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On the poset of copreconcets of a formal context.

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Title: On the poset of copreconcets of a formal context.
Authors: Kenfack, Kenne Zachée (AUTHOR) zkenfackkenne@gmail.com, Diékouam, Fotso Luc Éméry (AUTHOR) lucdiekouam@yahoo.fr, Kwuida, Léonard (AUTHOR) leonard.kwuida@bfh.ch, Dongho, Joseph (AUTHOR) josephdongho@yahoo.fr
Source: Discussiones Mathematicae: General Algebra & Applications. 2026, Vol. 46 Issue 1, p103-126. 24p.
Subjects: Partially ordered sets, Lattice theory, Duality theory (Mathematics), Ordered algebraic structures
Abstract: Formal Concept Analysis is an applied theory of complete lattices, with many applications in data analysis, logic, computer sciences, and ordered structures. In Formal Concept Analysis, a context is a triple (G, M, I) with I ⊆ G × M. In this paper we introduce the notion of a copreconcept of a context (G, M, I) as a pair (A, B) with A ⊆ G, B ⊆ M, A′ ⊆ B and B′ ⊆ A, where A′ (resp. B′) is the set of elements of M (resp. G) in relation with all elements in A (resp. B). We investigate the order structure of copreconcepts and obtain that, when ordered by (A1, B1) ≤ (A2, B2) iff A1 ⊆ A2 and B2 ⊆ B1, the set of copreconcepts is a multi-lattice. We give a sufficient condition for it to be a lattice. Many examples are provided based on context constructions and subcontexts. On our way, we also prove that coherent posets are multilattices. [ABSTRACT FROM AUTHOR]
Copyright of Discussiones Mathematicae: General Algebra & Applications is the property of University of Zielona Gora and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: On the poset of copreconcets of a formal context.
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  Data: <searchLink fieldCode="AR" term="%22Kenfack%2C+Kenne+Zachée%22">Kenfack, Kenne Zachée</searchLink> (AUTHOR)<i> zkenfackkenne@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Diékouam%2C+Fotso+Luc+Éméry%22">Diékouam, Fotso Luc Éméry</searchLink> (AUTHOR)<i> lucdiekouam@yahoo.fr</i><br /><searchLink fieldCode="AR" term="%22Kwuida%2C+Léonard%22">Kwuida, Léonard</searchLink> (AUTHOR)<i> leonard.kwuida@bfh.ch</i><br /><searchLink fieldCode="AR" term="%22Dongho%2C+Joseph%22">Dongho, Joseph</searchLink> (AUTHOR)<i> josephdongho@yahoo.fr</i>
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  Data: <searchLink fieldCode="JN" term="%22Discussiones+Mathematicae%3A+General+Algebra+%26+Applications%22">Discussiones Mathematicae: General Algebra & Applications</searchLink>. 2026, Vol. 46 Issue 1, p103-126. 24p.
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  Data: <searchLink fieldCode="DE" term="%22Partially+ordered+sets%22">Partially ordered sets</searchLink><br /><searchLink fieldCode="DE" term="%22Lattice+theory%22">Lattice theory</searchLink><br /><searchLink fieldCode="DE" term="%22Duality+theory+%28Mathematics%29%22">Duality theory (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Ordered+algebraic+structures%22">Ordered algebraic structures</searchLink>
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  Data: Formal Concept Analysis is an applied theory of complete lattices, with many applications in data analysis, logic, computer sciences, and ordered structures. In Formal Concept Analysis, a context is a triple (G, M, I) with I ⊆ G × M. In this paper we introduce the notion of a copreconcept of a context (G, M, I) as a pair (A, B) with A ⊆ G, B ⊆ M, A′ ⊆ B and B′ ⊆ A, where A′ (resp. B′) is the set of elements of M (resp. G) in relation with all elements in A (resp. B). We investigate the order structure of copreconcepts and obtain that, when ordered by (A1, B1) ≤ (A2, B2) iff A1 ⊆ A2 and B2 ⊆ B1, the set of copreconcepts is a multi-lattice. We give a sufficient condition for it to be a lattice. Many examples are provided based on context constructions and subcontexts. On our way, we also prove that coherent posets are multilattices. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Discussiones Mathematicae: General Algebra & Applications is the property of University of Zielona Gora and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=194843448
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        Value: 10.7151/dmgaa.1490
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      – SubjectFull: Partially ordered sets
        Type: general
      – SubjectFull: Lattice theory
        Type: general
      – SubjectFull: Duality theory (Mathematics)
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      – SubjectFull: Ordered algebraic structures
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              Text: 2026
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