Redução de reticulados conceituais - Sérgio Mariano Dias (2016)
An important formalism for knowledge representation, extraction and analysis is provided by the so-called formal concept analysis (FCA), an approach based on the mathematisation of the notion of concept and on the organization of concepts in a conceptual hierarchy.In FCA, the complexity of the concept lattice, as a function of the number of formal concepts and/or cardinality of the cover relation, is one of the most significant problems. The fact that all relationships between the concepts extracted from a formal context are present in the concept lattice is appropriate in terms of completeness, but generally results in a large number of relationships, thus overloading too much the lattice. In fact, FCA induces a potentially high combinatorial complexity, and the structures obtained, even from a small dataset, may become prohibitively large. In particular, key aspects, those that are indeed important, may be immersed in a maze of less relevant details.In this thesis, forty reduction techniques of concept lattices, selected from the most representative, are analyzed and divided into three classes. The analysis is based on seven dimensions, each consisting of a set of characteristics. Performing an analysis through AFC itself, considerations are made about computational complexity, feasibility and quality of the resulting concept lattice.The analysis of the main techniques showed a gap in techniques with the ability to abstract and generalize the knowledge expressed by a formal context. Given this finding, it is proposed here a reduction technique with such capabilities, and which does not require, unlike other techniques, the computation of the formal concepts of the original concept lattice. The technique, which has a satisfactory computational complexity, replaces groups of similar objects by representative objects, the similarity being measured on the basis of the relevance of attributes.The study of existing techniques also showed the absence of a methodology for analysis which was independent of its characteristics and intended application domain. Its is proposed here an application independent methodology of analysis. It is based on the use of implications as an alternative expression of the knowledge portrayed by a formal context. The methodology allows the identification of which knowledge is preserved, deleted, inserted and/or transformed by a reduction technique. Four complementary indexes are indicated to integrate the methodology.