{"id":{"repo_id":"qucosa-diss","oai_identifier":"oai:qucosa:de:qucosa:24973"},"canonical_url":"https://search.dev.ndltd.org/etd/qucosa-diss/oai:qucosa:de:qucosa:24973","repository":{"repo_id":"qucosa-diss","name":"QUCOSA","base_url":"http://www.qucosa.de/oai/"},"display":{"title":"Concept Approximations","abstract":"In this thesis, we present a lattice theoretical approach to the field of approximations. Given a pair consisting of a kernel system and a closure system on an underlying lattice, one receives a lattice of approximations. We describe the theory of these lattices of approximations. Furthermore, we put a special focus on the case of concept lattices. As it turns out, approximation of formal concepts can be interpreted as traces, which are preconcepts in a subcontext.","abstract_html":"In this thesis, we present a lattice theoretical approach to the field of approximations. Given a pair consisting of a kernel system and a closure system on an underlying lattice, one receives a lattice of approximations. We describe the theory of these lattices of approximations. Furthermore, we put a special focus on the case of concept lattices. As it turns out, approximation of formal concepts can be interpreted as traces, which are preconcepts in a subcontext.","abstract_has_math":false,"creators":["Meschke, Christian"],"institution":"Technische Universität Dresden","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Ganter, Bernhard","Kuznetsov, Sergei O."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-04-13","date_published":"2012-04-13","updated_at":"2026-07-24T03:59:09Z","subjects":["Formale Begriffe","Formale Begriffsanalyse","Rough Set","Approximation","Approximieren","Verbandstheorie","vollständiger Verband","Formal Concept","Formal Concept Analysis","lattice theory","complete lattice"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Ganter, Bernhard","Kuznetsov, Sergei O."]},{"key":"dc:creator","label":"Author","values":["Meschke, Christian"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden"]},{"key":"dc:type","label":"Dc Type","values":["doctoralThesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["thesis.doctoral"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Technische Universität Dresden"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Formale Begriffe","Formale Begriffsanalyse","Rough Set","Approximation","Approximieren","Verbandstheorie","vollständiger Verband","Formal Concept","Formal Concept Analysis","lattice theory","complete lattice"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis, we present a lattice theoretical approach to the field of approximations. Given a pair consisting of a kernel system and a closure system on an underlying lattice, one receives a lattice of approximations. We describe the theory of these lattices of approximations. Furthermore, we put a special focus on the case of concept lattices. As it turns out, approximation of formal concepts can be interpreted as traces, which are preconcepts in a subcontext.","In der vorliegenden Arbeit beschreiben wir einen verbandstheoretischen Zugang zum Thema Approximieren. Ausgehend von einem Kern- und einem Hüllensystem auf einem vollständigen Verband erhält man einen Approximationsverband. Wir beschreiben die Theorie dieser Approximationsverbände. Des Weiteren liegt dabei ein Hauptaugenmerk auf dem Fall zugrundeliegender Begriffsverbände. Wie sich nämlich herausstellt, lassen sich Approximationen formaler Begriffe als Spuren auffassen, welche diese in einem vorgegebenen Teilkontext hinterlassen."]},{"key":"dc:title","label":"Title","values":["Concept Approximations"]}]}],"canonical_facts":{"dc:contributor":["Ganter, Bernhard","Kuznetsov, Sergei O."],"dc:creator":["Meschke, Christian"],"dc:description.abstract":["In this thesis, we present a lattice theoretical approach to the field of approximations. Given a pair consisting of a kernel system and a closure system on an underlying lattice, one receives a lattice of approximations. We describe the theory of these lattices of approximations. Furthermore, we put a special focus on the case of concept lattices. As it turns out, approximation of formal concepts can be interpreted as traces, which are preconcepts in a subcontext.","In der vorliegenden Arbeit beschreiben wir einen verbandstheoretischen Zugang zum Thema Approximieren. Ausgehend von einem Kern- und einem Hüllensystem auf einem vollständigen Verband erhält man einen Approximationsverband. Wir beschreiben die Theorie dieser Approximationsverbände. Des Weiteren liegt dabei ein Hauptaugenmerk auf dem Fall zugrundeliegender Begriffsverbände. Wie sich nämlich herausstellt, lassen sich Approximationen formaler Begriffe als Spuren auffassen, welche diese in einem vorgegebenen Teilkontext hinterlassen."],"dc:publisher":["Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden"],"dc:subject":["Formale Begriffe","Formale Begriffsanalyse","Rough Set","Approximation","Approximieren","Verbandstheorie","vollständiger Verband","Formal Concept","Formal Concept Analysis","lattice theory","complete lattice"],"dc:title":["Concept Approximations"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Technische Universität Dresden"]},"updated_at":"2026-07-24T03:59:09Z"}