Abstract Concept lattice is a kind of efficient mathematical tools for data analysis and knowledge discovery. In this paper, dependence space models are constructed to obtain a concept lattice. For a formal context, a congruence relation is first defined based on a sufficiency operator on the power set of the attribute set. A dependence space is generated. By using the dependence space, we introduce a closure operator. Related properties of the operator are discussed. It is also proved that any closed element of the closure operator is the maximum element in the attribute granule generated by the element. Further, the closed element is just the intension of some formal concept. Similarly, we define a congruence relation on the basis of a sufficiency operator, and introduce a dependence space on the power set of the object set. A closure operator is proposed for the subset of objects. The corresponding closed element of the closure operator is the maximum element in each object granule. All maximum elements generate the set of all extensions of the concept lattice. An example is used to show the validity of the approach to obtain all intensions. Finally, we introduce a dominance congruence relation, which is used to produce a closure operator. The dependence of attributes is defined based on the closure operator. The related decision rules are discussed.

中文翻译：

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构建概念格的依赖空间模型

摘要 概念格是一种用于数据分析和知识发现的高效数学工具。在本文中，依赖空间模型被构建以获得概念格。对于形式上下文，首先基于属性集的幂集上的充分性算子定义同余关系。生成依赖空间。通过使用依赖空间，我们引入了一个闭包算子。讨论了运算符的相关属性。也证明了闭包算子的任何闭元素都是该元素生成的属性粒度中最大的元素。此外，封闭元素只是一些形式概念的内涵。类似地，我们在充分性算子的基础上定义了一个同余关系，并在对象集的幂集上引入了一个依赖空间。为对象的子集提出了一个闭包算子。闭包算子对应的闭元素是每个对象颗粒中的最大元素。所有最大元素生成概念格的所有扩展的集合。一个例子被用来证明获得所有内涵的方法的有效性。最后，我们引入了一个支配同余关系，用于产生一个闭包算子。属性的依赖是基于闭包算子定义的。讨论了相关的决策规则。我们引入了一个支配同余关系，它用于产生一个闭包算子。属性的依赖是基于闭包算子定义的。讨论了相关的决策规则。我们引入了一个支配同余关系，它用于产生一个闭包算子。属性的依赖是基于闭包算子定义的。讨论了相关的决策规则。