以奇異值調整法簡化模糊類神經網路

Abstract

摘要 本論文提供一種縮減規則庫的方法來提升模糊類神經網路的效能。其核心理論為藉由調整由輸入輸出向量構成之模糊類神經網路矩陣的奇異值來改變輸入輸出之間的關係。我們稱此方法奇異值調整法。此方法可避免隨著輸出情況的高度複雜化而來之規則庫增加的問題。因此模糊類神經網路將有更好的效率。另外，因為模糊類神經網路是以小的規則庫來運作，其對應到規則庫的權重值可以很容易地以最小平方法得到。因此，模糊類神經網路對於輸出情況的變化將有更迅速的反應。我們藉由幾個例子來分析其誤差。所得到的結果證實由簡化過的規則庫仍可將精確度維持在很高的水平，因而大幅提升了模糊類神經網路的效率。

ABSTRACT The main purpose of this paper is to enhance the efficiency of a fuzzy neural network (FNN) by proposing a new training methodology with rule reduction. The core of this methodology is to modify the input-output relations by updating the singular value set associated with the FNN matrix, which is composed of the rule vectors and desired output vectors. We name it for Singular Value Regulation (SVR). By adopting this method, the FNN can have a better efficiency owing to it is free from extension of rule base, which often accompanies with high complexity of the situation described by the desired output. In addition, updating the weighting factor set associated with the rule base can be easily determined using least square method since the FNN often performs with a small size of rule base. Therefore, the FNN can have an instant response of the alternation of the output situation. Error analysis has been performed with illustrated examples. The outcome shows that the precision can be well maintained with the simplified rule base so that the efficiency of FNN is greatly enhanced.