Three-way Interval-set Concept Lattice

The concept lattice theory was proposed in 1982 by Wille.R,a German mathematician.It reflects intuitively and succinctly the information hidden in the data set through the dependence of extent and intent and the hierarchical relationship of the concepts.The theory has been widely used in knowledge engineering,data mining,information retrieval,software engineering and other fields.The study of concept lattice theory mainly focuses on the solution of concept,the construction of concept lattice,the decomposition and synthesis of concept lattice and the reduction of concept lattice and so on.The interval-set concept is an effective tool for data analysis in which the available concepts are partly known or undefined.According to a set of evaluation criteria,the three-way decision divides the domain into three disjoint regions,namely positive domain,negative domain and boundary domain.In order to strengthen the analysis of partly known or undefined concepts,this thesis proposes the three-way interval-set concept lattice model.Based on this model,the main results are as follows:(1)The relationships between the interval-set concept lattice and the three-way interval-set concept lattice through the concept are discussed in the viewpoints of algebra and order relations.The necessary and sufficient conditions for constructing the threeway interval-set concept lattice by the interval-set concept lattice are examined,and the corresponding algorithm is further designed.(2)The relationship between the three-way interval-set concept and the classical concept is studied.The necessary and sufficient conditions for the construction of three-way interval-set concept from a classical concept are proved,and the corresponding algorithm is further formulated.(3)In order to simplify the structure of the three-way interval-set concept lattice,methods for obtaining the three-way interval-set attribute reduction are proposed by introducing the discernibility three-way interval-set attribute matrix on the basis of keeping all of the extensions in the three-way interval-set concept lattice.