在本論文中，我們將常用於線性參數化迴歸問題中以 Ramsay function為代價函數之M估測器推廣至可應用於非線性迴歸問題之非參數化Ramsay模糊神經網路。我們的重點特別放在這種模糊神經網路抑制離群值之韌性。當面對一般非線性學習問題時，它提供了另一種機器學習的選擇。在本論文中，我們將根據最陡梯度法與重複加權最小平方法提出簡單的權重更新規則。此外，我們將提供一些數值範例用以比較一般模糊神經網路和Ramsay模糊神經網路對於抑制離群值之韌性。經由模擬結果顯示，Ramsay模糊神經網路具有較佳抑制離群值之韌性。

In this thesis, M-estimators with Ramsay’s function used in robust regression theory for linear parametric regression problems will be generalized to nonparametric Ramsay fuzzy neural networks (RFNNs) for nonlinear regression problems. Emphasis is put particularly on the robustness against outliers. This provides alternative learning machines when faced with general nonlinear learning problems. Simple weight updating rules based on incremental gradient descent and iteratively reweighted least squares (IRLS) will be derived. Some numerical examples will be provided to compare the robustness against outliers for usual fuzzy neural networks (FNNs) and the proposed RFNNs. Simulation results show that the RFNNs proposed in this thesis have good robustness against outliers.

誌謝 i
摘要 ii
Abstract iii
圖形與表格目錄 iv
第一章 介紹 1
1.1 動機 1
1.2 論文內容簡述 3
第二章 模糊神經網路 5
2.1 模糊系統 5
2.2 模糊神經網路 11
第三章 Ramsay 模糊神經網路 17
3.1 線性 M 估測器 17
3.2 Ramsay 模糊神經網路 26
3.3 重複加權最小平方法 30
第四章 範例 33
第五章 結論與未來展望 50
參考文獻 52

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