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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。
By analyzing the relationship between multi-granularity and fuzzy rough set, a general multi-granularity fuzzy rough set model is established. First, we define the definition of approximate operator under generalized multi-granularity fuzzy rough set and the general approximate operator of multi-granularity fuzzy coarse rough set under the equivalent information system by defining the support function under the equivalent information system. Secondly, The properties of each operator are analyzed. The properties of upper approximation operators under general multi-granularity fuzzy rough set are also discussed. In addition, the relationship between the upper and lower approximation operators under the general multi-granularity fuzzy rough set is analyzed and discussed in detail, and the definition and properties of the roughness and precision of the general multi-granular fuzzy rough set model are studied. Finally, the example of Taobao shopping better illustrates the practical value of the general multi-granularity fuzzy rough set model.