Abstract This article introduces the notion of strong linear independence (SLI) for a set of fuzzy numbers. Based on this notion, we prove that there exist isomorphisms between R n and special classes of fuzzy numbers generated by SLI sets of n fuzzy numbers. Such a bijection can be used to induce the structure of Banach space on its range. We prove that the finite SLI sets are dense in the set of finite fuzzy numbers. Moreover, we proposed two methods to produce SLI sets based on consecutive powering hedges and Zadeh extension of polynomials.

中文翻译：

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由强线性无关模糊数生成的巴拿赫空间

摘要 本文介绍了一组模糊数的强线性独立性（SLI）的概念。基于这个概念，我们证明了 R n 与由 n 个模糊数的 SLI 集合生成的特殊类别的模糊数之间存在同构。这种双射可用于在其范围内归纳 Banach 空间的结构。我们证明了有限SLI集在有限模糊数集中是稠密的。此外，我们提出了两种基于连续供电对冲和多项式的 Zadeh 扩展来生成 SLI 集的方法。