The relationship among some special concepts from the perspective of formal context restoration

IF 3.4 2区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Applied Intelligence Pub Date : 2025-01-13 DOI:10.1007/s10489-025-06227-5

Siyu Zhao, Jianjun Qi, Ling Wei, Qing Wan

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Abstract

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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从形式语境还原的角度看一些特殊概念之间的关系

形式语境还原是形式概念分析（FCA）领域的一个新兴课题。它的目标是从一些已知的形式概念中恢复形式上下文。每种形式概念都使用其独特的视角来还原形式语境或概念格。研究了概念约简中对象概念、属性概念、连接不可约概念、满足不可约概念和形式概念这五类基本概念之间的关系。本文首先研究了形式概念基本集之间的基本关系，并用维恩图表示了这些基本关系。然后从恢复的角度探讨了基本概念集之间的关系，具体包括从形式语境恢复和概念格恢复的角度探讨了基本概念集之间的关系。然后将这些关系用于研究基本概念集之间的转换，并在形式上下文及其概念格中进行总结。最后，通过一个实例说明了本文所探讨的基本概念集之间的关系，包括基本概念集之间的关系，以及从形式语境恢复和概念格恢复的角度来看的关系。

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来源期刊

Applied Intelligence 工程技术-计算机：人工智能

CiteScore

6.60

自引率

20.80%

发文量

1361

审稿时长

5.9 months

期刊介绍： With a focus on research in artificial intelligence and neural networks, this journal addresses issues involving solutions of real-life manufacturing, defense, management, government and industrial problems which are too complex to be solved through conventional approaches and require the simulation of intelligent thought processes, heuristics, applications of knowledge, and distributed and parallel processing. The integration of these multiple approaches in solving complex problems is of particular importance. The journal presents new and original research and technological developments, addressing real and complex issues applicable to difficult problems. It provides a medium for exchanging scientific research and technological achievements accomplished by the international community.