关于模糊数的其他观点及其在模糊微分方程中的应用

arXiv - MATH - General Mathematics Pub Date : 2024-06-29 DOI:arxiv-2407.07906

Akbar H. Borzabadi, Mohammad Heidari, Delfim F. M. Torres

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摘要

我们考虑了来自$α-级集的两个参数表示的模糊带值函数。我们引入了新的概念，并将其与现有的方法进行了比较。根据提出的两种方法，我们研究了模糊微分方程。讨论了它们与 Zadeh 扩展原理和广义赫库哈拉导数的关系。此外，我们还证明了模糊微分方程的存在性和唯一性定理。并给出了说明性的例子。

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Alternative views on fuzzy numbers and their application to fuzzy differential equations

We consider fuzzy valued functions from two parametric representations of $\alpha$-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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arXiv - MATH - General Mathematics

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