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

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.