Reduction Associated With Grid-based Concept Lattice Theory And Methods

Formal Concept Analysis(FCA), proposed by R Wille in 1982, is a method for finding, ordering and displaying of concepts. Concept lattice theory is the core of FCA whose basic notions are formal context and formal concept. The problem related to the attribute reduction of concept lattice proposed by W X Zhang in 2005 has been intensively investigated by several authors completely and become one meaningful problem of FCA.For a classical formal context, its associated lattice is composed of the vectors 0 and 1. The associated lattice not only simplifies the process of attribute reduction, but also reduces the space complexity and time complexity. The attribute reduction of concept lattice with its associated lattice is very significant.The main results in the thesis are summarized as follows:1. The relation between the concept lattice and its associated lattice is derived.2. Based on the isomorphism between the concept lattice and its associated lattice, the reduction theory of associated lattice is investigated. Afterwards, the relation between the reduct vector of associated lattice and the reduct set of concept lattice is investigated. This paper proposes a novel method of reducing concept lattice by virtue of its associated lattice. Essentially, the attribute reduction method in this thesis concerns with the intent of concept lattice and the process of building the concept lattice. The attribute reduction is described by corresponding vectors. Furthermore, the existing theories of attribute reduction have been investigated via the extent and the intent of concept lattice.