解線性模糊等式系統的數值方法

Abstract

第一年：本計畫研究如何求模糊線性系統(FSLE)的解，在此計畫中我們將導出係數矩陣非奇異性的條件，我們將研發以疊代式求FSLE的數值解法。最後為了方便比較，我們採用文獻中出現的例子測試我們的數值方法。第二年：在第二年我們將研究如何求對稱完全模糊線性系統(SFFLE)的解，我們將提出SFFLE的解的定義並導出SFFLE唯一存在一組解的條件。最後將研究以目標線性規畫求SFFLE的解的模型，我們將採用文獻上的範例測試我們所求的數值解。

First Year: This project investigates the solution of fuzzy system of linear equations (FSLE). In this project we will derive the conditions for the singularity of the coefficient matrix. We will develop an iteration method for finding the solution of FSLE. The numerical results will be conducted for some problems which are cited from literature for compare purpose. Second Year: In the second year, we will investigate the solution of symmetric fully fuzzy linear systems (SFFLS). We will propose a definition for the solution of SFFLE and derive the conditions for the existence of a unique solution of a SFFLE. Finally, a goal programming model will be developed for calculating the solution of SFFLE. The numerical results will be carried with the examples cited from the literature.