一般多粒度模糊粗糙集模型

Generalized Multi-granulation Fuzzy Rough Set Model

通过分析多粒度和模糊粗糙集之间的联系,建立了一般多粒度模糊粗糙集模型。首先,通过定义等价信息系统下的支撑函数分别给出了等价信息系统下的一般多粒度模糊粗糙下近似算子和一般多粒度模糊粗糙上近似算子的定义;其次,为了更好的分析各算子的特性,还讨论了等价信息系统下一般多粒度模糊粗糙下、上近似算子的性质。另外,经过深入探讨分析等价信息系统下一般多粒度模糊粗糙下、上近似算子之间的关系,研究了一般多粒度模糊粗糙集模型粗糙度和精确度的定义及其性质。最后用淘宝购物这一实例更好地说明了一般多粒度模糊粗糙集模型的实际应用价值。

In recent years, the studies of multi-granulation fuzzy rough set and granular computing have become the hottest resear- ches. The generalized multi-granulation fuzzy rough set model based equivalent information system is established by analyzing the relationships between multi-granulation and fuzzy rough set in this paper. Firstly, the general multi-granulation fuzzy rough approxi- mation lower and upper operators are defined by support function which is based on equivalent information system. Secondly, the properties of the approximation operators based on equivalent information system are discussed. What＇s more, the definitions and properties of rough measure and precision are studied. Finally, an example about taobao shopping illustrates the value on practical application of this model.