{"title":"Three-way concept lattice based on Boolean formal context","authors":"Dong-Yun Niu , Ju-Sheng Mi","doi":"10.1016/j.ijar.2024.109286","DOIUrl":null,"url":null,"abstract":"<div><p>The theory of formal concept analysis (FCA) is an important mathematical method for knowledge representation and knowledge discovery. The Boolean formal context is proposed by introducing Boolean matrices and logical operations into FCA. Based on the concept lattice of the Boolean formal context and the column vector(row-vector)-oriented concept lattice of the Boolean formal context, this paper proposes the column vector(row vector)-induced three-way concept lattice of the Boolean formal context and the column vector(row vector)-induced three-way column vector(row vector)-oriented concept lattice of the Boolean formal context, and proves their rationality. Then, the isomorphism between the three-way concept lattice of the Boolean formal context and the three-way concept lattice of the general formal context is proved.</p></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"175 ","pages":"Article 109286"},"PeriodicalIF":3.2000,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Approximate Reasoning","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0888613X24001737","RegionNum":3,"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}
引用次数: 0
Abstract
The theory of formal concept analysis (FCA) is an important mathematical method for knowledge representation and knowledge discovery. The Boolean formal context is proposed by introducing Boolean matrices and logical operations into FCA. Based on the concept lattice of the Boolean formal context and the column vector(row-vector)-oriented concept lattice of the Boolean formal context, this paper proposes the column vector(row vector)-induced three-way concept lattice of the Boolean formal context and the column vector(row vector)-induced three-way column vector(row vector)-oriented concept lattice of the Boolean formal context, and proves their rationality. Then, the isomorphism between the three-way concept lattice of the Boolean formal context and the three-way concept lattice of the general formal context is proved.
期刊介绍：
The International Journal of Approximate Reasoning is intended to serve as a forum for the treatment of imprecision and uncertainty in Artificial and Computational Intelligence, covering both the foundations of uncertainty theories, and the design of intelligent systems for scientific and engineering applications. It publishes high-quality research papers describing theoretical developments or innovative applications, as well as review articles on topics of general interest.
Relevant topics include, but are not limited to, probabilistic reasoning and Bayesian networks, imprecise probabilities, random sets, belief functions (Dempster-Shafer theory), possibility theory, fuzzy sets, rough sets, decision theory, non-additive measures and integrals, qualitative reasoning about uncertainty, comparative probability orderings, game-theoretic probability, default reasoning, nonstandard logics, argumentation systems, inconsistency tolerant reasoning, elicitation techniques, philosophical foundations and psychological models of uncertain reasoning.
Domains of application for uncertain reasoning systems include risk analysis and assessment, information retrieval and database design, information fusion, machine learning, data and web mining, computer vision, image and signal processing, intelligent data analysis, statistics, multi-agent systems, etc.
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