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| 粗糙近似算子的公理化刻画:综述 | |
| 引用本文： | 吴伟志.粗糙近似算子的公理化刻画:综述[J].模式识别与人工智能,2017,30(2):137-151. |
| 作者姓名： | 吴伟志 |
| 作者单位： | 浙江海洋大学 数理与信息学院 舟山 316022 浙江海洋大学 浙江省海洋大数据挖掘与应用重点实验室 舟山316022 |
| 基金项目： | 国家自然科学基金项目(No.41631179,61573321,61272021)资助 |
| 摘 要： | 从近似空间导出的一对下近似算子与上近似算子是粗糙集理论研究与应用发展的核心基础,近似算子的公理化刻画是粗糙集的理论研究的主要方向.文中回顾基于二元关系的各种经典粗糙近似算子、粗糙模糊近似算子和模糊粗糙近似算子的构造性定义,总结与分析这些近似算子的公理化刻画研究的进展.最后,展望粗糙近似算子的公理化刻画的进一步研究和与其它数学结构之间关系的研究. |
| 关 键 词： | 粗糙集 粗糙模糊集 模糊粗糙集 近似算子 |
| 收稿时间： | 2016-12-12 |
A Survey on Axiomatic Characterizations of Rough Approximation Operators |
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| WU Weizhi.A Survey on Axiomatic Characterizations of Rough Approximation Operators[J].Pattern Recognition and Artificial Intelligence,2017,30(2):137-151. | |
| Authors: | WU Weizhi |
| Affiliation: | School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan 316022 Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province, Zhejiang Ocean University, Zhoushan 316022 |
| Abstract: | Lower and upper approximation operators are the foundation in the study of theoretic aspect of rough set theory as well as its practical applications. One of the main directions of the theoretic study of rough sets is the axiomatic characterization of rough approximation operators. Based on various binary relations, constructive definitions of classical rough approximation operators, rough fuzzy approximation operators, and fuzzy rough approximation operators are firstly introduced. Axiomatic characterizations of these approximation operators are then summarized and analyzed. Finally, perspectives and comparison of rough set approximation operators with other mathematical structures are discussed. |
| Keywords: | Rough Set Rough Fuzzy Set Fuzzy Rough Set Approximation Operator |
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