Formal concept analysis,proposed by Wille in 1982,is a theory which gives the mathematical form of concepts and their hierarchy structure and shows how to acquire knowledge from the concepts.As an efficient knowledge discovery tool,formal concept analysis has been applied in computer network,machine learning,analysis of traditional Chinese medicine,decision analysis and expert system.Formal context and formal concept are two basic notions in formal concept analysis,and these two notions are foundation for acquiring knowledge.Different contexts can be used to deal with different problems,and different concepts can reflect different kinds of knowledge.Based on the different sources of data uncertainty and different contexts and concepts,this dissertation studies knowledge acquisition of uncertain data.In order to deal with the random data,the probability context is given,and the concepts and rules in probability context are defined;In order to simplify the conceptual knowledge of inconsistent data,the four different attribute reductions of three-way concept lattices are discussed;In the incomplete context,the structures of three different partially-known concepts are analysed,and the relationships among partially-known concepts and the relationships between the partially-known concepts and the classical formal concepts in completions are studied;Based on the similarity measurement,the mathematical form of concepts under the prototype view is proposed.The main results and originalities in this dissertation are summarized as follows:(1)In order to deal with the random data,the probability contexts are proposed,and based on the maximum likelihood method,the way to obtain a probability context is given.The probability concepts in a probability context are defined.The probability decision contexts are proposed by adding decision attributes,and the way to acquire rules from the conditional probability concept lattice and the decision probability concept lattice is given.(2)Simplify the conceptual knowledge of inconsistent data.From the perspectives of preserving lattice,the meet(join)irreducible elements and the granules,four kinds of attribute reductions of three-way concept lattices are proposed and the relationships among these four different attribute reductions are shown.Furthermore,based on the discernibility matrix and the relationships among different reductions,the computing methods of attribute reductions are given.(3)The structures of partially-known formal concepts in the incomplete context are studied.The partial order on partially-known concept set,and the infimum and supremum between two partially-known concepts are defined.Thus,the three different partially-known formal concepts can form three different lattices.The relationships among three types of partially-known formal concepts are discussed.Also,the relationships between partially-known formal concepts and classical formal concepts in completions are studied.(4)Based on similarity measurement,the mathematical form of concepts under the prototype view is defined as k-cutting concepts.The properties of k-cutting concepts are also discussed.Compared with the classical formal concepts and the approximate concepts based on k-grade relation on object set,the k-cutting concepts are regarded as the extension of classical formal concepts and approximate concepts.Meanwhile,the granular structures of k-cutting concepts are discussed.Finally,the acquisition algorithms of k-cutting concepts are proposed. |