Abstract The present paper is concerned with the solutions of first-order linear fuzzy differential equations under the condition of LC-differentiability. Motivated by the fact that the structure of the space of linearly correlated fuzzy numbers strongly depends on the symmetry of the basic fuzzy number, here we address first-order linear fuzzy differential equations by distinguishing whether the basic fuzzy number is symmetric or not. In the non-symmetric case, a first-order linear fuzzy differential equation may be transformed into an equivalent system of ordinary differential equations related to the representation functions of the linearly correlated fuzzy number-valued function. In the symmetric case, according to the monotonicity of the diameter of the fuzzy solution, a first-order linear fuzzy differential equation may be transformed into a system of ordinary differential equations associated with the representation functions of the canonical form of the linearly correlated fuzzy number-valued function. In addition, using our extension method one may obtain solutions with either increasing or decreasing diameters. Several examples are provided in order to illustrate the proposed method.

中文翻译：

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线性相关模糊数空间上的一阶线性模糊微分方程

摘要 本文研究了LC可微性条件下一阶线性模糊微分方程的解。由于线性相关模糊数的空间结构强烈依赖于基本模糊数的对称性这一事实，我们在这里通过区分基本模糊数是否对称来解决一阶线性模糊微分方程。在非对称情况下，可以将一阶线性模糊微分方程转化为与线性相关模糊数值函数的表示函数相关的常微分方程的等价系统。在对称情况下，根据模糊解直径的单调性，可以将一阶线性模糊微分方程转换为与线性相关模糊数值函数的规范形式的表示函数相关联的常微分方程组。此外，使用我们的扩展方法可以获得增加或减少直径的解决方案。提供了几个例子来说明所提出的方法。