臺灣博碩士論文加值系統

本論文是以模糊超立方體（Fuzzy hypercube）為基礎，從資料中自動建立模糊規則庫應用於分類系統上，並以數個範例加以實驗測試以證明此演算法的正確性。
論文中所提出的方法是先輸入所有的訓練資料，並記錄下各類別
每一個輸入變數的最小和最大值來建立包圍類別區域的超立方體。接著測試這些超立體之間是否重疊，若沒有表示此資料分佈可以被直線分割，若有則對於重疊區域內的資料依其分佈動態建立屬於各類的聚集。最後再針對每個超立方體建立模糊規則來描述以達到分類的效果。我們的想法即是對於資料分佈較明確較密集的地方使用大的超立方體來減少其規則數，而資料較分散不確定的地方則以較小的超立方體來近似以提升分類的正確性。
本論文所提出之方法訓練系統和決策分類的時間都相當短，而且和其他方法的分類結果比較起來也有較佳的效果。

This thesis proposed a new method for extracting fuzzy rules directly from numerical data for pattern classification. First, we represent the existence region of data for a class by activation hypercube and define the overlapping region of each activation hypercube by inhibition hypercube to inhibit the existence of data for that class. Then, we generate dynamic cluster for the data that exist in the inhibition hypercube. Our fuzzy classifier composed of fuzzy rules that are described by these hypercubes. Finally, some examples are given to demonstrate the performance and the validity of this algorithm.

摘 要 I
ABSTRACT II
誌 謝 III
圖 索 引 IV
表 索 引 V
目 錄 VI
第一章 緒論 1
1.1 研究動機 1
1.2 研究目的及方法 3
1.3 內容大綱 4
第二章 資料分類的介紹 5
2.1 理想分類系統的特性 6
2.2 分類的方法 8
2.3 分類器的效能評估 10
2.4 樣本空間正規化 12
第三章 模糊集合和模糊超立方體的介紹 13
3.1 模糊集合 14
3.2 模糊邏輯 17
3.3模糊推論（Fuzzy Inference） 19
3.4 解模糊化（Defuzzification） 22
3.5 模糊超立方體表示法 23
3.5.1模糊超立方體歸屬函數 23
3.5.2 模糊超立方體的規則推論 24
第四章 研究方法 26
4.1 建立作用超立方體 28
4.2 決定抑制超立方體 29
4.3 動態產生聚集的演算法 32
4.3.1 聚集擴張 34
4.3.2 重叠測試 35
4.3.3 聚集分割 36
第五章 實驗結果與比較 39
5.1 範例一：自行建立的資料 39
5.2 範例二：酒的資料（Wine data） 41
5.3 範例三：蝴蝶花資料（Iris data） 45
5.4 範例四：甲狀腺資料（Thyroid data） 47
5.5 範例五：美國威斯康辛州乳癌診斷資料庫（Wisconsin Breast Cancer Diagnostic Database） 50
5.6 範例六：玻璃資料（glass data） 52
第六章 結論 54
參考文獻 56

[1]P. K. Simpson, “Fuzzy min-max neural networks─Part 1：Classification,” IEEE Trans. Neural Network, vol. 3, pp. 776-786, Sept. 1992.
[2]B. Gabrys and A. Bargiela, “General Fuzzy Min-Max Neural Network for Clustering and Classification,” IEEE Trans. Neural Network, vol. 11, no. 3, pp. 769-783, May 2000.
[3]S. Abe and M-S. Lan, “A Method for Fuzzy Rules Extraction Directly from Numerical Data and Its Application to Pattern Classification,” IEEE Trans. Fuzzy Systems, vol. 3, No. 1, Feb 1995.
[4]J. C. Bezdek, Fuzzy Mathematics in Pattern Classification. Phd thesis, Applied Math. Center, Cornell University, Ithaca, 1973.
[5]S. E. Papadakis and J. B. Theocharis, “A GA-based fuzzy modeling approach for generating TSK models,” FUZZY Set And Systems, pp. 1-32, 2002.
[6]S. Abe “Training of Fuzzy Classifier with Ellipsoidal Regions by Dynamic Cluster Generation,” Second International Conference on Knowledge-Based Intelligent Electronic Systems, pp. 21-23, April. 1998.
[7]L. Zadeh, “Fuzzy sets,” Inform. and Control, vol. 8, pp. 338-353, 1965.
[8]I. H. Suh, J. —H. Kim and F. C. —H. Rhee, “Convex-set-based fuzzy clustering,” IEEE Trans. On Fuzzy Systems, vol. 7, no. 3, pp. 271-285, jun. 1999.
[9]P. J. Werbos, “Beyond regression：New tools for prediction and analysis in the behavioral sciences,” Doctoral dissertation, Harvard University, 1974.
[10]H. M. Lee, C. M. Chen, J. M. Chen, and Y. L. Jou, “An efficient fuzzy classifier with feature selection based on fuzzy entropy,” IEEE Trans. Syst., Man, Cybern., Vol. 31, No. 3, June 2001.
[11]K. Nozaki, H. Ishibuchi and H. Tanaka, “Adaptive Fuzzy Rule-Based Classification Systems,” IEEE Trans. Fuzzy Systems, vol. 4, No. 3,Aug. 1996.
[12]S. Abe and M-S. Lan “Fuzzy rules extraction directly from numerical data for function approximation,” IEEE Trans. Syst., Man, Cybern., vol. 25, pp. 119—129,Jan. 1995.
[13]J. -S. R. Jang “ANFIS: Adaptive-network-based fuzzy inference system,” IEEE Trans. Syst., Man, Cybern., vol. 23, pp. 665—685, May/June 1993.
[14]S. L. Chiu, “Fuzzy model identification based on cluster estimation,” J.Intell. Fuzzy Syst., vol. 2, pp. 267—278, 1994.
[15]L. -X. Wang and J. M. Mendel, “Generating fuzzy rules by learning from examples,” IEEE Trans. Syst., Man, Cybern., vol. 22, pp. 1414—1427,Nov./Dec. 1992.
[16]F. Uebele, S .Abe, and M-S. Lan, “A Neural Network-Based Fuzzy Classifier,” IEEE Tran. Systems,Man,and Cybernetics, vol. 25, no. 2, pp. 353-361,1995.
[17]M. T. Musavi, W. Ahmed, K. H. Chan, K. B. Faris, and D. M. Hummels, “On the Training of Radial Basis Function Classifiers,” Neural Networks, vol. 5, no. 4, pp. 595-603,1992.
[18]S. Abe, Neural Networks and Fuzzy Systems: Theory and Applications, Kluwer Academic, Boston, 1996.
[19]S. Abe, and R. Thawonmas, “A Fuzzy Classifier with Ellipsoidal Regions,” IEEE, Trans. Fuzzy Systems, vol. 5, no. 3, pp. 358-368, 1997.
[20]T. Takigawa, T. Shimozaki and S. Abe, “Training a fuzzy classifier with Polyhedral regions,” IEEE Neural Networks, vol. 2, pp. 1350-1355, 2001.
[21]D. E. Goldberg, Genetic Algorithm in Search, Optimization, and Machine Learning. Reading, MA:Addison-Wesley, 1989.
[22]H. Ishibuchi, T. Nakashima and T. Murata, “Performance evaluation of fuzzy classifier systems for multidimensional pattern classification problems,” IEEE Trans. Syst., Man, Cybern., vol. 29, NO. 5, Oct. 1999.
[23]A. L. Corcoran and S. Sen, “Using real-valued genetic algorithms to evolve rule sets for classification,” in Proc. 1st IEEE Conf. Evolut. Computat., Orlando, FL, June 1994, pp. 120—124.
[24]F. Rosenblatt, “The perceptron：A probabilistic model for information storage and organization in the brain,” Psychological Review, vol. 65, pp. 386-408, 1958.
[25]S. Salzberg, “A nearest hyperrectangle learning method,” Mach. Learn., vol. 6, no. 3, pp. 251—276, May 1991.
[26]蘇木春、張孝德，“機器學習：類神經網路、模糊系統以及基因演算法則”，全華科技圖書，民國八十八年。
[27]孫宗瀛、楊英魁，“Fuzzy控制：理論、實作與應用”，全華科技圖書，民國八十三年。
[28]Joseph Giarratano and Gary Riley, “Expert Systems：Principles and Programming,” PWS-KENT Publishing Company,1989.
[29]E. H. Mamdani, “Application of fuzzy logic to approximate reasoning using linguistic synthesis,” IEEE Trans. Computer, Vol. C-26,1977.
[30]L. A. Zadeh, “Outline of a new approach to the analysis of complex and systems and decision processes,” IEEE Trans. Syst. Man, Cybern., vol 3, n0. 1, pp. 28-44, 1973.
[31]C. C. Lee. “Fuzzy Logic in Control Systems： Fuzzy Logic Controller Part I, II,” IEEE Tran. Syst. Man, Cybern. Vol. 20 1990.