可適性模糊系統之語言意義及數值精確性

Linguistic Meaning and Numerical Precision of Adaptive Fuzzy Systems

鄧竣銘(Jiun-Ming Deng)

指導教授 ： 李 穎

元智大學/工程學院/電機與資訊工程研究所/碩士(1997年)

摘要

模糊推論系統的特色在於其輸入輸出關係除了可表示
成數值函數，還可表示為語言型態的Fuzzy If-Then規則。
一般也相信，語言規則可視為是對數值函數較粗略的一種
描述。然而在時序實驗中，我們發現可適性模糊推論系統
實現的數值函數與語言規則描述之間似乎並不配合。因此
本論文定義一新的性能指標 : Dis。以此性能指標量測模
糊推論系統的數值函數與語言規則描述之間的配合程度，
並說明模糊系統在精確性(降低MSE)與語言意義(降低Dis)
間須做一適當的取捨。本論文使用Mackey-Glass Chaotic
Time Series與Box and Jenkins時序預測為例，說明使用
模糊系統的語言意義能對系統參數初值做較佳的設定，並
就參數調整法對可適性模糊推論系統的性能影響做一分析。
我們也對具相似數學結構的FBFN(使用正規化高斯輸入歸屬
函數)與RBFN(使用高斯輸入歸屬函數)之性能做比較，研究
輸入歸屬函數正規化與否對模糊推論系統的性能有何影響。

關鍵字

可適性 ； 語言意義 ； 數值精確性 ； 模糊

並列摘要

The distinctive feature of fuzzy inference systems is that their
input-output relations can not only be described by numerical functions,
but can also be described by linguistic fuzzy If-Then rules. We usually
assume that the linguistic rules provide a rough description of the
numerical function. But in a time series prediction experiment, we discover
that the numerical function and the linguistic rules of an adaptive fuzzy
system may appear to disagree with each other significantly. We thus define
a new performance index : Dis to measure the discrepancy between the
numerical function and the linguistic rules of fuzzy inference systems.
We explain why adaptive fuzzy inference systems have a trade-off between
numerical precision and linguistic meaning. Simulations are performed
using Mackey-Glass Chaotic Time Series and Box & Jenkins Time Series data.
We show that the linguistic meaning of fuzzy inference systems can help
provide better initial values for system parameters. Performance of several
parameter adjustment algorithms for adaptive fuzzy systems are compared.
We also compare the performance of FBFN using normalized Gaussian input
membership functions with that of RBFN using non-normalized Gaussian input
membership functions.

並列關鍵字

Adaptive ； Linguistic Meaning ； Numerical Precision ； Fuzzy

參考文獻

[1]L. A. Zadeh, "Fuzzy Sets," Information and Control, 8, 338-353, 1965.

[2]J.-S. R. Jang, "ANFIS : Adaptive-Network-Based Fuzzy Inference system, "IEEE Trans. On Systems, Man, and Cybernetics, Vo1.23, No.3, pp.665-685, May 1993.

[4]M. C. Mackey and L. Glass, "Oscillation and Chaos in physiological control systems," Science, 197:287-289, July 1997.

[11]S. Chen, S. Mclaughlin and B. Mulgrew, "Complex-valued radial basis function networks , Part1: Network architecture and learning algorithms," Signal Processing, Vol.35, pp.19-13, 1994.

[13]M. Carlin, "An Introduction to Radial Basis Function Networks and Potentional Function Networks," SINTEF Instrumentation, Sep. 1997.