Bibliographic Details
| 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] |
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| Database: |
Engineering Source |
