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研究生:蔡金川
研究生(外文):Chin-Chuan Tsai
論文名稱:模糊關係方程式的模糊矩陣可解條件探討
論文名稱(外文):A Discussion on Feasible Conditions of Fuzzy Matrix in Fuzzy Relation Equation
指導教授:劉俞志劉俞志引用關係
學位類別:碩士
校院名稱:元智大學
系所名稱:資訊管理學系
學門:電算機學門
學類:電算機一般學類
論文種類:學術論文
論文出版年:2008
畢業學年度:96
語文別:中文
論文頁數:31
中文關鍵詞:最大-乘積運算模式模糊關係方程式模糊矩陣一致性
外文關鍵詞:max-product compositionFuzzy relation equationFuzzy matrixConsistency
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模糊關係方程式問題已被廣泛應用於各種實務領域中,亦有非常多的文獻就其求解的方式或最佳化進行探討,模糊關係方程式的應用已融入我們日常生活當中,且不斷地蓬勃發展。
模糊關係方程式求解的探討文獻很多,但尚無研究探討可行解之條件,本文期望透過檢視與調整最大-乘積運算模式(max-product composition)的模糊關係方程式中模糊矩陣,先行知悉該方程式有無可行解及如何調整成可解的數值,並藉由實例驗證,讓我們對最大-乘積運算模式的模糊關係方程式的結構及求解的程序有更深入的瞭解。
本文另外針對尋求一致性多重模糊關係方程式求解規則亦進行探討,期望藉由尋求其”一致性”(Consistency)來加速求解過程。
Fuzzy Relation Equation has been widely applied into various pedagogical fields. There is plenty of literature on the discussions of ways of solutions or optimizations. The Fuzzy Relation Equation has not only been widely used in our daily life but also developed constantly and prosperously.
Many documents about the solutions to Fuzzy Relation Equation can now be found, but yet there is still no research on feasible conditions so far. Therefore, the purpose of this study is to examine and adjust the fuzzy matrix in Fuzzy Relation Equation among max-product composition in order to find out if there are possible solutions to this equation and the ways to revise and meet the desired computations. Besides, through some practical examples, it is expected to reach a better understanding of the structure of Fuzzy Relation Equation among max-product composition and its solving process.
In addition, this research also intends to seek the consistent rules when solving multiple fuzzy relations. It is hoped that through the discussion and searching of “Consistency,” the process of satisfying the equation can be facilitated.
書名頁 ………………………………………………………………… i
論文口試委員審定書 ………………………………………………… ii
授權書 ………………………………………………………………… iii
中文摘要 ……………………………………………………………… iv
英文摘要 ……………………………………………………………… v
誌謝 …………………………………………………………………… vi
目錄 …………………………………………………………………… vii
表目錄 ………………………………………………………………… viii
圖目錄 ………………………………………………………………… ix
第一章 緒論 ………………………………………………………… 1
第二章 文獻探討 …………………………………………………… 3
2.1 模糊關係方程式 …………………………………………… 3
2.2 模糊關係方程式的應用與求解 …………………………… 4
第三章 模糊矩陣可解條件探討 …………………………………… 8
3.1 模糊關係方程式數學模式 ………………………………… 8
3.2 模糊矩陣檢視與調整步驟 ………………………………… 10
第四章 實例驗證 …………………………………………………… 15
第五章 一致性多重模糊關係方程式最佳化探討 ………………… 22
第六章 結論與建議 ………………………………………………… 27
6.1 結論 ………………………………………………………… 27
6.2 未來研究建議 ……………………………………………… 27
參考文獻 ……………………………………………………………… 28
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