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Two basic problems of incremental construction in Formal Concept Analysis
Title statement Two basic problems of incremental construction in Formal Concept Analysis [rukopis] / Martin Kauer Additional Variant Titles Formální konceptuální analýza Personal name Kauer, Martin (dissertant) Issue data 2019 Phys.des. 86 : il., grafy, tab. Note Ved. práce Michal Krupka Another responsib. Krupka, Michal (thesis advisor) Another responsib. Univerzita Palackého. Katedra informatiky (degree grantor) Keywords formal concept analysis * concept lattice construction * incremental algorithms * incidence removal * preconcept removal * substructures of concept lattices * generated complete sublattices * semi-closed subrelations * interval-preconcepts * basic theorem * formal concept analysis * concept lattice construction * incremental algorithms * incidence removal * preconcept removal * substructures of concept lattices * generated complete sublattices * semi-closed subrelations * interval-preconcepts * basic theorem 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 book
Kvalifikační práce Downloaded Size datum zpřístupnění 00213906-477199974.pdf 41 1.2 MB 02.01.2019 Posudek Typ posudku 00213906-ved-176369560.pdf Posudek vedoucího 00213906-opon-343296322.pdf Posudek oponenta Průběh obhajoby datum zadání datum odevzdání datum obhajoby přidělená hodnocení typ hodnocení 00213906-prubeh-169925831.pdf 01.01.2012 02.01.2019 03.05.2019 S 2
Formal Concept Analysis (FCA) is a field of applied mathematics based on formalization of the notion of concept from cognitive psychology and has been widely studied in the last several decades. From a description of objects by their features FCA derives a hierarchy of concepts which is formalized by a complete lattice called a concept lattice. We explore some fundamental aspects of FCA. First, we focus on incremental concept lattice construction and analysis of its basic step, removal of an incidence, and propose two algorithms for incremental concept lattice construction. Second, we study generated complete sublattices and show how their corresponding closed subrelations can be efficiently computed. Lastly, we investigate a new type of subrelations from which a new formal rectangle type arises, we provide motivation from cognitive psychology for it and propose a basic theorem for lattices of such rectangles.Formal Concept Analysis (FCA) is a field of applied mathematics based on formalization of the notion of concept from cognitive psychology and has been widely studied in the last several decades. From a description of objects by their features FCA derives a hierarchy of concepts which is formalized by a complete lattice called a concept lattice. We explore some fundamental aspects of FCA. First, we focus on incremental concept lattice construction and analysis of its basic step, removal of an incidence, and propose two algorithms for incremental concept lattice construction. Second, we study generated complete sublattices and show how their corresponding closed subrelations can be efficiently computed. Lastly, we investigate a new type of subrelations from which a new formal rectangle type arises, we provide motivation from cognitive psychology for it and propose a basic theorem for lattices of such rectangles.
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