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

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.