E-Book, Englisch, 284 Seiten, eBook
Ganter / Wille Formal Concept Analysis
1999
ISBN: 978-3-642-59830-2
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
Mathematical Foundations
E-Book, Englisch, 284 Seiten, eBook
ISBN: 978-3-642-59830-2
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
This first textbook on formal concept analysis gives a systematic presentation of the mathematical foundations and their relations 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. The mathematical foundations are treated thoroughly and are illuminated by means of numerous examples, making the basic theory readily accessible in compact form.
Zielgruppe
Lower undergraduate
Weitere Infos & Material
0. Order-theoretic Foundations.- 0.1 Ordered Sets.- 0.2 Complete Lattices.- 0.3 Closure Operators.- 0.4 Galois Connections.- 0.5 Hints and References.- 1. Concept Lattices of Contexts.- 1.1 Context and Concept.- 1.2 Context and Concept Lattice.- 1.3 Many-valued Contexts.- 1.4 Context Constructions and Standard Scales.- 1.5 Hints and References.- 2. Determination and Representation.- 2.1 All Concepts of a Context.- 2.2 Diagrams.- 2.3 Implications between Attributes.- 2.4 Dependencies between Attributes.- 2.5 Hints and References.- 3. Parts and Factors.- 3.1 Subcontexts.- 3.2 Complete Congruences.- 3.3 Closed Subrelations.- 3.4 Block Relations and Tolerances.- 3.5 Hints and References.- 4. Decompositions of Concept Lattices.- 4.1 Subdirect Decompositions.- 4.2 Atlas-decompositions.- 4.3 Substitution.- 4.4 Tensorial Decompositions.- 4.5 Hints and References.- 5. Constructions of Concept Lattices.- 5.1 Subdirect Product Constructions.- 5.2 Gluings.- 5.3 Local Doubling.- 5.4 Tensorial Constructions.- 5.5 Hints and References.- 6. Properties of Concept Lattices.- 6.1 Distributivity.- 6.2 Semimodularity and Modularity.- 6.3 Semidistributivity and Local Distributivity.- 6.4 Dimension.- 6.5 Hints and References.- 7. Context Comparison and Conceptual Measurability.- 7.1 Automorphisms of Contexts.- 7.2 Morphisms and Bonds.- 7.3 Scale Measures.- 7.4 Measurability Theorems.- 7.5 Hints and References.- References.
