Clustering Compression And Dynamic Update Method Of Attribute-induced Three-Way Concept Lattices

Three-way concept analysis is an important theory for knowledge representation and knowledge discovery which is combining three-way decision with formal concept analysis.It is the core data analysis tools to attribute-induced three-way concept lattices and objectinduced three-way concept lattices in three concept analysis.They contain more information than classical concept lattices.So,the time complexity and space occupation are high for constructing three-way concept lattice.Nowadays,a large number of fields have to face massive,multidimensional,fuzzy and dynamic complex data with the advent of the era of big data.It will consume a lot of time and space resources to process the kind of complex data by three-way concept analysis.It can save a lot of time and space resources,reduce the complexity of system calculation,and facilitate decision-makers to make decisions more clearly by the cluster compression and dynamic update of three-way concepts.At the same time,the paper defines the distance formula of the fuzzy concepts,and uses the improved K-Means clustering and t-delete transformation to cluster compression for the fuzzy concept lattice based on the fuzzy set theory and formal concept analysis.Also,we get the concept similarity through three-way concept information systems based on three-way decision which is combining negative domain,boundary domain and positive domain.It is proposed to compress three-way concept lattice by an improved K-Modes clustering algorithm and kdelete transformation.Finally,it is used to obtain the updating way of three-way granular concepts by the incremental learning technology and the idea of granular computing in the context of dynamic formal concept.The main innovations of this paper are described as follows:1.The paper introduces the cardinal number of fuzzy concepts and defines the distance formula of fuzzy concepts based on the fuzzy formal context.The distance formula is used to cluster the fuzzy concepts in order to establish the cluster compression model of the fuzzy concept lattice,and its basic properties is studied.In addition,we study the relationship between the compression effect,the time consumption,the number of clusters and the size of the data set.2.The fuzzy formal context can be transformed into classical formal context by threshold.And the distance between two objects is defined by the characteristics of three-way decision and the different domains of two concepts.Then,we can get the similarity and difference between the two attribute-induced three-way concepts.In the meantime,we use the principle of minimum distance and the improved method of updating cluster center to compress attribute induced three-way concept.The average radius is used to verify the superiority of the improved clustering compression method.Finally,we study the relationship between the original concept lattice and the compressed concept lattice.3.In the classical formal context,attribute-induced three-way concepts is variation with the objects or attributes.In this paper,it is proposed to dynamic updating method of attributeinduced three-way concept and compared with the static updating method.