The Axiomatization And Reduction Of Generalized Formal Contexts

The concept lattice theory was oriented towards the discovery of formal concepts and the construction of concept hierarchy structures. Nowadays, formal concept analysis has shown a trend of intersection and fusion of multidiscipline and has become more effective for data mining and knowledge processing.Because of many kinds of reasons, we would face the cases of the relationship missing or considerable uncertainty between some objects and attributes, in which the formal context is regarded as incomplete formal context, so that we can’t determine whether the existence of the relationship between the objects and attributes or not. The axiomatic characterizations of approximate concept lattices in incomplete contexts is expected enormous value for data analysis.As another kinds of problem on the multivalued formal context, the concept learning and the hierarchical construction finding are more difficult than the situations on classic formal decision context, while the structuring concept lattice of formal decision context is appropriate to object reducing. On the multivalued formal context, novel methods of object reduction are needed developing practically and theoretically.In this paper, the original work obtained includes two aspects as follows:1) A method of structuring concept lattice is proposed by decomposing the incomplete context into two complete contexts. Axiomatic characterizations of approximate concept lattices in complete contexts are obtained based on those of Wille’s concept lattices in formal contexts. Then a novel method of building approximate concept lattice is presented, which can enrich the existing theory related to the approximate concept lattice.2) The object subcontexts is proposed in real decision context to calculate the concept lattices of object subcontexts. Based on this method, a theoretical framework of object compression is developed to compute a reduction in the real decision context which is keep the non-redundant L-decision rules invariant.The complete algorithm is developed either.