一阶线性模糊微分方程的模糊结构元解法

Solution algorithm of first order linear fuzzy differential equations using fuzzy structuring element

文章利用模糊结构元原理,研究了一阶线性模糊微分方程的模糊初值问题,证明了方程解的存在性和唯一性条件,给出了解的模糊结构元的解析表达形式,讨论了同其他求解方法之间的关系。结果表明,模糊结构元方法是研究模糊微分方程的一个有效工具。

In this paper, the fuzzy initial conditions of first order linear fuzzy differential equations are studied by utilizing the theory of fuzzy structuring element. The existence and uniqueness of the solu- tion for fuzzy differential equations are proved, the analytical expression of the solution is given based on the fuzzy structuring element and the relationship between the proposed solution and other inter- pretations is discussed. It is concluded that the method of fuzzy structuring element is an effective tool for solving fuzzy differential equations.