解模糊關係方程式之改良演算法及非線性最佳化問題應用

The Improved Algorithm for Solving Fuzzy Relation Equation and Its Application of Nonlinear Optimization Problem

葉松林(Yeh Sung-Lin)

指導教授 ： 曾煥雯

國立臺灣師範大學/科技學院/應用電子科技研究所/碩士(2006年)

摘要

模糊關係方程式是模糊理論之中的一門學問。當我們去探討模糊關係方程式的逆運算時，變成是一種逆向思考的數學描述。專家思維中將各種因素評估結果與權重分配相結合，就如同模糊關係方程式的逆運算。經由解模糊關係方程式，藉由已知的各種因素評估與整體分析結果，推論出專家思維中的權重分配。
本研究前期以廣泛涉略，通識性基礎的建立，然後開始在有限的領域裡面，做深入的思維與討論。除了對模糊關係方程式詳加說明外，文獻整理與歸納也是本研究重點之一，做到截長補短、去蕪存菁，且容易理解。本研究的貢獻之一是將各種解模糊關係方程式的方法做成表格以便進行比較。
最後本研究提出改良之解模糊關係方程式方法，實驗中證明比文獻方法有更好的解。本改良方法，不僅可有效率的分析，並且實際用演算法於電腦程式上實現。結合模糊關係方程式限制用以解非線性最佳化問題的遺傳演算法亦成功印證本研究方法之可行性，並進行分析與討論。

關鍵字

專家系統 ； 模糊關係方程式 ； 模糊矩陣方程式 ； 遺傳演算法 ； 非線性最佳化

並列摘要

Fuzzy relation equation is one branch of fuzzy theory. When we probe into the inverse operation of fuzzy relation equation, it will become a kind of reverse thinking of mathematical description. Various kinds of factors are estimated the results and combined with weighting assigning in the expert thinking like the inverse operation of fuzzy relation equation. Through solving the fuzzy relation equation, we can infer the weighting assigning of the expert thinking by kinds of factors’ evaluations and whole analysing results that are already known.
This research is to extensively involve and open knowing basic setting-up in early, then to begin to do deeply thinking and discussion inside limited field. Besides going into details about the fuzzy relation equation, it is also one focal points of this research that literatures are put in order and summed up. This research is to draw on the strength of each to offset the weakness of the other, and to get rid of the weed and keep the flower of the leek and understand easily. One of the contributions of this research is to make all kinds of solving methods of fuzzy relation equation into the form in order to compare.
Finally, this research purposes the improved method of fuzzy relation equation, and it proves that the method has better solutions than the method of literatures in the experiment. The improved method not only has very efficient analysis, but also realizes in the computer procedure with the algorithm.
The genetic algorithm for solving nonlinear optimization problem with the fuzzy relation equation constraints is also successfully confirming that the method of this research is feasible. This research is also proceeding to analyze and discuss.

並列關鍵字

Expert system ； Fuzzy relation equation ； Fuzzy matrix equation ； Genetic algorithm ； Non-linear optimization

參考文獻

[1] George J. Klir, Bo Yuan, FUZZY SETS AND FUZZY LOGIC: Theory and Applications, Pearson Education Taiwan, 2005.7.

[2] J.-S. R. JANG, C.-T. Sun, E. Mizutani, Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence, Pearson Education Taiwan, 2004.

[3] Fu Cheng, Tang, “Perturbation techniques for fuzzy matrirx equations”, Fuzzy Sets and Systems, vol. 109, Issue: 3, pp. 363-369, February 1, 2000.

[4] Jianjun Lu, Shu-Cherng Fang, “Solving nonlinear optimization problems with fuzzy relation equation constraints”, Fuzzy Sets and Systems, vol. 119, Issue: 1, pp. 1-20, April 1, 2001.

[5] Leh Luoh, Wen-June Wang, Yi-Ke Liaw, “New algorithm for solving fuzzy relation equations”, Mathematics and Computers in Simulation, vol. 59, Issue: 4, pp. 329-333, June 1, 2002.