【摘要】 本文研究了粗糙模糊集的截集性质,粗糙模糊集的上、下近似算子具有保截集性质.在此基础上给出了粗糙模糊集的分解定理,证明了模糊上、下近似算子是其限制在经典集合上算子的典范扩张.最后,利用截集性质简化了模糊集的粗糙度和精度的计算,并给出一个应用实例.更多还原

【Abstract】 In this paper,properties of cut set of rough fuzzy sets are studied.The upper and lower approximation operators of rough fuzzy sets preserve the property of cut set.In this basis,the decomposition theorem of rough fuzzy sets is obtained.It is proved that fuzzy upper and lower approximation operators are the canonical extension of the operators which are the restriction of fuzzy upper and lower approximation operators to crisp sets.Finally,the calculation of roughness and accuracy measure of fuzzy sets is simplified by means of properties of cut set.And an application example is given.更多还原