一类线性模糊常微分方程的模糊结构元解法

Solution algorithm of linear fuzzy ordinary differential equations using fuzzy structuring element

基于扩张原理建立起来的模糊值函数以及微积分在表述上存在着遍历性的困难,使得模糊微分方程求解变得异常困难,模糊结构元方法有效地解决了模糊数和模糊值函数以及微积分表述上的困难。利用模糊值函数分析学的模糊结构元表述理论,讨论了模糊常微分方程求解的模糊结构元方法,对于一类线性模糊常微分方程的通解给出了基于模糊结构元的表达形式,并结合实例进行说明。结论表明,模糊结构元方法简化了计算,在求解一类线性模糊微分方程时显得简单,同时也能给出解的解析表达形式,说明了模糊结构元方法是克服模糊微分方程求解困难的一个有效的工具。

There are some difficulties in expressing calculus and fuzzy-value functions which is based on fuzzy extension principle. Also it becomes difficult to obtain a solution for fuzzy differential equations. However, fuzzy structured element can be used to denote the calculus of fttzzy-value function, and avoid ergodic problem. In this paper, a fuzzy structured element solution algorithm for linear fuzzy ordinary differential equations is investigated based on the theory of fuzzy structured element in fuzzy-valued function and calculus. The paper presents the expression of the general solution of linear fuzzy ordinary differential equations. The case study demonstrates that the fuzzy structured element method simplifies the calculation of fuzzy differential equation. In particular, the solution is analytical. It concludes that the fuzzy structured element method is an effective mean for solving the fuzzy differential equation.