About: Characterizing trees in concept lattices

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Concept lattices are systems of conceptual clusters, called formal concepts, which are partially ordered by the subconcept/superconcept relationship. Concept lattices are basic structures used in formal concept analysis. In general, a concept lattice may contain overlapping clusters and need not be a tree. On the other hand, tree-like classification schemes are appealing and are produced by several clustering methods. In this paper, we present necessary and sufficient conditions on input data for the output concept lattice to form a tree after one removes its least element. We present these conditions for input data with yes/no attributes as well as for input data with fuzzy attributes. In addition, we show how Lindig's algorithm for computing concept lattices gets simplified when applied to input data for which the associated concept lattice is a tree after removing the least element. The paper also contains illustrative examples. Concept lattices are systems of conceptual clusters, called formal concepts, which are partially ordered by the subconcept/superconcept relationship. Concept lattices are basic structures used in formal concept analysis. In general, a concept lattice may contain overlapping clusters and need not be a tree. On the other hand, tree-like classification schemes are appealing and are produced by several clustering methods. In this paper, we present necessary and sufficient conditions on input data for the output concept lattice to form a tree after one removes its least element. We present these conditions for input data with yes/no attributes as well as for input data with fuzzy attributes. In addition, we show how Lindig's algorithm for computing concept lattices gets simplified when applied to input data for which the associated concept lattice is a tree after removing the least element. The paper also contains illustrative examples. (en)
Title	Characterizing trees in concept lattices Characterizing trees in concept lattices (en)
skos:prefLabel	Characterizing trees in concept lattices Characterizing trees in concept lattices (en)
skos:notation	RIV/61989592:15310/08:00005378!RIV12-MSM-15310___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(1ET101370417), P(GA201/05/0079), Z(MSM6198959214)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2012
http://linked.open...aciTvurceVysledku	Outrata, Jan Vychodil, Vilém Bělohlávek, Radim
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Palackého v Olomouci / Přírodovědecká fakulta
http://linked.open...dnocenehoVysledku	359626
http://linked.open...ai/riv/idVysledku	RIV/61989592:15310/08:00005378
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Concept lattice, tree, formal concept, attribute implication. (en)
http://linked.open.../riv/klicoveSlovo	Concept lattice tree formal concept attribute implication.
http://linked.open...odStatuVydavatele	SG - Singapurská republika
http://linked.open...ontrolniKodProRIV	[007980EEF944]
http://linked.open...i/riv/nazevZdroje	International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
http://linked.open...in/vavai/riv/obor	BD
http://linked.open...ichTvurcuVysledku	3 (xsd:int)
http://linked.open...cetTvurcuVysledku	4 (xsd:int)
http://linked.open...vavai/riv/projekt	Hierarchical analysis of complex data Formal concept analysis of indeterminate and large data: theory, methods, and applications
http://linked.open...UplatneniVysledku	2008
http://linked.open...v/svazekPeriodika	16
http://linked.open...iv/tvurceVysledku	Bělohlávek, Radim Outrata, Jan Vychodil, Vilém De Baets, Bernard
http://linked.open...n/vavai/riv/zamer	Matematické modely a struktury
issn	0218-4885
number of pages	15 (xsd:int)
http://localhost/t...ganizacniJednotka	15310
is http://linked.open...avai/riv/vysledek of	Characterizing trees in concept lattices Characterizing trees in concept lattices

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