模糊数的替代视角及其在模糊微分方程中的应用
Alternative views on fuzzy numbers and their application to fuzzy differential equations
AI总结：
本文从 $α$-水平集的两种参数表示研究模糊值函数，引入新概念并探讨模糊微分方程与 Zadeh 扩展原理及广义 Hukuhara 导数的关系，证明了存在性与唯一性定理。
摘要：
我们考虑来自 $α$-水平集两种参数表示的模糊值函数。引入新概念并与现有概念进行比较。遵循这两种方法，我们研究模糊微分方程。讨论了它们与 Zadeh 扩展原理和广义 Hukuhara 导数的关系。此外，我们证明了模糊微分方程的存在性与唯一性定理。给出了说明性示例。
英文摘要：
We consider fuzzy valued functions from two parametric representations of $α$-level sets. New concepts are introduced and compared with available notions. Following the two proposed approaches, we study fuzzy differential equations. Their relation with Zadeh's extension principle and the generalized Hukuhara derivative is discussed. Moreover, we prove existence and uniqueness theorems for fuzzy differential equations. Illustrative examples are given.
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