期刊信息
- 刊名： 河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
- 主办： 河北师范大学
- ISSN： 1000-5854
- CN： 13-1061/N
- 中国科技核心期刊
- 中国期刊方阵入选期刊
- 中国高校优秀科技期刊
- 华北优秀期刊
- 河北省优秀科技期刊
The Solution Concept and Quality of Systems of Linear Equations with Fuzzy Number-valued Coefficients
摘要/Abstract
介绍了有关的研究背景,说明模糊数矩阵方程组x=Ax+b与(I-A)x=b的等价性.对模糊数线性方程组当系数矩阵为方的且非奇异时,给出方程组的6种解的形式,并说明其中5种具有一致性.当系数矩阵行列任意时,借助广义逆给出了解的定义,证明了此定义的合理性,并验证了此解与前人给出的解是一致的.最后给出最小范数解、最小二乘解和最小范数最小二乘解的定义形式.
The relative background of the study is introduced,and the linear equations with fuzzy number x=Ax+b与(I-A)x=b being equal explained.When the fuzzy matrix of the linear equations is square and non-singular,five of the six solutions are identical;when the fuzzy matrix is arbitrar,generalized inverses is used to define the solution of the equations and prove that it is reasonable.In addition,the study verifies that this def inition is identical with formers.Lastly,it provides three other forms of solution:least norms solution,least squares solut ion and least norms-squares solution.