Textural formal context


DİKER M., Ugur A., Bayhan S.

INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, vol.114, pp.182-203, 2019 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 114
  • Publication Date: 2019
  • Doi Number: 10.1016/j.ijar.2019.08.011
  • Journal Name: INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.182-203

Abstract

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 Duntsh 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. (C) 2019 Elsevier Inc. All rights reserved.