三支半概念的广义结构及粗糙集近似算子  

Generalized Structures and Rough Set Approximation Operators of Three-way Semiconcepts

作　　者：毛华[1,2] 马经泽 牛振华 张植明[1] 杨兰珍[1] MAO Hua;MA Jing-ze;NIU Zhen-hua;ZHANG Zhi-ming;YANG Lan-zhen(College of Mathematics and Information on Science,Hebei University,Baoding 071002,China;Hebei Key Laboratory of Machine Learning and Computational Intelligence,Hebei University,Baoding 071002,China)

机构地区：[1]河北大学数学与信息科学学院,河北保定071002 [2]河北大学河北省机器学习与计算智能重点实验室,河北保定071002

出　　处：《模糊系统与数学》2022年第6期89-101,共13页Fuzzy Systems and Mathematics

摘　　要：随着形式概念分析理论的发展,经典半概念理论也受到了广泛关注。三支半概念是将经典半概念与三支决策相结合而产生的新理论,也是一个知识发现与数据挖掘的有效工具。本文主要对三支半概念的结构和性质两个方面进行研究,首先将三支半概念拓广到了广义三支半概念——OE-半概念和AE-半概念,给出了寻找二者的算法,接下来分别针对两种广义三支半概念构建了纯双布尔代数结构。此外,研究了三支半概念与经典半概念之间的关系,分别证明了它们之间的保运算以及序同构关系。最后利用粗糙集理论分别构建了经典半概念的两对算子,给出该算子的相关性质,并证明这两对算子为粗糙集近似算子。With the development of formal concept analysis, classical semiconcepts has been received widely attentions. Three-way semiconcepts is a novel theory which combining classical semiconcepts and three-way decisions. It is also a new efficient tool for knowledge discovery and data mining. This paper focus on both the structures and properties of three-way semiconcepts. First, three-way semiconcepts are extended to two kinds of generalized three-way semiconcept — OE-semiconcept and AE-semiconcept. The algorithms for finding generalized three-way semiconcepts are given. After that, the structures for pure double Boolean algebra of two kinds of generalized three-way semiconcepts are constructed, respectively. Moreover, the relationships between three-way semiconcepts and classical semiconcepts are presented. We prove that they are operators-preserving and order-isomorphism. Finally, using rough set theory, two pairs of operators based on classical three-way semiconcepts, are built up, respectively. And some relative properties of them are presented. It can be proved that these two pairs of operators are rough set approximation operators.

关 键 词：三支半概念 广义三支半概念 三支决策 纯双布尔代数 粗糙集近似算子 

分 类 号：O159[理学—数学]