Abstract
Hypergraphs can be built from a formal context, and conversely formal contexts can be derived from a hypergraph. Establishing such links allows exploiting morphological operators developed in one framework to derive new operators in the other one. As an example, the combination of derivation operators on formal concepts leads to closing operators on hypergraphs which are not the composition of dilations and erosions. Several other examples are investigated in this paper, with the aim of processing formal contexts and hypergraphs, and navigating in such structures.
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Notes
- 1.
In this paper we consider only the four basic operators (dilation, erosion, opening, closing).
- 2.
In the table we denote by \(Inv(\varphi )\) the set of fixed points of an operator \(\varphi \) (i.e. \(x \in Inv(\varphi )\) iff \(\varphi (x)=x\)).
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This work has been partly supported by the French ANR LOGIMA project.
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Bloch, I. (2017). Morphological Links Between Formal Concepts and Hypergraphs. In: Angulo, J., Velasco-Forero, S., Meyer, F. (eds) Mathematical Morphology and Its Applications to Signal and Image Processing. ISMM 2017. Lecture Notes in Computer Science(), vol 10225. Springer, Cham. https://doi.org/10.1007/978-3-319-57240-6_2
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