On the optimal solution of the fuzzy linear systems

• Main Authors: FUH-CHERNG JOU, 周富成
• Other Authors: 劉宣谷
• Format: Others
• Language: zh-TW
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/emy5wd

碩士 === 國立臺北教育大學 === 數學暨資訊教育學系(含數學教育碩士班) === 97 === Summary Fuzzy linear systwms play a major role in various areas, Such as mathematics, physics, statistics, engineering, and social, sciences. Because of that some system’s parameters and measurement in various application are expressed by fuzzy numbers rather than clear numbers, to develop mathematical models and numerical procedures that could suitably analyse and solve general fuzzy linear systems is very important. In this chapter, we apply He's homotopy method to solve fuzzy linear systems, and deduce homotopy series’s convergent condition. Furthermore, we also adapt the Richardson method, the Jacobi method and the Gauss-Seidel method because they are appropriate to choose the splitting matrix. There are some auxiliary parameter and auxiliary matrix we add in the homotopy method. And apply the homotopy perturbation method to find the solution. We use the solution named HPM which involve auxiliary parameter and the auxiliary matrix to solve AX=b and find the approximation From the study we found,It is adaptable to choosing the splitting matrix with Richardson method, the Jacobi method and the Gauss-Seidel method. Moreover, It can converge rapidly when we chosen the appropriate auxiliary matrix. Summary Fuzzy linear systwms play a major role in various areas, Such as mathematics, physics, statistics, engineering, and social, sciences. Because of that some system’s parameters and measurement in various application are expressed by fuzzy numbers rather than clear numbers, to develop mathematical models and numerical procedures that could suitably analyse and solve general fuzzy linear systems is very important. In this chapter, we apply He's homotopy method to solve fuzzy linear systems, and deduce homotopy series’s convergent condition. Furthermore, we also adapt the Richardson method, the Jacobi method and the Gauss-Seidel method because they are appropriate to choose the splitting matrix. There are some auxiliary parameter and auxiliary matrix we add in the homotopy method. And apply the homotopy perturbation method to find the solution. We use the solution named HPM which involve auxiliary parameter and the auxiliary matrix to solve AX=b and find the approximation From the study we found,It is adaptable to choosing the splitting matrix with Richardson method, the Jacobi method and the Gauss-Seidel method. Moreover, It can converge rapidly when we chosen the appropriate auxiliary matrix.