Lattice-theoretic three-way formal contexts and their concepts
Lattice-theoretic three-way formal contexts and their concepts
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DOI：
10.1007/s00500-022-07294-3
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发表时间：
2022-07
期刊：
影响因子：
4.1
通讯作者：
Ninghua Gao;Zixuan Cao;Qingguo Li;W. Yao;Haojie Jiang
中科院分区：
文献类型：
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作者：
Ninghua Gao;Zixuan Cao;Qingguo Li;W. Yao;Haojie Jiang
三向概念分析为三向决策提供了一种新的模型，同时也扩展了近年来备受关注的经典形式概念分析。通过忘记点集，许多与集合相关的数学结构可以推广到幂集的某些结构上，从而可以作为有序结构来研究；这方面的研究已经取得了一些有趣的结果。为了研究有序结构中的三向概念分析，本文首次提出了一种格论形式背景。首先，我们介绍了格论三向形式概念格。其次，研究了格论三向形式概念与格论形式概念之间的关系。再次，我们证明了格论三向形式概念格是基于三向决策的L-模糊形式概念的直接推广。第四，研究了格论三向形式背景特例的基本定理。最后，我们证明了格论三向概念是某些经典概念的无点形式，并利用基本定理得到了经典三向概念格、三向粗概念格和混合概念格的刻划定理，并与已有的结果进行了比较。
Three-way concept analysis provides a novel model for three-way decisions and also extends the classical formal concept analysis, which has attracted many attentions in recent years. By forgetting the point set, many mathematical structures related to sets can be extended to certain structures of powersets and consequently be studied as ordered structures; research in this area has yielded some interesting results. In order to study three-way concept analysis in the ordered structures, in this paper, a kind of lattice-theoretic formal contexts is proposed unprecedentedly. Firstly, we introduce the lattice-theoretic three-way formal concept lattices. Secondly, the relationship between lattice-theoretic three-way formal concepts and the lattice-theoretic formal concepts is investigated. Thirdly, we illustrate that the lattice-theoretic three-way formal concept lattice is a direct generalization ofL-fuzzy formal concepts based on three-way decisions. Fourthly, the fundamental theorem for the special cases of lattice-theoretic three-way formal contexts is studied. Finally, we show that the lattice-theoretic three-way concepts are pointfree forms of some kinds of classical concepts; moreover, by the fundamental theorem, we get the characterization theorems for the classical three-way concept lattices, three-way rough concepts lattices and mixed concepts lattices; these results are compared with the available ones.