Independent subcontexts and blocks of concept lattices. Definitions and relationships to decompose fuzzy contexts

TL;DR

This paper introduces a formal approach to decomposing datasets using independent subcontexts and blocks within concept lattices, applicable to fuzzy data analysis.

Contribution

It defines independent contexts in multi-adjoint concept lattices and relates lattice decomposition to context decomposition, enabling algorithms for datasets with imperfect info.

Findings

Defined independent context within multi-adjoint concept lattices.

Analyzed lattice decomposition into blocks and its relation to context independence.

Facilitates development of dataset decomposition algorithms for fuzzy contexts.

Abstract

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.