| 摘要: |
| 侧重于建立形式概念分析与粗糙集之间融合的理论基础.利用形式概念分析中名义梯级背景(nominal scale)的概念,对信息系统进行平面梯级(plain scaling)得到了衍生的形式背景.证明了粗糙集理论中的划分、上下近似、独立、依赖、约简等核心概念都可以在相应的衍生背景中进行表示.揭示了粗糙集理论在分析处理数据时的局限性,指出了利用梯级的方法可以扩展粗糙集理论. |
| 关键词: 粗糙集 形式概念分析 名义梯级背景 平面梯级 概念格 |
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| 基金项目:Supported by the National Natural Science Foundation of China under Grant Nos.60573074, 70471003 (国家自然科学基金); the Natural Science Foundation of Shanxi Province of China under Grant No.2007011040 (山西省自然科学基金); the Foundation of Doctoral Program Research of the Ministry of Education of China under Grant No.20050108004 (高等学校博士学科点专项科研基金) |
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| Representation and Extension of Rough Set Theory Based on Formal Concept Analysis |
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QU Kai-She,ZHAI Yan-Hui,LIANG Ji-Ye,LI De-Yu
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| Abstract: |
| This paper aims to establish the relationship between formal concept analysis and rough set theory.The following results are obtained:(1)a derivative formal context of an information system can be induced by the notion of nominal scale and the technique of plain scaling in formal concept analysis;(2)some core notions in rough set theory such as partition,upper and lower approximations,independence,dependence and reduct can be reinterpreted in derivative formal contexts.In addition,the limitation of rough set theory to data processing is analyzed.The results presented in this paper provide a basis for the synthesis of formal concept analysis and rough set theory. |
| Key words: rough set formal concept analysis nominal scale plain scaling concept lattice |
