Lattice-theoretic three-way formal contexts and their concepts

被引：0
作者：
Ninghua Gao
Zixuan Cao
Qingguo Li
Wei Yao
Haojie Jiang
机构：
[1] Zhejiang University of Science and Technology,School of Science
[2] Hunan University,College of Mathematics and Econometrics
[3] Nanjing University of Information Science and Technology,School of Mathematics and Statistics
[4] Zhejiang University of Technology,College of Mechanical Engineering
[5] Hunan University,State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body
[6] XGM Corporation Limited,undefined
来源：
Soft Computing | 2022年 / 26卷
关键词：
Lattice-theoretic three-way formal contexts; Concepts lattice; Fundamental theorem; Algorithm;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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 of L-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.
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页码：8971 / 8985
页数：14
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