Formal concept analysis and applications

Formal concept analysis (FCA) has been a topic of interest for many researches since its introduction in 1982. The field of FCA gives a formal definition of what is meant by a concept, studies the mathematical properties that follow from this definition, and applies the idea of concept in many applications. In this thesis, we apply the existing notion of concept, which we call atomic concept, in an application to data mining. We show how atomic concepts can be used efficiently to discover representative association rules which is a set of rules from which all association rules can be generated. This results in a big reduction in the input size for algorithms to find representative association rules, and therefore, faster algorithms. The notion of atomic concept allows only for conjunctions in its definition. For many applications, such as information retrieval, such a definition is not enough. We generalize the notion of concept to allow for disjunctions in addition to conjunctions and introduce definable concepts. We study order-theoretic properties of definable concepts and prove that the set of definable concepts on a given context forms a complete lattice. To complete our general view of a concept, we also introduce the notion of non-definable concepts. Non-definable concepts are important from an application point of view where the situation under investigation can not be described as a definable concept. We introduce the notion of concept approximation for finding formal concepts—definable or atomic—that approximate non-definable concepts