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Journal of Logic and Computation, Volume 10, Issue 6, pp. 823-845: Abstract.

Similarity relations in concept lattices

R Belohlavek

Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Bráfova 7, 701 03 Ostrava, Czech Republic, Department of Computer Science, Technical University of Ostrava, tr. 17. listopadu, 708 33 Ostrava-Poruba, Czech Republic, E-mail: radim.belohlavek@osu.cz

This paper studies the issue of similarity relations in fuzzy concept lattices. Fuzzy concepts and fuzzy concept lattices represent a formal approach to the modelling of non-sharp (fuzzy) concepts and conceptual structures in the sense of traditional (Port-Royal) logic. Applications of concept lattices are in representation of conceptual knowledge and in conceptual analysis of (fuzzy) data. Similarity relations are defined and considered on three levels: similarity of objects (and similarity of attributes), similarity of concepts, and similarity of concept lattices. We show a way to factorize (simplify) concept lattices by the similarity of concepts. Also shown is how to reduce the computation of the similarity relations.

Keywords: concept, similarity, fuzzy logic, residuated lattice, concept lattice, tolerance

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