■_0(R^m)中Fuzzy级数的收敛性

On the Convergence of Fuzzy Series on ■_O(R^m)

[1]～[4]讨论了■_0(R^1)中Fuzzy级数的收敛性,及收敛的Fuzzy级数的各种基本性质。本文研究■_0(R^m)中Fuzzy级数的收敛性。由于ccR^1可以等距嵌入到一个二维实线性赋范空间RccR^1中去,故关于■_0(R^1)中Fuzzy级数的收敛性质的讨论基本上可以化成对由端点函数构成的两个数项级数的相应性质的讨论。在论域为R^m时,ccR^m却不能嵌入到某个有限维线性赋范空间中去,故讨论自然要困难一些。本文证明了,■_0(R^1)中Fuzzy级数所具有的各项基本性质同样为■_0(R^m)中Fuzzy级数所具有。

The various conergence properties of fuzzy series on ■_O(R') have been discussed in [1]～[4]. In this paper the same properties arc discussed when the serie are on ■_O(R^m) instead of ■_O(R^m). It is proved in the paper that the basic convergence properties of fuzzy series on ■_O(R') are also possessed by the fuzzy series on ■_O(R^m).