Beihang University, Beijing, China
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 θ satisfying θ(a, b) = θ(1 − b, 1 − a) and its dual σ, a pair of (θ, 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.
