Some relationships between fuzzy sets, mathematical morphology, rough sets, F-transforms, and formal concept analysis
Atif, Jamal; Bloch, Isabelle; Hudelot, Céline (2016), Some relationships between fuzzy sets, mathematical morphology, rough sets, F-transforms, and formal concept analysis, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 24, Suppl. 2, p. 1-32. 10.1142/S0218488516400080
TypeArticle accepté pour publication ou publié
Journal nameInternational Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
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Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Laboratoire Traitement et Communication de l'Information [LTCI]
Mathématiques et Informatique pour la Complexité et les Systèmes [MICS]
Abstract (EN)In this paper we extend some previously established links between the derivation operators used in formal concept analysis and some mathematical morphology operators to fuzzy concept analysis. We also propose to use mathematical morphology to navigate in a fuzzy concept lattice and perform operations on it. Links with other lattice-based for malisms such as rough sets and F-transforms are also established. This paper proposes a discussion and new results on such links and their potential interest.
Subjects / KeywordsData analysis; Formal concept analysis; fuzzy formal concepts; mathematical morphology; residuated lattice; fuzzy sets; rough sets; F-transforms
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