Abstract Using the notion of preconcept, we generalize Pawlak’s approximation operators from a one-dimensional space to a two-dimensional space in a formal context. In a formal context, we present two groups of approximation operators in a two-dimensional space: one is aided by an equivalence relation defined on the attribute set, and another is aided by the lattice theoretical property of the family of preconcepts. In addition, we analyze the properties of those approximation operators. All these results show that we can approximate all the subsets in a formal context assisted by the family of preconcepts using the above groups of approximation operators. Some biological examples show that the two groups of approximation operators provided in this article have potential ability to assist biologists to do the phylogenetic analysis of insects.

中文翻译：

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基于先入之见的近似算子

摘要 使用先入之见的概念，我们将 Pawlak 逼近算子从一维空间推广到正式上下文中的二维空间。在正式的上下文中，我们在二维空间中提出了两组近似算子：一组由定义在属性集上的等价关系辅助，另一组由先入之见的格理论属性辅助。此外，我们分析了这些近似算子的性质。所有这些结果表明，我们可以使用上述近似算子组在先入之见系列的帮助下，在正式上下文中近似所有子集。一些生物学实例表明，本文提供的两组近似算子具有辅助生物学家进行昆虫系统发育分析的潜在能力。