We prove an analogue of the Donsker theorem under the Lindeberg condition in a fuzzy setting. Specifically, we consider a certain triangular system of d -dimensional fuzzy random variables {Xn,i∗ },$\begin{array}{} \{X_{n,i}^*\}, \end{array}$ n ∈ ℕ and i = 1, 2, …, k n , which take as their values fuzzy vectors of compact and convex α -cuts. We show that an appropriately normalized and interpolated sequence of partial sums of the system may be associated with a time-continuous process defined on the unit interval t ∈ [0, 1] which, under the assumption of the Lindeberg condition, tends in distribution to a standard Brownian motion in the space of support functions.

中文翻译：

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Lindeberg条件下的Donsker模糊不变性原理

我们证明了在Lindeberg条件下模糊设置下Donsker定理的类似物。具体来说，我们考虑d维模糊随机变量{Xn，i ∗}，$ \ begin {array} {} \ {X_ {n，i} ^ * \}，\ end {array} $ n的某个三角系统∈ℕ和i = 1，2，…，kn，它们以紧凑和凸α割的模糊矢量为值。我们表明，适当的归一化和内插的系统的部分和序列可以与在单位间隔t∈[0，1]上定义的时间连续过程相关，在Lindeberg条件下，该过程倾向于分布为支持功能空间中的标准布朗运动。