The Granules Of Formal Concept

Formal Concept was first introduced by the German professor R. Wille in 1982. It is a theory which use the most basic elements of human thinking called "concept" and its hierarchy to investigate, analyze, research in mathematics. It is a branch of theory of lattice. "Granular Computing" was proposed by T.Y.Yao in 1997. It has produced a great influence on various subject areas in the past decade. "Granular Computing" thinking has infiltrated into the area of Formal Concept. And the combination of "Granular Computing" and Formal Concept arouses more and more people's attention. This paper researches on the granules of formal concept. Main contents were as follow:Congruence granule space and its hierarchy. I focuse on the fundamental nature of congruence granule space: the lattice is composed of all congruence granules, and the lattice is composed of all congruence granule space.Tolerance granular space and its hierarchy. I focuse on the fundamental nature of tolerance granule space: the lattice is composed of all tolerance granules, and the lattice is composed of all tolerance granule space.Applications of equivalence granule space. I mainly introduce applications of equivalence granule space in the formal concept. It was applied to decompose and restore the concept lattice. Comparatively, Other methods require quite rigorous preconditions. But this method has no precondition. So it can be applied to the naturally occurring data.