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Constructing three-way concept lattices based on apposition and subposition of formal contexts

机译：基于形式上下文的并置和子代构造三向概念格

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摘要

Three-way concept analysis provides a new model to make three-way decisions. Its basic structure can be shown by the three-way concept lattices. Thus, how to construct three-way concept lattices is an important issue in the three-way concept analysis. This paper proposes approaches to create the three-way concept lattices of a given formal context. First, we can transform the given formal context and its complementary context into new formal contexts which are isomorphic to the given formal context and its complementary context respectively. And then, Type I-combinatorial context and Type II combinatorial context are defined, which are apposition and subposition of these new formal contexts, respectively. Second, we prove that the concept lattice of Type I-combinatorial context is isomorphic to object-induced three-way concept lattice and the concept lattice of Type II-combinatorial context is isomorphic to attribute-induced three-way concept lattice of the given formal context. And then, the approaches of creating the three-way concept lattices are proposed based on the concept lattices of Type I-combinatorial context and Type I-combinatorial context. Finally, we give the corresponding algorithms of constructing three-way concept lattices based on the above approaches and conduct several experiments to illustrate the efficient of proposed algorithms. (C) 2016 Elsevier B.V. All rights reserved.
机译：三向概念分析为制定三向决策提供了新模型。它的基本结构可以通过三向概念格来表示。因此，如何构造三向概念格是三向概念分析中的重要问题。本文提出了创建给定形式上下文的三向概念格的方法。首先，我们可以将给定的形式上下文及其互补上下文转换为新的形式上下文，这些新的形式上下文分别与给定的形式上下文及其互补上下文同构。然后，定义了I类组合上下文和II类组合上下文，它们分别是这些新形式上下文的并置和子并置。其次，我们证明类型I组合上下文的概念格与对象诱导的三向概念格同构，类型II组合上下文的概念格与给定形式的属性诱导的三向概念格同构上下文。然后，基于I类组合上下文和I类组合上下文的概念格，提出了建立三元概念格的方法。最后，基于上述方法，给出了构造三元概念格的相应算法，并进行了若干实验，说明了所提算法的有效性。 （C）2016 Elsevier B.V.保留所有权利。

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