The presented mathematical model of sets with incomplete information is based on L-valued sets in universes endowed with symmetric and transitive L-valued relations R where L is a complete and atomic Boolean algebra. Values R(x, x) express incomplete information about the presence of elements in universes. In addition, incomplete information about the equality of elements and membership relations of sets is modeled. The work introduces a logic for structures with incomplete information and preliminary results on ordered sets and concept lattices with incomplete information.
Anotace v angličtině
The presented mathematical model of sets with incomplete information is based on L-valued sets in universes endowed with symmetric and transitive L-valued relations R where L is a complete and atomic Boolean algebra. Values R(x, x) express incomplete information about the presence of elements in universes. In addition, incomplete information about the equality of elements and membership relations of sets is modeled. The work introduces a logic for structures with incomplete information and preliminary results on ordered sets and concept lattices with incomplete information.
Klíčová slova
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Klíčová slova v angličtině
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Rozsah průvodní práce
87 s
Jazyk
AN
Anotace
The presented mathematical model of sets with incomplete information is based on L-valued sets in universes endowed with symmetric and transitive L-valued relations R where L is a complete and atomic Boolean algebra. Values R(x, x) express incomplete information about the presence of elements in universes. In addition, incomplete information about the equality of elements and membership relations of sets is modeled. The work introduces a logic for structures with incomplete information and preliminary results on ordered sets and concept lattices with incomplete information.
Anotace v angličtině
The presented mathematical model of sets with incomplete information is based on L-valued sets in universes endowed with symmetric and transitive L-valued relations R where L is a complete and atomic Boolean algebra. Values R(x, x) express incomplete information about the presence of elements in universes. In addition, incomplete information about the equality of elements and membership relations of sets is modeled. The work introduces a logic for structures with incomplete information and preliminary results on ordered sets and concept lattices with incomplete information.
Klíčová slova
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Klíčová slova v angličtině
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Zásady pro vypracování
Student se seznámí s dostupnou literaturou o zpracování neúplných tabulkových dat (zejména z pohledu formální konceptuální analýzy). Ve vlastním výzkumu se zaměří zejména na možnosti vytváření konceptuálních svazů nad těmito daty.
Zásady pro vypracování
Student se seznámí s dostupnou literaturou o zpracování neúplných tabulkových dat (zejména z pohledu formální konceptuální analýzy). Ve vlastním výzkumu se zaměří zejména na možnosti vytváření konceptuálních svazů nad těmito daty.
Seznam doporučené literatury
- Ganter, B., Wille, R.: Formal Concept Analysis -- Mathematical Foundations. Springer (1999)
- Belohlavek, R.: Fuzzy Relational Systems: Foundations and Principles. Kluwer
Academic Publishers, Norwell, USA (2002)
- Burmeister, P., Holzer, R.: On the treatment of incomplete knowledge in formal
concept analysis. In: Ganter, B., Mineau, G. (eds.) Conceptual Structures:
Logical, Linguistic, and Computational Issues, Lecture Notes in Computer
Science, vol. 1867, pp. 385--398. Springer Berlin / Heidelberg (2000)
- Obiedkov, S.: Modal logic for evaluating formulas in incomplete contexts. In:
Priss, U., Corbett, D., Angelova, G. (eds.) Conceptual Structures:
Integration and Interfaces, Lecture Notes in Computer Science, vol. 2393, pp.
314--325. Springer Berlin / Heidelberg (2002)
Seznam doporučené literatury
- Ganter, B., Wille, R.: Formal Concept Analysis -- Mathematical Foundations. Springer (1999)
- Belohlavek, R.: Fuzzy Relational Systems: Foundations and Principles. Kluwer
Academic Publishers, Norwell, USA (2002)
- Burmeister, P., Holzer, R.: On the treatment of incomplete knowledge in formal
concept analysis. In: Ganter, B., Mineau, G. (eds.) Conceptual Structures:
Logical, Linguistic, and Computational Issues, Lecture Notes in Computer
Science, vol. 1867, pp. 385--398. Springer Berlin / Heidelberg (2000)
- Obiedkov, S.: Modal logic for evaluating formulas in incomplete contexts. In:
Priss, U., Corbett, D., Angelova, G. (eds.) Conceptual Structures:
Integration and Interfaces, Lecture Notes in Computer Science, vol. 2393, pp.
314--325. Springer Berlin / Heidelberg (2002)