How to reduce the complexity of lattice construction is an important research topic in formal concept analysis. Based on granularity tree, the relationship between the extent and the intent of the attribute (object)-oriented concept before and after granularity transformation are investigated. Then, zoom algorithms for attribute (object)-oriented concept lattices are proposed. Specifically, zoom-in algorithm is applied to change the attribute granularity from coarse-granularity to fine-granularity, and zoom-out algorithm achieves changing the attribute granularity from fine-granularity to coarse-granularity. Zoom algorithms deal with the problems of fast construction of the attribute (object)-oriented multi-granularity concept lattices. By using zoom algorithms, the attribute (object)-oriented concept lattice based on different attribute granularity can be directly generated through the existing attribute (object)-oriented concept lattice. The proposed algorithms not only reduce the computational complexity of concept lattice construction, but also facilitate further data mining and knowledge discovery in formal contexts. Furthermore, the transformation algorithms among three kinds of concept lattice are proposed.

中文翻译：

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面向属性（对象）的多粒度概念格的构造

如何减少晶格构造的复杂性是形式概念分析中的重要研究课题。基于粒度树，研究了粒度转换前后面向属性（对象）概念的程度和意图之间的关系。然后，提出了面向属性（对象）的概念格缩放算法。具体地，应用放大算法以将属性粒度从粗粒度改变为细粒度，并且缩小算法实现将属性粒度从细粒度改变为粗粒度。缩放算法处理快速构造面向属性（对象）的多粒度概念格的问题。通过使用缩放算法，通过现有的面向属性（对象）的概念格可以直接生成基于不同属性粒度的面向属性（对象）的概念格。所提出的算法不仅降低了概念格构造的计算复杂度，而且还促进了形式上下文中的进一步数据挖掘和知识发现。此外，提出了三种概念格之间的转换算法。