區間第二型模糊邏輯系統應用於模糊時間序列預測

Abstract

本研究提出區間第二型模糊理論系統(IT2FLS)基於差異區間應用於模糊時間序列(DIFTS)模型，包含兩種不同的DIFTS模型：IT2FLS基於差異區間應用於單變量模糊時間序列(DIUFTS)模型、IT2FLS基於差異區間應用於雙變量模糊時間序列(DIBFTS)模型。DIUFTS模型使用主要因子去預測未來，而DIBFTS模型考慮主要因子與第二因子去預測未來。DIFTS模型包含三個主要的方法：模糊時間序列預測方法、區間第二型模糊邏輯系統與差異區間。於預測過程中，模糊時間序列預測方法可以解決語言項的問題，它的架構包含四個主要的步驟。步驟一：定義與劃分論域；步驟二：定義模糊集合與模糊化時間序列；步驟三：建立模糊關係；步驟四：預測與解模糊化預測結果。DIFTS模型採用這個架構去預測未來，首先，找出數據間的差異而最大差異與最小差異使用於論域區間設定。第二，根據尋得的差異定義IT2FLS的輸入模糊集合與輸出差異區間，時間序列數據模糊襪變成模糊集合進而形成語言項。第三，在訓練階段中，模糊集合在時間 與時間 為 ；在試驗階段中，模糊集合在時間 與時間 為 ( 為未知的數值)。此外，模糊關係地圖(FRM)是根據在訓練階段的模糊關係計數所建立。第四，IT2FLS是以它比第一型模糊邏輯系統有較高的設計自由度於模糊集合而聞名。計算預測是考慮歷史數據之間的差異，使用此差異作為IT2FLS的輸入，而IT2FLS的輸出為預測的差異。最後，時間 的預測值為時間 的數據加上預測的差異。 於本研究中，DIFTS模型應用於不同的領域，包含大學註冊人數、股價指數、害蟲族群與輸電線溫度。其中許多研究已發表大學註冊人數與股價指數之預測模型，這些研究之預測結果將用來與DIUFTS模型所產生的結果做比較，以證明DIUFTS模型的預測精準度，且DIUFTS模型與其他的預測方法相比有較小均方根誤差，以證明所提出之DIUFTS模型具有較佳的預測精準度。 本研究所提出之DIUFTS模型與DIBFTS模型將應用於兩個不同的領域：害蟲族群的與輸電線溫度。於害蟲族群預測中，其主要因子為害蟲數據而第二因子為環境溫度；而於輸電線的溫度預測中，其主要因子為輸電線溫度而第二因子為風速。結果顯示DIFTS模型應用於不同的領域中皆可達到較高預測精準度基於該模型具有較高的設計自由度。

An interval type-2 fuzzy logic system (IT2FLS) based on difference-based intervals for fuzzy time series forecasting (DIFTS) is proposed in this study, including two different DIFTS models – the IT2FLS based on difference-based intervals for univariate fuzzy time series forecasting (DIUFTS) model and the IT2FLS based on difference-based intervals for bivariate fuzzy time series forecasting (DIBFTS) model – are selected. The DIUFTS model uses the main factor to predict the future while the DIBFTS model considers both the main factor and the second factor and uses them to predict the future. The proposed DIFTS model includes three major methods: a fuzzy time series forecasting method, an IT2LFS, and difference-based intervals. The fuzzy time series forecasting method can overcome the linguistic term problems during the forecasting process, and its framework comprised four major steps: Step 1) Defining and partitioning the universe of discourse; Step 2) Defining fuzzy sets and fuzzifying time series; Step 3) Establishing fuzzy relationships; and Step 4) Forecasting and defuzzifying forecasting results. The proposed DIFTS model follows this framework to forecast the future. First, differences between the data are found, and the maximum difference and the minimum difference are used for interval settings of the universe of discourse. Second, the input fuzzy sets and output difference intervals of IT2FLS are defined based on the found differences. The time series data are fuzzified into fuzzy sets to form linguistic terms. Third, the fuzzy set between time t and time t + 1 is Ai→Aj in the training phase, and the fuzzy set between time t and time t + 1 is Ai→* (* is the unknown value) in the testing phase. Moreover, the fuzzy relationship map (FRM) is established by the count of fuzzy relationship Ai→Aj in the training phase. Fourth, an IT2FLS is known for its higher design degree of freedom on fuzzy sets compared to a type-1 fuzzy logic system. The computation of the prediction is that the differences between considered historical data are used as the inputs of the IT2FLS, and the outputs of the IT2FLS are the forecasting differences. Finally, the forecasting value at time t + 1 is the data point at time t plus the forecasting differences. In this study, the proposed DIFTS model is applied to different areas, including college enrollment, stock indices, pest population, and temperature of power transmission lines. College enrollment prediction and stock index prediction have been investigated by many studies. The prediction results of these studies are compared with the results generated by the proposed DIUFTS model to verify the forecasting accuracy of the proposed DIUFTS model, and the proposed DIUFTS model is found that it have smaller RMSEs than other forecasting methods. The verified DIUFTS model and the DIBFTS model are then applied to two different areas: pest population and temperature of power transmission lines. In the pest population prediction, the main factor is the pest data and the second factor is the environmental temperature. In the temperature prediction of power transmission lines, the main factor is the temperature of power transmission lines and the second factor is wind speed. The results show that the proposed DIFTS model all achieves higher forecasting accuracy in different areas due to its higher design degree of freedom.