Attribute combination reduction in formal concept analysis: A theoretical characterization

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

International Journal of Approximate Reasoning Pub Date : 2025-06-06 DOI:10.1016/j.ijar.2025.109498

Qin Zhang , Jianjun Qi , Ling Wei , Siyu Zhao

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引用次数: 0

Abstract

Formal concept analysis is an approach relying on hierarchies of formal concepts to acquire knowledge from formal contexts, and is developed on the foundation of lattice theory. In formal concept analysis, reduction theory mainly consists of two types: attribute reduction and concept reduction. The former achieves data reduction but inevitably leads to the loss of the original information in the formal context. The latter involves the deletion of formal concepts while preserving the original information. This paper proposes a new type of reduction called attribute combination reduction to preserve object intents, which leverages the strengths of both attribute reduction and concept reduction while avoiding the limitations of attribute reduction. First, the definition of attribute combination reducts and the judgment theorem of attribute combination consistent sets are given. Then, the relationship between attribute combination reducts and concept reducts is investigated, and the properties of attribute combination reducts are explored. In addition, to narrow the scope for searching attribute combination reducts, a lower bound and an upper bound for their cardinality are provided from the perspectives of the set dimension and the Ferrers dimension of a formal context.

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形式概念分析中的属性组合约简：一个理论表征

形式概念分析是在格理论的基础上发展起来的一种依靠形式概念层次从形式语境中获取知识的方法。在形式概念分析中，约简理论主要包括两种类型：属性约简和概念约简。前者实现了数据约简，但不可避免地导致了形式语境中原始信息的丢失。后者涉及在保留原始信息的同时删除形式概念。本文提出了一种新的属性组合约简，利用属性约简和概念约简的优点，避免了属性约简的局限性，以保持对象的意图。首先给出了属性组合约简的定义和属性组合一致集的判断定理。然后，研究了属性组合约简与概念约简的关系，探讨了属性组合约简的性质。此外，为了缩小属性组合约简的搜索范围，从形式上下文的set维和Ferrers维的角度给出了属性组合约简基数的下界和上界。

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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.