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.

The problem of reducing information in databases is an important topic in formal concept analysis, which has been studied in several articles. In this article, we consider the fuzzy environment of the multi-adjoint concept lattices, since it is a general fuzzy framework that allows us to easily establish degrees of preference on the elements of the considered database. We introduce algorithms to discover the information contained in the relational system. By means of these algorithms, we classify the attributes of a multi-adjoint context, and build a minimal subset of attributes preserving the information of the original knowledge system.

Attribute reduction is an important issue in different frameworks. Formal concept analysis (FCA) and object-oriented concept lattices (which is a generalization of rough sets) have been related in different papers. This contribution studies the attribute reduction in object-oriented concept lattices from the one recently given in FCA. As a consequence, we have proven that the study of the classification of the attributes in absolutely necessary, relatively necessary and unnecessary attributes is equivalent in both frameworks. An illustrative example has also been introduced.

Recently α-cut irreducible and δ1δ2-multi-adjoint concept lattices have been introduced as two different methodologies focus on reducing the size of a given fuzzy concept lattice. The philosophy of both methodologies is completely different and so, the obtained lattices too. This paper analyzes the differences and proposes that the best is to combine both methodologies in order to obtain new procedures to reduce the information retrieval, only considering the important information for the user and with the advantages of both philosophies.