Independent subcontexts and blocks of concept lattices. Definitions and relationships to decompose fuzzy contexts
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908964760846336 |
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| author | Aragón, Roberto G. Medina, Jesús Ramírez-Poussa, Eloísa |
| author_facet | Aragón, Roberto G. Medina, Jesús Ramírez-Poussa, Eloísa |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_13039 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Independent subcontexts and blocks of concept lattices. Definitions and relationships to decompose fuzzy contexts Aragón, Roberto G. Medina, Jesús Ramírez-Poussa, Eloísa Databases 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. |
| title | Independent subcontexts and blocks of concept lattices. Definitions and relationships to decompose fuzzy contexts |
| topic | Databases |
| url | https://arxiv.org/abs/2604.13039 |