求解模糊线性微分方程组的几何方法
A Geometric Approach to Solve Fuzzy Linear Systems of Differential Equations
AI总结：
提出一种基于线性变换几何表示的新方法，将解视为实向量函数的模糊集，从而求解系数为清晰实数、初始条件为模糊数向量的线性微分方程组。
摘要：
本文研究了具有清晰实数系数和模糊数向量初始条件的线性微分方程组。提出了一种基于线性变换几何表示的新方法来求解。该方法与以往论文中提出的方法最重要的区别在于，解被视为实向量函数的模糊集，而不是模糊向量函数。该集合中的每个成员都以一定的可能性满足给定的系统。结果表明，在任何时刻，解构成坐标空间中的一个模糊区域，其α-截集是嵌套的平行六面体。通过实例对所提出的方法进行了说明。
英文摘要：
In this paper, systems of linear differential equations with crisp real coefficients and with initial condition described by a vector of fuzzy numbers are studied. A new method based on the geometric representations of linear transformations is proposed to find a solution. The most important difference between this method and methods offered in previous papers is that the solution is considered to be a fuzzy set of real vector-functions rather than a fuzzy vector-function. Each member of the set satisfies the given system with a certain possibility. It is shown that at any time the solution constitutes a fuzzy region in the coordinate space, alfa-cuts of which are nested parallelepipeds. Proposed method is illustrated on examples.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
