[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-665489-105":3,"detail-sidebar-cat-0-en-105":79,"doc-detail-665489-en":129},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":72,"head_meta":74,"extra_data":76,"updated_unix":78},105,"en","line-diagrams-of-hierarchical-concept-systems","Line Diagrams of Hierarchical Concept Systems","","Line Diagrams of Hierarchical Concept Systems presents a set-theoretical model for visualizing conceptual relationships in hierarchical concept systems. It explains how concepts within a fixed context form a complete lattice, called the “concept lattice,” enabling concept analysis using order and lattice theory. The work studies line diagrams aligned with DIN 2331 and extends the approach via graded line diagrams, allowing hierarchies with several hundred concepts. It also interprets elements of modified line diagrams as scales within conceptual measurement theory.",{"@graph":14,"@context":71},[15,34,54],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & Report",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/line-diagrams-of-hierarchical-concept-systems/665489/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":48,"encodingFormat":47,"isAccessibleForFree":49,"interactionStatistic":50},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/line-diagrams-of-hierarchical-concept-systems/665489.png","ImageObject",300,407,{"name":42,"@type":43},"McQueen","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-29",true,{"@type":51,"interactionType":52,"userInteractionCount":4},"InteractionCounter",{"@type":53},"ViewAction",{"@type":55,"mainEntity":56},"FAQPage",[57,63,67],{"name":58,"@type":59,"acceptedAnswer":60},"What mathematical structure does a hierarchical concept system form for a fixed context?","Question",{"text":61,"@type":62},"For a fixed context, the concepts related by the hierarchical relation (subconcept-superconcept) form a complete lattice called the “concept lattice.”","Answer",{"name":64,"@type":59,"acceptedAnswer":65},"How do line diagrams relate to DIN 2331?",{"text":66,"@type":62},"The paper studies line diagrams as described in DIN 2331 and uses them extensively in lattice theory as a representation method.",{"name":68,"@type":59,"acceptedAnswer":69},"What extension do graded line diagrams provide?",{"text":70,"@type":62},"Graded line diagrams extend the representation method, making it possible to visualize hierarchies containing several hundred concepts.","https://schema.org",{"og:url":32,"og:type":73,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":75,"canonical":32},"index,follow",{"doc_id":77,"site_id":7},665489,1793304488,{"code":4,"msg":80,"data":81},"success",[82,86,90,94,99,104,109,113,118,121,125],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":83,"show_sort_weight":84,"slug":85},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":87,"show_sort_weight":88,"slug":89},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":91,"show_sort_weight":92,"slug":93},"Exam",70,"exam",{"id":95,"doc_module":4,"doc_module_name":25,"category_name":96,"show_sort_weight":97,"slug":98},5,"Comic",60,"comic",{"id":100,"doc_module":4,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},6,"Technology",50,"technology",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},7,"Healthcare",40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":111,"slug":112},8,30,"research-report",{"id":114,"doc_module":4,"doc_module_name":25,"category_name":115,"show_sort_weight":116,"slug":117},9,"Religion & Spirituality",20,"religion-spirituality",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":119,"show_sort_weight":116,"slug":120},"World Cup","world-cup",{"id":122,"doc_module":4,"doc_module_name":25,"category_name":123,"show_sort_weight":122,"slug":124},10,"Lifestyle","lifestyle",{"id":126,"doc_module":4,"doc_module_name":25,"category_name":127,"show_sort_weight":95,"slug":128},19,"General","general",{"code":4,"msg":80,"data":130},{"doc_id":77,"user_id":131,"nickname":42,"user_avatar":132,"doc_module":4,"category_id":110,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":133,"file_id":134,"file_url":135,"file_type":136,"file_size":137,"view_count":4,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":122,"language":138,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":139,"faqs":140,"seo_title":141,"seo_description":12,"update_tm":78,"read_time":142},5909890329169,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","Rudolf Wille  \nTechnical University, Darmstadt, FRG  \nLine Diagrams of Hierarchical Concept Systems  \nWille, R.: Line diagrams of hierarchical concept systems.  \nIn: lot. Classif. 11 (1984)No,2, 'p. 77-86, 23 iefs.  \nThe possibility of visualizing conceptual relationships by graphic representation of hierarchies has been used in the stan_dard DIN 2331 and'is demonstrated here using a set-theoretical model for hierarchical concept systems. For a fixed context it is provable that the concepts in generic relationship (subconceptsuperconcept) form-as a mathematical structure-a complete lattice called the \"concept lattice\" of the context. Methods and results of order and lattice theory can thereby be used for concept analysis. Line diagrams, as described in DIN 2331, are studied and used a great deal in lattice theory. By introducing graded line diagrams, the use of this representation method can be considerably extended, to the point where it is possible to visualize_ hierarchies with several hundred concepts. It is also shown -__that building blocks of modified line diagrams maybe understood as scales in the sense of a conceptual measure· ment theory. (Author)  \nO. Introduction  \nThe German standards DIN 2330 \"Begriffe und Benen· nungen; Allgemeine Grundsiitze\" (4) and DIN 2331 \"Begriffssysteme und ihre Darstellung\" (5) were written to aid the use and understanding of conceptual tools in sciences, industry, and administration. The definitions of a concept and a concept system, which the standards have taken over from traditional philosophy, may be formulated within a set-theoretical model with respect to a fixed context. It is then provable that the concepts of a context together with the hierarchical relation \"sub concept·superconcept\" form as a mathematical structure a complete lattice called the \"concept lattice\" of the context. Methods and results of order and lattice theor/ can thereby be used for concept analysis. This idea shall be discussed in this note with respect to the graphic representation of concept systems. The line diagrams described in DIN 2331 are studied and used a good deal in lattice theory (12) . By introducing graded line diagrams, the use of this method of representation can be considerably extended, to the point where it is possible  \nto visualize hierarchies with several hundred concepts. The graded line diagram is based on the construction of subdirect products. There are also other construction methods in lattice theory which yield useful modifications of line diagrams, a fact which shall be demonstrated by the sum of an atlas of lattices. The building blocks of a modified line diagram may be understood as  \n* English translation of a paper presented at the 8th Annual Conference of the Gesellschaft fair Klassifikation eV, Hofgeis· mar, April 10-13, 1984.  \nInt. Classif. 11 (1984) No. 2 Wille-Line diagrams  \nscales in the sense of a conceptual measurement theory. In closing, this final aspect of modified line diagrams shall be discussed.  \n1. Concept Lattices  \nIn concept theory, a concept is viewed as a pair consist · · ing of an extension and an intension [comprehension]: the extension consists Qf all objects (or entities) belong · ing to the concept, while the intension comprises all attributes (or properties) valid for all those objects (16) . In handling concepts and relations between concepts, tlje difflculty often arises that the extension and the intension of a concept cannot be completely described (consider the concept \"human being\", for example). For this reason, DIN 2330 proposes to restrict to those attributes which are clearly identified with the objects under consideration. The set-theoretical model for hierarchical concept systems is based on the following definition (18) which incorporates this limitation: A context is a triple (G, M, I) where G and M are sets, and I is a binary relation between G and M (i.e. I C; G x M); the elements of G and M are called objects and attributes, respe","cbCaif4uOfduogtX","https://ap.wps.com/l/cbCaif4uOfduogtX","pdf",862975,"English","# Introduction\n## Concept Lattices","[{\"question\":\"What mathematical structure does a hierarchical concept system form for a fixed context?\",\"answer\":\"For a fixed context, the concepts related by the hierarchical relation (subconcept-superconcept) form a complete lattice called the “concept lattice.”\"},{\"question\":\"How do line diagrams relate to DIN 2331?\",\"answer\":\"The paper studies line diagrams as described in DIN 2331 and uses them extensively in lattice theory as a representation method.\"},{\"question\":\"What extension do graded line diagrams provide?\",\"answer\":\"Graded line diagrams extend the representation method, making it possible to visualize hierarchies containing several hundred concepts.\"}]","Line Diagrams of Hierarchical Concept Systems | PDF",25]