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arXiv · 2604.13039

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

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

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Roberto G. Aragón, Jesús Medina, Eloísa Ramírez-Poussa. 2026-02-25. Independent subcontexts and blocks of concept lattices. Definitions and relationships to decompose fuzzy contexts. https://doi.org/10.1016/j.fss.2025.109345

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