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Closure and Interior Structures in Relational Data Analysis and Their Morphisms
Title statement Closure and Interior Structures in Relational Data Analysis and Their Morphisms [rukopis] / Jan Konečný Additional Variant Titles Closure and Interior Structures in Relational Data Analysis and Their Morphisms Personal name Konečný, Jan (dissertant) Translated title Closure and Interior Structures in Relational Data Analysis and Their Morphisms Issue data 2012 Phys.des. 86 : il. Note Ved. práce Radim Bělohlávek Another responsib. Bělohlávek, Radim, 1971- (školitel) Another responsib. Univerzita Palackého. Katedra informatiky (degree grantor) Keywords 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 Form, Genre disertace dissertations UDC (043.3) Country Česko Language angličtina Document kind PUBLIKAČNÍ ČINNOST Title Ph.D. Degree program Doktorský Degree program Informatika Degreee discipline Informatika 
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Kvalifikační práce Downloaded Size datum zpřístupnění 00165405-389304042.pdf 27 719.1 KB 11.07.2012 Posudek Typ posudku 00165405-ved-114274928.jpg Posudek vedoucího 00165405-opon-193477978.pdf Posudek oponenta
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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