Textural formal context

In this paper, we discuss formal context in textures. A texturing is a family of subsets of a domain of discourse satisfying certain conditions. Considering a t-formal context, we formulate the notions of extent and intent in terms of p-sets and q-sets. Then we define t-formal concept and t-formal c...

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Bibliographic Details
Published in:International journal of approximate reasoning 2019-11, Vol.114, p.182-203
Main Authors: Diker, Murat, Altay Uğur, Ayşegül, Bayhan, Sadık
Format: Article
Language:English
Subjects:
Direlation
Dual formal concept
Formal concept
Formal context
Sufficiency operator
Texture space
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Summary:In this paper, we discuss formal context in textures. A texturing is a family of subsets of a domain of discourse satisfying certain conditions. Considering a t-formal context, we formulate the notions of extent and intent in terms of p-sets and q-sets. Then we define t-formal concept and t-formal co-concept. For complemented direlations, we prove that they give two different concept lattices which are dually isomorphic to each other. These lattices correspond to a concept lattice in the sense of R. Wille and a dual concept lattice given by Düntsh and Gediga, respectively. In particular, we observe that a texturing, as an imperfect collection of sets of a domain of discourse, provides a remarkable setting which still ensures information with respect to given system. Finally, we prove the main theorem of formal concept analysis for textures.
ISSN:0888-613X
1873-4731
DOI:10.1016/j.ijar.2019.08.011