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Closure and Interior Structures in Relational Data Analysis and Their Morphisms
Údaje o názvu Closure and Interior Structures in Relational Data Analysis and Their Morphisms [rukopis] / Jan Konečný Další variantní názvy Closure and Interior Structures in Relational Data Analysis and Their Morphisms Osobní jméno Konečný, Jan (autor diplomové práce nebo disertace) Překl.náz Closure and Interior Structures in Relational Data Analysis and Their Morphisms Vyd.údaje 2012 Fyz.popis 86 : il. Poznámka Ved. práce Radim Bělohlávek Dal.odpovědnost Bělohlávek, Radim, 1971- (školitel) Dal.odpovědnost Univerzita Palackého. Katedra informatiky (udelovatel akademické hodnosti) Klíč.slova Formal concept analysis * fuzzy Galois connections * formal context * concept lattice * relational products * matrix decompositions * block relations * Formal concept analysis * fuzzy Galois connections * formal context * concept lattice * relational products * matrix decompositions * block relations Forma, žánr disertace dissertations MDT (043.3) Země vyd. Česko Jazyk dok. angličtina Druh dok. PUBLIKAČNÍ ČINNOST Titul Ph.D. Studijní program Doktorský Studijní program Informatika Studijní obor Informatika 
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We study relationships between compositions of fuzzy relations (for- mal fuzzy contexts) and morphisms of the structures (concept lat- tices) associated to the fuzzy relations. In particular, we study concept lattices of both, isotone and antitone concept-forming operators which are associated to the fuzzy relations. The presented theory brings new results on characterization, reduction, and similarity issues regarding concept lattices. Moreover, it brings a new insight to Boolean matrix theory generalizing some of its well-known results to fuzzy setting. In addition, we provide illustrative examples of applications of the presented theory, namely, conceptual scaling to fuzzy attributes and use of block relation to reduce size of a concept lattice.We study relationships between compositions of fuzzy relations (for- mal fuzzy contexts) and morphisms of the structures (concept lat- tices) associated to the fuzzy relations. In particular, we study concept lattices of both, isotone and antitone concept-forming operators which are associated to the fuzzy relations. The presented theory brings new results on characterization, reduction, and similarity issues regarding concept lattices. Moreover, it brings a new insight to Boolean matrix theory generalizing some of its well-known results to fuzzy setting. In addition, we provide illustrative examples of applications of the presented theory, namely, conceptual scaling to fuzzy attributes and use of block relation to reduce size of a concept lattice.
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