Rule Extraction In Incomplete Formal Context And Dynamic Update Of Rules Based On Granularity Trees

In formal concept analysis,rule extraction is an important and meaningful research topic.As the data is constantly updated,concept lattice needs to be adjusted and rules extracted based on concept lattice need to be updated accordingly.We know that the process of extracting concepts and constructing concept lattices again after data changes is very time-consuming.In general,any small change in the formal context will lead to reprocessing the updated formal context as a new one,so one of the most valuable research topics is to update the existing rules while the data changes,instead of extracting it from scratch.To this end,this thesis investigates the update method of association rules at different granularities based on attribute granularity trees.In order to enrich the knowledge discovery model in the incomplete formal context,this thesis combines the idea of three-way to construct the common-possible(cp)approximation concept in incomplete formal context using positive operator and necessity-possibility operators in rough set theory,and discusses the acquisition of two different types of rules in incomplete decision formal context by common-possible(cp)approximation concept based on consistence and minimal closed-label approximation concept lattice,respectively.Finally,the nonredundancy and completeness of the rules are investigated.In this thesis,the main results are summarized as follows:(1)From the operator’s point of view,the common-possible approximation concept for object-induced and attribute-induced by positive operator and necessary-possibility operator are respectively constructed in incomplete formal context,and their lattice structure is further proved.(2)We define strongly consistence and OE-cp-consistence in incomplete formal decision context,respectively.Decision rules are extracted based on two types of consistence,and non-redundant decision rules are given.Then,we compare the relationship between rules in the OE-cp-consistence sense and rules obtained under strongly consistence.A minimal closed-label approximation concept lattice is defined on the basis of the OE-cp-approximation concept lattice model.The restricted approximate decision rules and their corresponding redundancy rules are studied based on the minimal closedlabel approximate concept lattice.The characterization of the restricted approximation decision rule is given,and the restricted Π-maximum approximation decision rule is also obtained.Finally,it is proved that the restricted Π-maximum approximate decision rule set is a minimal rule set.(3)The association rules are defined in the formal context by parent-child relationships between concepts.Based on the attribute granularity tree,the update of association rules when attributes are refined and coarsened is discussed.The zoom-in and zoom-out algorithms for rule updating are proposed,and then the effectiveness of the algorithms is experimentally verified.