Abstract Attribute and size reductions are key issues in formal concept analysis. In this paper, we consider a special kind of equivalence relation to reduce concept lattices, which will be called local congruence. This equivalence relation is based on the notion of congruence on lattices, with the goal of losing as less information as possible and being suitable for the reduction of concept lattices. We analyze how the equivalence classes obtained from a local congruence can be ordered. Moreover, different properties related to the algebraic structure of the whole set of local congruences are also presented. Finally, a procedure to reduce concept lattices by the new weaker notion of congruence is introduced. This procedure can be applied to the classical and fuzzy formal concept analysis frameworks.

中文翻译：

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通过较弱的同余概念减少概念格

摘要 属性和尺寸缩减是形式概念分析中的关键问题。在本文中，我们考虑一种特殊的等价关系来减少概念格，称为局部同余。这种等价关系基于格上同余的概念，目标是尽可能少地丢失信息，适合概念格的约简。我们分析了如何对从局部同余获得的等价类进行排序。此外，还介绍了与整个局部同余集的代数结构相关的不同性质。最后，介绍了通过新的较弱的同余概念来减少概念格的过程。该过程可以应用于经典和模糊形式概念分析框架。