Incremental Construction Algorithms For Three-Way Concept Lattices And Their Application

Three-way concept analysis,the combination of formal concept analysis and three-way decision,is a new theory of knowledge representation and knowledge discovery.The premise of applying formal concept analysis is to generate classical formal concepts and lattices.Similarly,the premise of applying three-way concept analysis is to generate three-way concepts and lattices.Up to now,most of the construction algorithms for three-way concept lattices aim at static formal contexts.However,the formal contexts in a real world are usually dynamic.Therefore,it is necessary to study the incremental construction algorithms for three-way concept lattices for dynamic formal contexts.The thesis mainly studies the incremental construction algorithms for three-way concept lattices and their application in the multi-classification file management method based on concept lattices.First of all,the thesis proposes two object-incremental construction algorithms for three-way concept lattices on the basis of the analysis of existing incremental construction algorithms for classical concept lattices.One is LO3CL which is based on the concept lattices and the other is CO3CL which is based on the formal contexts.LO3CL reads the concept lattices and reduces the traversal range of the concept lattices by quickly finding canonical generators or canonical destructors,therefore it updates the concepts and partial order relations more efficiently.While CO3CL reads only a formal context,not a concept lattice,it reduces the generation of repeated concepts through canonicity test,and reduces the traversal range by adding additional flag.The effectiveness of the algorithms is verified by multiple sets of randomized experiments,and the experimental results show that LO3CL and CO3CL are more suitable for handling dynamic formal contexts with object additions and deletions than the existing batch construction algorithms.Secondly,the thesis proposes two attribute-incremental construction algorithms for threeway concept lattices since a three-way concept no longer has the duality of a classical formal concept.One is LA3CL which is based on the concept lattices and the other is CA3CL which is based on the formal contexts.The effectiveness of the algorithms is verified by multiple sets of randomized experiments,and the experimental results show that LA3CL and CA3CL are more suitable for handling dynamic form contexts with attribute additions and deletions than the existing batch construction algorithms.Finally,the thesis proposes a method to manage multi-classification file based on concept lattices,and designs and implements the corresponding prototype system.In this system,virtual objects are introduced to ensure the consistency between concept lattice hierarchy and user-specified hierarchy.The classical concept lattice only manages positive categories,while the three-way concept lattice manages both positive and negative categories.In the UI,a tree view converted from concept lattice is also provided for better compatibility with user habits in addition to the view of concept lattice.