在資料的處理上，利用一些已知的資料來建立規則基底的分類系統是很重要研究範疇。已有許多論文提出使用基因演算法來設計更有效率的分類系統。而本篇論文提出以三層的控制基因和退火演算法來建立模糊分類系統並使用較少的模糊規則。
在規則的選取問題上有三大目標：(1)最多的正確分類樣本、(2)使用較少的模糊規則和(3)使用較少的輸入特徵。基因演算法便是用來解決這個選取問題。我們將模糊規則編碼成二進位的字串而這一長串的字串就代表基因演算法中的一個個體。接著利用適應函數來計算每個個體的適應函數值。而適應函數的設計就是來自於以上所提出的三個目標。在利用退火演算法與三層的基因演算法做結合，可以更有效率的選取某一層的控制基因。
在實際的執行上，我們將已知的資料取一半作為訓練用而另一半為測試用。在實驗中，我們主要是以規則性的iris和不規則性的spiral兩組資料為主。經由實驗我們可以看出我們所提出的方法確實能以較少的模糊規則得到較佳辨識的結果。

Building a rule-based classification system for a training data set is an important research topic in the area of data mining, knowledge discovery and expert systems. Recently, the GA-based fuzzy approach is shown to be an effective way to design an efficient evolutionary fuzzy system. In this thesis a three layers genetic algorithm with Simulated Annealing for selecting a small number of fuzzy if-then rules to building a compact fuzzy classification system will be proposed.
The rule selection problem with three objectives: (1) maximize the number of correctly classified patterns, (2) minimize the number of fuzzy if-then rules, and (3) minimize the number of required features. Genetic algorithms are applied to solve this problem. A set of fuzzy if-then rules is coded into a binary string and treated as an in-dividual in genetic algorithms. The fitness of each individual is specified by three ob-jectives in the combinatorial optimization problem. Simulated annealing (SA) is op-tionally cooperated with three layers genetic algorithm to effectively select some layer control genes.
The performance of the proposed method for training data and test data is ex-amined by computer simulations on the iris data set and spiral data set, and comparing the performance with the existing approaches. It is shown empirically that the pro-posed method outperforms the existing methods in the design of optimal fuzzy sys-tems.

Abstract Ⅰ
List of Tables Ⅳ
List of Figures Ⅴ
Symbol Table Ⅵ

1 Introduction 1

2 Fuzzy System 4
2.1 Fuzzy Sets and Basic Operations on Fuzzy Set 5
2.2 Fuzzy Relations 7
2.3 Linguistic Variables and Fuzzy IF-THEN Rules 8
2.4 Fuzzy Rule Base and Fuzzy Inference Engine 9
2.5 Fuzzifiers and Defuzzifiers 11
2.6 Fuzzy Clustering 13

3 Genetic Algorithms 17
3.1 Chromosome Representation 18
3.2 Fitness Function 18
3.3 Selection 19
3.4 Crossover 20
3.5 Mutation 21
3.6 Parameter Gene and Control Gene 22

4 GA Based Fuzzy Classifier 23
4.1 Fuzzy Partition 23
4.2 Fuzzy Classification Method with Fuzzy IF-THEN Rules 24
4.3 Fitness Function 29
4.4 Chromosome Representation 29
4.4.1 Grid Partition 29
4.4.2 Scatter Partition 31
4.5 Simulated Annealing 32
4.6 Combine GA and SA 33

5 Pformance 35
5.1 The Iris Data Set 35
5.1.1 Grid partition without SA 35
5.1.2 Scatter partition without SA 36
5.1.3 Scatter partition with SA 37
5.2 The Spiral Data Sets 41

6 Conclusion 44

Reference 45

Reference

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