Research On Multi-scale Formal Concept Analysis Based On Attribute Granulation

Formal Concept Analysis(FCA)is a powerful tool proposed by Wille for data analysis and rule extraction from formal context.Formal context and concept lattice are its core concepts.However,in the existing formal concept analysis,the relationship between objects and attributes is given by a single granularity information.For the same object and the same attribute,the information of the object is different at different scales.It is proposed that the attribute value of the object under the attribute of color is green in a coarser scale.At a fine scale,the object may have a light green or dark green.Naturally,the conceptual information obtained from the formal concept analysis based on different scale information is different.From the perspective of human cognition,formal concept analysis based on multi-scale information helps the parties to select the appropriate scale for conceptual analysis according to actual needs,which can effectively reduce the complexity of conceptual analysis.Based on the above considerations,this thesis studies the formal concept analysis theory based on multi-scale information.by introducing the rough set approximation operator into the multi-scale formal context,the object-oriented and attribute-oriented formal concept analysis theory is studied,and the internal relations between formal concepts at different scales are discussed,which proves the coarse scale.The inclusion relationship between the conceptual epitaxial set and the conceptual epitaxial set at the fine scale and the mutual transformation relationship between the connotations at different scales,and the necessary and sufficient conditions for the equality of the conceptual epitaxial sets at different scales are given.The coarse scale and the concept generation method from coarse scale to fine scale,and further study the intrinsic relationship between formal concept analysis based on attribute granulation and formal concept analysis based on attribute clustering.It is proved that for the Wille form concept analysis,the attribute granulation based method is a special case based on the attribute clustering method.Similarly,for the object-oriented formal concept analysis,the attribute granulation based method is also based on attribute aggregation.A special case of a method of a class.