半连续模糊映射的性质

Properties of Semicontinuous Fuzzy Mapping

利用模糊数参数形式的概念,重新定义由Bao和Wu提出的上下半连续映射的概念.在由Goetschel和Voxman提出的模糊数的线性准则基础上,证明了在n维欧式空间Rn的一个非空开区间里,存在一个有界闭集,使得上半连续模糊映射是有界的;同样的在n维欧式空间Rn的一个非空开区间里,存在一个有界闭集,使得下半连续模糊映射是有界的.

By using the concept of parameter form of fuzzy number, this paper redefines the concept of upper and lower semicontinuous mapping proposed by Bao and Wu, based on linear norm of fuzzy number introduced by Goetsehel and Voxman, proves that in a nonempty open interval of n-dimensional Euclidean space Rn, there is a bounded closed set which makes upper semicontinuous fuzzy mapping be bounded, and that in a nonempty open interval of n-dimensional Euclidean space Rn, there is a bounded closed set which makes lower semicontinuous mapping be bounded