Independent subcontexts and blocks of concept lattices. Definitions and relationships to decompose fuzzy contexts

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2025-02-28 DOI:10.1016/j.fss.2025.109345

Roberto G. Aragón, Jesús Medina, Eloísa Ramírez-Poussa

引用次数: 0

Abstract

The decomposition of datasets is a useful mechanism in the processing of large datasets and it is required in many cases. In formal concept analysis (FCA), the dataset is interpreted as a context and the notion of independent context is relevant in the decomposition of a context. In this paper, we have introduced a formal definition of independent context within the multi-adjoint concept lattice framework, which can be translated to other fuzzy approaches. Furthermore, we have analyzed the decomposition of a general bounded lattice in pieces, that we have called blocks. This decomposition of a lattice has been related to the existence of a decomposition of a context into independent subcontexts. This study will allow to develop algorithms to decompose datasets with imperfect information.

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独立的子上下文和概念格块。用于分解模糊上下文的定义和关系

数据集分解是处理大型数据集的一种有用的机制，在许多情况下都是必需的。在形式概念分析（FCA）中，数据集被解释为上下文，独立上下文的概念与上下文的分解有关。在本文中，我们引入了多伴随概念格框架中独立上下文的形式化定义，它可以转化为其他模糊方法。此外，我们分析了一般有界晶格的分解，我们称之为块。晶格的这种分解与上下文分解为独立子上下文的存在性有关。这项研究将允许开发算法来分解具有不完全信息的数据集。

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

Fuzzy Sets and Systems 数学-计算机：理论方法

CiteScore

6.50

自引率

17.90%

发文量

321

审稿时长

6.1 months

期刊介绍： Since its launching in 1978, the journal Fuzzy Sets and Systems has been devoted to the international advancement of the theory and application of fuzzy sets and systems. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including (and not restricted to) aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. Fuzzy sets are also the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling: fuzzy rule-based systems. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies. In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Furthermore, fuzzy sets have strong logical underpinnings in the tradition of many-valued logics.