臺灣博碩士論文加值系統

所謂型態降階即是計算出在第二型模糊集合的質心。經由解模糊化的過程，可以得到在第一型態集合相對應的明確數值結果。型態降階在第二型模糊推論中已經是一項非常重要的過程，因此在第二型模糊系統的應用上，使得型態降階更有效率的執行是一件非常有意義的事情。Liu介紹了α平面的概念，就是一種水平切面表示法，並且提出了對於第二型模糊集合的型態降階方法。其中我們於一些型態降階的有效特性，藉著探索α平面表示法和區間第二型模糊集合的，開發出一個更快速的方法去計算第二型模糊集合的質心，在計算次數和比較次數上有效的減少了，根據結果，型態降階可以更有效率的完成計算和比較次數上的減少。我們將會以數學分析和實驗結果來證明我們所提出的方法是很有效率的。

Type reduction does the work of computing the centroid of a type-2 fuzzy set. The result is a type-1 fuzzy set from which a corresponding crisp number can then be obtained through defuzzification. Type reduction is one of the major operations involved in type-2 fuzzy inference. Therefore, making type reduction efficient is a significant task in the application of type-2 fuzzy systems. Liu introduced a horizontal slice representation, called the α-plane representation, and proposed a type reduction method for a type-2 fuzzy set. By exploring some useful properties of the α-plane representation and of the type reduction for interval type-2 fuzzy sets, we develop a fast method for computing the centroid of a type-2 fuzzy set. The number of computations and comparisons involved is greatly reduced. As a result, type reduction can be done much more efficiently. The effectiveness of the proposed method is analyzed mathematically and demonstrated by experimental results.

摘　要 i
Abstract ii
圖 次 v
表 次 vi
第一章 緒論 1
第一節 研究動機 1
第二節 論文架構 3
第二章 文獻探討 4
第一節 概述 4
第二節 第二型模糊集合 4
第三節 區間第二型模糊集合 6
第四節 增強型Karnik-Mendel演算法 8
第三章 Liu的型態降階方法 11
第一節 α平面表示法 11
第二節 Liu的方法 12
第四章 我們的改良式方法 14
第一節 觀察增強型Karnik-Mendel演算法 14
第二節 觀察Liu的方法 18
第三節 我們的方法 20
第四節 複雜度比較 26
第五章 範例 28
第六章 實驗結果 37
第一節 環境介紹 37
第二節 實驗一 37
第三節 實驗二 43
第七章 結論與未來展望 49
參考文獻 50

[1] O. Castillo and P. Melin, “A new approach for plant monitoring using type-2 fuzzy logic and fractal theory,” International Journal of General Systems, 33(2-3):305.319, 2004.
[2] O. Castillo and P. Melin, “Comparison of hybrid intelligent systems, neural networks and interval type-2 fuzzy logic for time series prediction,” In International Joint Conference on Neural Networks, pages 3086.3091, 2007.
[3] J. R. Castro, O. Castillo, P. Melin, and A. Rodr guez-D z, “A hybrid learning algorithm for a class of interval type-2 fuzzy neural networks,” Information Sciences, 179(13):2175.2193, 2009.
[4] N. Cazares-Castro, L. Aguilar, and O. Castillo, “Designing type-2 fuzzy logic system controllers via fuzzy lyapunov synthesis for the output regulator of a servomechanism with nonlinear backlash,” In IEEE International Conference on Systems, Man and Cybernetics, pages 268.273, 2009.
[5] N. R. Cazarez-Castro, L. T. Aguilar, and O. Castillo, “Hybrid genetic-fuzzy optimization of a type-2 fuzzylogic controller,” In International Conference on Hybrid Intelligent Systems, pages 216–221, 2008.
[6] S. Coupland and R. John, “A fast geometric method for defuzzification of type-2 fuzzy sets,” IEEE Transactions on Fuzzy Systems, 16(4):929–941, 2008.
[7] L. Di Lascio, A. Gisolfi, and A. Nappi, “Medical differential diagnosis through type-2 fuzzy sets,” In IEEE International Conference on Fuzzy Systems, pages 371–376, 2005.
[8] H. Hagras, “A hierarchical type-2 fuzzy logic control architecture for autonomous mobile robots,” IEEE Transactions on Fuzzy Systems, 12(4):524–539, 2004.
[9] R. I. John, P. R. Innocent, and M. R. Barnes, “Neurofuzzy clustering of radiographic tibia image data using type 2 fuzzy sets,” Information Sciences, 125(1-4):65–82, 2000.
[10] N. N. Karnik and J. M. Mendel, “Centroid of a type-2 fuzzy set,” Information Sciences, 132(1-4):195–220, 2001.
[11] G. J. Klir and B. Yuan. Fuzzy sets and fuzzy logic: theory and applications. Prentice-Hall, Inc., Upper Saddle River, NJ, USA, 1995.51
[12] Q. Liang and J. Mendel, “Interval type-2 fuzzy logic systems,” In IEEE International Conference on Fuzzy Systems, volume 1, pages 328–333, 2000.
[13] F.-J. Lin and P.-H. Chou, “Adaptive control of two-axis motion control system using interval type-2 fuzzy neural network,” IEEE Transactions on Industrial Electronics, 56(1):178–193, 2009.
[14] F. Liu, “An efficient centroid type-reduction strategy for general type-2 fuzzy logic system,” Information Sciences, 178(9):2224–2236, 2008.
[15] L. Lucas, T. Centeno, and M. Delgado, “General type-2 fuzzy inference systems: Analysis, design and computational aspects,” In IEEE International Conference onFuzzy Systems, pages 1–6, 2007.
[16] L. A. Lucas, T. M. Centeno, and M. R. Delgado, “Land cover classification based
on general type-2 fuzzy classifiers,” International Journal of Fuzzy Systems, 10(3):207–216, 2008.
[17] R. Mart nez, O. Castillo, and L. T.Aguilar, “Optimization of interval type-2 fuzzy
logic controllers for a perturbed autonomous wheeled mobile robot using genetic algorithms,” Information Sciences, 179(13):2158–2174, 2009.
[18] P. Melin and O. Castillo, “An intelligent hybrid approach for industrial quality control combining neural networks, fuzzy logic and fractal theory,” Information Sciences, 177(7):1543–1557, 2007.
[19] J. Mendel. Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions. Prentice-Hall, Inc., Upper Saddle River, NJ, USA, 2001.
[20] J. Mendel, “Computing derivatives in interval type-2 fuzzy logic systems,” IEEE Transactions on Fuzzy Systems, 12(1):84–98, 2004.
[21] J. Mendel, “Type-2 fuzzy sets and systems: an overview,” IEEE Computational Intelligence Magazine, 2(1):20–29, 2007.
[22] J. Mendel and R. John, “Type-2 fuzzy sets made simple,” IEEE Transactions on Fuzzy Systems, 10(2):117–127, 2002.
[23] J. Mendel, R. John, and F. Liu, “Interval type-2 fuzzy logic systems made simple,” IEEE Transactions on Fuzzy Systems, 14(6):808–821, 2006.
[24] J. M. Mendel, “Advances in type-2 fuzzy sets and systems,” Information Sciences, 177(1):84–110, 2007.
[25] H. B. Mitchell, “Pattern recognition using type-II fuzzy sets,” Information Sciences, 170(2-4):409–418, 2005.
[26] T. Ozen and J. M. Garibaldi, “Investigating adaptation in type-2 fuzzy logic systems applied to umbilical acidbase assessment,” In European Symposium on Intelligent Technologies, Hybrid Systems and Their Implementation on Smart
Adaptive Systems, pages 289–294, 2003.
[27] R. Sep′uveda, O. Castillo, P. Melin, A. Rodr′ıguez-D′az, and O. Montiel, “Experimental study of intelligent controllers under uncertainty using type-1 and type-2 fuzzy logic,” Information Sciences, 177(10):2023–2048, 2007.
[28] W.-W. Tan and D. Wu, “Design of type-reduction strategies for type-2 fuzzy logic systems using genetic algorithms,” In L. C. Jain, V. Palade, and D. Srinivasan,editors, Advances in Evolutionary Computing for System Design, pages 169–187, Springer, 2007.
[29] D. Wu and J. M. Mendel, “Enhanced Karnik-Mendel algorithms,” IEEE Transactions on Fuzzy Systems, 17(4):923–934, 2009.
[30] L. A. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning–I,” Information Sciences, 8(3):199–249, 1975.
[31] M. F. Zarandi, B. Rezaee, I. Turksen, and E. Neshat, “A type-2 fuzzy rule-based expert system model for stock price analysis,” Expert Systems with Applications,36(1):139–154, 2009.
[32] J. Zeng and Z.-Q. Liu, “Type-2 fuzzy Markov random fields and their application to handwritten chinese character recognition,” IEEE Transactions on Fuzzy Systems, 16(3):747–760, 2008.