The properties of 3-valued formal contexts in a cognitive viewpoint

IF 3 3区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

International Journal of Approximate Reasoning Pub Date : 2025-09-12 DOI:10.1016/j.ijar.2025.109573

Huilai Zhi , Qing Wan , Ting Qian , Yinan Li , Jiang Yang

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引用次数: 0

Abstract

3-valued formal contexts are abstracted from various types of applications such as incomplete formal context based data mining, shadow sets based knowledge discovery and conflict analysis. 3-valued formal contexts differ from binary-valued formal contexts in many aspects, and many distinguished details have not been investigated. To this end, some of the most important properties of 3-valued formal contexts are systematically explored in a cognitive viewpoint based on formal concept analysis. At first, 3-valued concept lattices and formal concept lattices are compared from multiple perspectives, including the connections between formal concepts and 3-valued concepts, and the meet-preserving mappings from formal concept lattices to 3-valued concept lattices. After that, based on the completions of 3-valued contexts, the connections between 3-valued concept lattices and three-way concept lattices are explored. Finally, it is proved that a 3-valued concept lattice is the minimum closure that contains formal concept lattices, and there is an order-preserving mapping from formal concepts to equivalence classes of 3-valued concepts.

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认知视点下三值形式语境的性质

三值形式上下文是从基于不完全形式上下文的数据挖掘、基于阴影集的知识发现和冲突分析等不同类型的应用中抽象出来的。三值形式语境与二值形式语境在许多方面存在差异，许多值得注意的细节尚未得到研究。为此，本文从基于形式概念分析的认知观点出发，系统地探讨了三值形式语境的一些最重要的属性。首先从形式概念格与3值概念格之间的联系、形式概念格与3值概念格之间的保满足映射等多个角度对3值概念格与3值概念格进行了比较。然后，基于3值语境的补全，探讨了3值概念格与三向概念格之间的联系。最后，证明了3值概念格是包含形式概念格的最小闭包，并且从形式概念到3值概念的等价类之间存在保序映射。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Approximate Reasoning 工程技术-计算机：人工智能

CiteScore

6.90

自引率

12.80%

发文量

170

审稿时长

67 days

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.