Incremental Construction And Maintenance Of Three-way Concept Lattice

Three-way concept lattice is the basic data structure of three-way concept analysis,and it is widely used in three-way decision-making.In the classical concept lattice,there are only two choices: acceptance and rejection,while the three-way concept lattices can fully express three choices: acceptance,rejection and non-commitment.At present,the theory of three-way concept analysis is still in its infancy.Therefore,the main contents of this study can be divided into three sections:(1)incremental construction of three-way concept lattices;(2)maintenance of three-way concept lattices;(3)application of three-way concept lattices.Firstly,the construction of three-way concept lattices is the precondition and basis for its maintenance and application,and it is a NP-hard problem to construct three-way concept lattices from the formal context,so the generation of three-way concept lattices is also a research focus of three-way concept analysis.This study focuses on the incremental generation algorithm of object-induced three-way concept lattices.According to the duality principle,this dissertation directly derives the incremental generation algorithm of attribute-induced three-way concept lattices.This research shows that when the objects are inserted in the formal context in turn,the number of new concepts added in the three-way concept lattice is less,and does not increase with the increase of the scale of the concept lattice,which improves the efficiency of concept generation.In the real environment,things are always in dynamic change.When the formal context changes,it is time consuming to reconstruct the three-way concept lattices.Therefore,the maintenance of three-way concept lattices is also a problem worthy of further study.This dissertation mainly studies three kinds of maintenance of three-way concept lattices.Changing attribute values as the first kind of maintenance which is reflected in the formal context by adding or deleting a symbol "*";this study calls deleting objects(attributes)on object-induced(attribute-induced)three-way concept lattices as the second kind of maintenance;adding or deleting attributes(objects)on object-induced(attribute-induced)three-way concept lattices,this is the third kind of maintenance.This dissertation discusses the above three kinds of maintenance processes in detail and proposes corresponding algorithms.Finally,this dissertation applies relevant theories of three-way concept lattices to the field of conflict analysis and proposes a different method of conflict analysis from the tradition rough set theory.The three-way concept lattice model is not only simpler and clearer than the traditional conflict analysis method,but also can analyzes the conflict of sets,which is also impossible for traditional rough set theory to realize.