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Erschienen in:
2013 | OriginalPaper | Buchkapitel
Mathematical Morphology Operators over Concept Lattices
verfasst von : Jamal Atif, Isabelle Bloch, Felix Distel, Céline Hudelot
Erschienen in: Formal Concept Analysis
Verlag: Springer Berlin Heidelberg
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Although mathematical morphology and formal concept analysis are two lattice-based data analysis theories, they are still developed in two disconnected research communities. The aim of this paper is to contribute to fill this gap, beyond the classical relationship between the Galois connections defined by the derivation operators and the adjunctions underlying the algebraic mathematical morphology framework. In particular we define mathematical morphology operators over concept lattices, based on distances, valuations, or neighborhood relations in concept lattices. Their properties are also discussed. These operators provide new tools for reasoning over concept lattices.