模糊线性系统解空间的结构

Structure of solution spaces of fuzzy linear systems

使用代数的方法研究了模糊线性系统解空间的结构.类似于普通实数的线性系统,齐次模糊线性系统的解空间是Rn的一个线性子空间,非齐次模糊线性系统的一个解加上对应齐次模糊线性系统的解仍然是该非齐次模糊线性系统的解,但是非齐次模糊线性系统的所有解并不能由此非齐次模糊系统的一个特解加上对应的齐次模糊线性系统的通解得到.特别的,如果一个三角模糊线性系统有非三角模糊解向量,那它也有三角模糊解向量.

Structure of solution spaces of fuzzy linear systems was discussed by using algebraic method. Similar to the usual crisp linear systems, the solution space of homogeneous fuzzy linear system is a linear subspace of R^n. A solution of non-homogeneous fuzzy linear system was added to a solution of corresponding homogeneous one is also a solution of the non-homogeneous. However, all of solutions of nonhomogeneous fuzzy linear system cannot be obtained by adding a solution of non-homogeneous fuzzy linear system to the usual solution of the corresponding homogeneous one. Especially, if a triangular fuzzy linear system has non-triangular fuzzy vector solution, then it has triangular fuzzy vector solution as well.