Formal Concept Analysis: Mathematical Foundation
This is the first textbook on formal concept analysis. It gives a systematic presentation of the mathematical foundations and their relation to applications in computer science, especially in data analysis and knowledge processing. Above all, it presents graphical methods for representing conceptual systems that have proved themselves in communicating knowledge. Theory and graphical representation are thus closely coupled together. The mathematical foundations are treated thoroughly and illuminated by means of numerous examples.
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Concept Lattices of Contexts
Determination and Representation
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algorithm arbitrary arrow relations atomistic attribute concepts attribute extents attribute set automorphisms bijective block relation called closed relation closure system compatible subcontext complete homomorphism complete lattice complete sublattice complete tolerance relation completely distributive concept lattice concept of G congruence relation contains context G convex corresponding define Definition direct product distributive lattices doubly founded context dual dually equivalent example factor lattice Ferrers relation Figure Formal Concept Analysis furthermore Galois connection gluing Hence holds implications infimum infimum-dense intent irreducible elements isomorphic lattice theory line diagram lower neighbour many-valued context means morphisms object concepts object g obtain order dimension order ideals order-embedding order-preserving ordered set pre-image precisely Proof properties Proposition 13 prove pseudo-intent reduced context respect Rudolf satisfies semimodularity set representation subdirect decomposition subdirect product subset substitution sum supremum surjective tensor product upper neighbour