Research On Matrix Approach To Attribute Reduction In Concept Lattice Model

The formal concept analysis theory,proposed by Wille in 1982,has become an effective tool for knowledge discovery,and has been widely applied in machine learning,pattern recognition and data mining and so on.Many extended models have been proposed for developing the application scope of classical concept lattice model,including fuzzy concept lattices,variable threshold concept lattices,multigranularity concept lattices and so on.Different patterns can deal with different problems,including but not limited to concept knowledge acquisition,attribute reduction,decision rules and so on.From the perspective of matrix theory,the research of attribute reduction can not only obtain more concise knowledge,but also has high time efficiency,which is conducive to decision analysis.Therefore,this article attempts to combine Boolean matrix and three-way decision with classical concept lattice model and fuzzy concept lattice model.Then we discuss their structure properties,and investigate the matrix approach to attribute reduction.This paper mainly studies the following aspects.The first chapter mainly introduces the corresponding research background and current situation.Then we recommend the fundamental research work and preliminaries.In the second chapter,based on granular reduction proposed by Wu et al.,but the matrix characteristics of formal context is not considered.Based on the operational properties of matrix,the extensionx9((9))of the object concept is represented,and the properties of object granular matrix are discussed.Subsequently,we present an attribute reduction theory to preserve the object granules unchanged.With respect to formal decision context,the measurement of similarity between attributes via Boolean matrix is characterized.Meanwhile,we design a heuristic attribute-reduction algorithm.Then the proposed method is compared with the existing algorithms through UCI data experiments to explain the effectiveness and efficiency of the algorithm.In the third chapter,in order to better and comprehensive use of the positive and negative information of formal fuzzy context,we apply the idea of three-way decision theory to one-sided fuzzy concept lattice and formulate the notions of one-sided fuzzy three-way concept lattices.Afterwards,we define the partial order relation,supremum and infimum with one-sided fuzzy three-way concepts,and prove that all one-sided fuzzy three-way concepts form a complete lattice.Then the relationships between the two models and the existing models are described.Furthermore,the attribute(object)discernibility matrix is proposed to simplify the approach of attribute reduction.