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An Order-Theoretic Study on Formal Concept Analysis
Version 1
: Received: 13 September 2023 / Approved: 13 September 2023 / Online: 13 September 2023 (09:32:42 CEST)
A peer-reviewed article of this Preprint also exists.
Syau, Y.-R.; Lin, E.-B.; Liau, C.-J. An Order-Theoretic Study on Formal Concept Analysis. Axioms 2023, 12, 1099. Syau, Y.-R.; Lin, E.-B.; Liau, C.-J. An Order-Theoretic Study on Formal Concept Analysis. Axioms 2023, 12, 1099.
Abstract
In this paper, we study properties of formal concepts from an order-theoretic perspective. We first establish a natural correspondence between formal contexts and preorders as well as their induced posets. Then, based on the poset induced from a formal context, we provide characterization for join-irreducible or meet-irreducible elements of finite concept lattices. In addition, we introduce the notion of rough conceptual approximations based on topological closure and interior operators. In contrast with the conventional definition of equivalence class of an object used in Pawlakian approximation spaces, we instead utilize the extent of an object concept. We show that rough conceptual approximations are equivalent to approximation operators in the generalized approximation space associated with the preorder corresponding to a formal context. We also illustrate these theoretical results with examples and discuss their potential applications.
Keywords
Formal concept analysis; Object concepts; Attribute concepts; Join-irreducibility; Meet-irreducibility; Rough conceptual approximations
Subject
Computer Science and Mathematics, Computer Science
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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