運用統計和分群演算法定義模糊集個數

Determining fuzzy sets: empirical studies on statistical and clustering approaches

謝承廷(Hsieh, Cheng-Ting)

指導教授 ： 柯士文

中原大學/電機資訊學院/資訊工程研究所/碩士(2016年)

https://doi.org/10.6840/cycu201600114

摘要

隨著模糊理論的發展，在模糊控制中模糊集的數量是影響控制決策的因素，因此我們透過資料的分佈找出適合的模糊集數量及劃分方法是本實驗最主要的目的。本實驗提供了評估的方法，將規則推理的結果透過不同精簡化的等級來評估模糊集個數估計方法及模糊劃分，由於精簡化是依據亂度而將規則做合併，因此從規則數量及準確率的改變，可以發現準確率下降越少，規則數量下降越多，表示此一方法的模糊集個數及模糊劃分是適合此資料集的。
實驗中比較Fuzzy C-Means(FCM)、Hierarchical Fuzzy Partitioning(HFP)和Regular三種的模糊劃分後，再分別估計Partition Entropy(PE)、Information Gain(IG)、Relief-F(RF)、Wang & Mendel(WM)四種模糊集個數。資料集是從UC Irvine Machine Learning Repository(UCI)中以數值屬性(Numerical)和類別結果(Classification)的資料，由FisPro做模糊劃分。用Fuzzy Decision Trees(FDT)、Wang and Mendel(WM)來產生規則，並以Simplification(規則精簡化)方法為WM做1%、5%、10%、20%、30%程度的規則推理(Loss of performance)，並比較準確率和規則數量的改變。而規則推理是希望能減少規則來提升模糊控制的效率，然而在各類別的準確率實驗中發現，若是某類別的筆數較少，則會造成沒有辦法建立此類別的狀況，因此在一些緊急的控制系統就不適合做規則推理，因為通常緊急系統的資料會是較少量的資料。
在本實驗的結果顯示為評估適合的方法，為每個資料集都找出適合的方法：Iris以Regular 劃分的PE的方法較為適合、Glass是FCM劃分的RF、Seeds是FCM劃分的RF、Page Blocks是FCM 劃分的IG、Statlog(Shuttle)是HFP劃分的RF。而討論到FDT都以FCM劃分的IG結果表現最好，是因為FDT可以從大量的模糊集個數中選出其重要的模糊集合做判斷，因此IG的方法適合FDT。

關鍵字

模糊理論、模糊集合個數估計、模糊劃分、規則推理

並列摘要

With the development of fuzzy theory, the number of fuzzy sets in fuzzy control is the factor that influences control decisions, thus the main purpose of this study is to investigate ways to determine the number of fuzzy sets and the division method through the distribution of data. This study provides a method of assessment, which determines the method to estimate the number of fuzzy sets and the fuzzy division through different simplified levels. Since the simplification is based on the degree of disorder to consolidate rules, it is observed through the change in accuracy and the number of rules that as the former declines less, the latter declines more, and this indicates that the number of fuzzy sets and fuzzy division in this method are suitable for the given dataset.
In this study, three fuzzy divisions, Fuzzy C-Means (FCM), Hierarchical Fuzzy Partitioning (HFP) and Regular, are compared and four different methods including Partition Entropy (PE), Information Gain (IG), Relief-F (RF) and Wang & Mendel (WM), which are used to estimate number of fuzzy sets. After referring to information on numerical property and classification from UC Irvine Machine Learning Repository (UCI) for this dataset, using FisPro as the fuzzy partition. Fuzzy Decision Trees (FDT) and Wang and Mendel (WM) are used to generate rules, simplification is used for WM to do loss of performance to the degrees of 1%, 5%, 10%, 20% and 30%, and changes in accuracy and number of rules are compared. In particular, loss of performance is used to eliminate rules to improve the efficiency of fuzzy control, however it’s observed from accuracy tests in different divisions that if a certain class lacks data, the class itself may not be established. Therefore, loss of performance is not recommended for some urgent control systems.
Suited methods are identified from the experimental results for the datasets. For instance, PE coupled with regular division works better with Iris dataset while RF with FCM suits the Glass and Seeds datasets, IG with FCM suits Page Blocks and RF with HFP suits the Statlog(Shuttle) dataset. As for FDT, since it can select the crucial fuzzy sets out of a vast amount of fuzzy set individuals for judgement, method of IG with FCM suits FDT better.

並列關鍵字

Fussy Theory, Estimation of the number of Fuzzy Sets , Fuzzy Partition, Fuzzy inference

參考文獻

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