粗糙近似算子的公理化刻画:综述

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.%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.