{"title":"从形式语境还原的角度看一些特殊概念之间的关系","authors":"Siyu Zhao, Jianjun Qi, Ling Wei, Qing Wan","doi":"10.1007/s10489-025-06227-5","DOIUrl":null,"url":null,"abstract":"<div><p>Formal context restoration is a recently developing topic in the field of formal concept analysis (FCA). Its goal is to restore a formal context from some known formal concepts. Each type of formal concept uses its unique perspective to restore formal contexts or concept lattices. This paper investigates the relationship among five types of basic concepts: the object concepts, the attribute concepts, the join-irreducible concepts, the meet-irreducible concepts, and the formal concepts in concept reducts. This paper first studies the elementary relationship among the basic sets of formal concepts and presents these relationship in a Venn diagram. Then the relationship among the basic concept sets are explored from a restoration perspective, specifically including the relationship among basic concepts from the perspectives of formal context restoration and concept lattice restoration. These relationship are then used to study the transformation between the basic concept sets, and are summarised in a formal context and its concept lattice. Finally, a practical case is given to illustrate the relationship among the basic concept sets explored in this paper, including the elementary relationship, and the relationship from the perspectives of formal context restoration and concept lattice restoration.</p></div>","PeriodicalId":8041,"journal":{"name":"Applied Intelligence","volume":"55 4","pages":""},"PeriodicalIF":3.4000,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The relationship among some special concepts from the perspective of formal context restoration\",\"authors\":\"Siyu Zhao, Jianjun Qi, Ling Wei, Qing Wan\",\"doi\":\"10.1007/s10489-025-06227-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Formal context restoration is a recently developing topic in the field of formal concept analysis (FCA). Its goal is to restore a formal context from some known formal concepts. Each type of formal concept uses its unique perspective to restore formal contexts or concept lattices. This paper investigates the relationship among five types of basic concepts: the object concepts, the attribute concepts, the join-irreducible concepts, the meet-irreducible concepts, and the formal concepts in concept reducts. This paper first studies the elementary relationship among the basic sets of formal concepts and presents these relationship in a Venn diagram. Then the relationship among the basic concept sets are explored from a restoration perspective, specifically including the relationship among basic concepts from the perspectives of formal context restoration and concept lattice restoration. These relationship are then used to study the transformation between the basic concept sets, and are summarised in a formal context and its concept lattice. Finally, a practical case is given to illustrate the relationship among the basic concept sets explored in this paper, including the elementary relationship, and the relationship from the perspectives of formal context restoration and concept lattice restoration.</p></div>\",\"PeriodicalId\":8041,\"journal\":{\"name\":\"Applied Intelligence\",\"volume\":\"55 4\",\"pages\":\"\"},\"PeriodicalIF\":3.4000,\"publicationDate\":\"2025-01-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Intelligence\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10489-025-06227-5\",\"RegionNum\":2,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Intelligence","FirstCategoryId":"94","ListUrlMain":"https://link.springer.com/article/10.1007/s10489-025-06227-5","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
The relationship among some special concepts from the perspective of formal context restoration
Formal context restoration is a recently developing topic in the field of formal concept analysis (FCA). Its goal is to restore a formal context from some known formal concepts. Each type of formal concept uses its unique perspective to restore formal contexts or concept lattices. This paper investigates the relationship among five types of basic concepts: the object concepts, the attribute concepts, the join-irreducible concepts, the meet-irreducible concepts, and the formal concepts in concept reducts. This paper first studies the elementary relationship among the basic sets of formal concepts and presents these relationship in a Venn diagram. Then the relationship among the basic concept sets are explored from a restoration perspective, specifically including the relationship among basic concepts from the perspectives of formal context restoration and concept lattice restoration. These relationship are then used to study the transformation between the basic concept sets, and are summarised in a formal context and its concept lattice. Finally, a practical case is given to illustrate the relationship among the basic concept sets explored in this paper, including the elementary relationship, and the relationship from the perspectives of formal context restoration and concept lattice restoration.
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