Eloísa Ramírez-Poussa

Roberto G. Aragón, Jesús Medina, Eloísa Ramírez-Poussa

Factorizing datasets is an interesting process in a multitude of approaches, but many times it is not possible or efficient the computation of a factorization of the dataset. A method to obtain independent subcontexts of a formal context with Boolean data was proposed in~\cite{dubois:2012}, based on the operators used in possibility theory. In this paper, we will analyze this method and study different properties related to the pairs of sets from which a factorization of a formal context arises. We also inspect how the properties given in the classical case can be extended to the fuzzy framework, which is essential to obtain a mechanism that allows the computation of independent subcontexts of a fuzzy context.

Roberto G. Aragón, Jesús Medina, Eloísa Ramírez-Poussa

The decomposition of datasets is a useful mechanism in the processing of large datasets and it is required in many cases. In formal concept analysis (FCA), the dataset is interpreted as a context and the notion of independent context is relevant in the decomposition of a context. In this paper, we have introduced a formal definition of independent context within the multi-adjoint concept lattice framework, which can be translated to other fuzzy approaches. Furthermore, we have analyzed the decomposition of a general bounded lattice in pieces, that we have called blocks. This decomposition of a lattice has been related to the existence of a decomposition of a context into independent subcontexts. This study will allow to develop algorithms to decompose datasets with imperfect information.

Roberto G. Aragón, Jesús Medina, Eloísa Ramírez-Poussa

The process of decomposing databases into smaller datasets, with the objective of extrapolating the information obtained in the smaller ones to the original database, represents a relevant and complex challenge in real applications. It is particularly relevant in the context of fuzzy formal concept analysis, where the complexities of knowledge extraction from datasets characterized by incomplete and imperfect data are considerable. This paper will analyze a mechanism and different properties for detecting independent subcontexts from a given context, using modal operators within the multi-adjoint concept lattice framework.