Independent subcontexts and blocks of concept lattices. Definitions and relationships to decompose fuzzy contexts
This work addresses dataset decomposition for researchers in formal concept analysis and fuzzy logic, but it is incremental as it builds on existing frameworks without major breakthroughs.
The paper tackles the problem of decomposing large datasets with imperfect information by introducing a formal definition of independent contexts within the multi-adjoint concept lattice framework and relating it to lattice decomposition into blocks, enabling future algorithm development for such datasets.
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.