International Journal of Excellence Innovation and Development ||Volume 1, Issue 1, Nov. 2018||Page No. 018-024||
Forecasting Gasonline Price in Vietnam Based on Fuzzy Time Series and Automatic Clustering Technique Nghiem Van Tinh, Nguyen Tien Duy Thai Nguyen University – Thai Nguyen University of Technology
Abstract––Partitioning the universe of discourse and determining effective intervals are critical for forecasting in fuzzy time series. Equal length intervals used in most existing literatures are convenient but subjective to partition the universe of discourse. In this paper, a new forecasting model based on two computational methods, the fuzzy logical relationship groups and automatic clustering technique is presented for forecasting Gasonline Price. Firstly, we use the automatic clustering algorithm to divide the historical data into clusters and adjust them into intervals with different length. Then, based on the new obtained intervals, we fuzzify all the historical data into fuzzy sets and calculate the forecasted output by the proposed method. To illustrate the forecasting process, a numerical data sets of Gasonline Prices in Viet Nam is utilized to calculate by step. The results show that the proposed model gets forecasting accuracy for a higher high – order compare with first – order fuzzy time series model. Index Terms––Forecasting, FTS, fuzzy logical relationships, automatic clustering, Gasonline prices
INTRODUCTION Recently, fuzzy time series has been widely used for forecasting data of dynamic and non-linear data in nature. Many previous models have been discussed for forecasting used fuzzy time series, such as enrolment [1], [2], [3][11], [10], crop forecast [6], [7], the temperature prediction [14], stock markets [15], etc. There is the matter of fact that the traditional forecasting methods cannot deal with the forecasting problems in which the historical data are represented by linguistic values. Ref. [1], [2] proposed the time-invariant fuzzy time and the time-variant time series model which use the max–min operations to forecast the enrolments of the University of Alabama. However, the main drawback of these methods is huge computation burden. Then, Ref. [3] proposed the first-order fuzzy time series model by introducing a more efficient arithmetic method. After that, fuzzy time series has been widely studied to improve the accuracy of forecasting in many applications. Ref. [4] considered the trend of the enrolment in the past years and presented another forecasting model based on the first-order fuzzy time series. At the same time, Ref. [8],[11] proposed several forecast models based on the high-order fuzzy time series to deal with the enrolments forecasting problem. Ref. [9] predicted the Taiwan weighted index. Ref. [13] presented a new forecast model based on the trapezoidal fuzzy numbers. Ref. [12] showed that the www.ijeid.com
different lengths of intervals may affect the accuracy of forecasting. Recently, Ref.[17] used particle swarm optimization method to search for a suitable partition of universe. Additionally, Ref. [18] proposed a new method to forecast enrolments based on automatic clustering techniques and fuzzy logical relationships. In this paper, we proposed a new forecasting model combining the fuzzy time series and automatic clustering technique. The method is different from the approach [3] and [17]in the way where the fuzzy relationship groups are created. Based on the model proposed in [20], we have developed a new fuzzy time series model by combining the automatic clustering technique and fuzzy time series with the aim to increase the accuracy of the forecasting model. The rest of this paper is organized as follows. In Section II, we provide a brief review of fuzzy time series and itâ€&#x;s model. In Section III, we present a model for forecasting the Gasonline price in VietNam based on the automatic clustering technique and fuzzy time series. Then, the experimental results are shown and analyzed in Section IV. Finally, Conclusions are given in Section V.
BASIC CONCEPTS OF FUZZY TIME SERIES This section introduces some important literatures, which includes fuzzy time series[1],[2] and itâ€&#x;s model. Basic concepts of fuzzy time series Conventional time series refer to real values, but fuzzy time series are structured by fuzzy sets [1]. Let U = {u1 , u2 , ‌ , un } be an universal set; a fuzzy set Ai of U is defined as đ??´đ?‘– = { fA (u1 )/u1 +, fA (u2 )/u2 ‌ + fA (un )/un }, where fA is a membership function of a given set A, fA :Uď‚Ž[0,1], fA (ui ) indicates the grade of membership of ui in the fuzzy set A, fA (ui ) Ďľ [0, 1], and 1≤ i ≤ n. General definitions of FTS are given as follows: Definition 1: Fuzzy time series Let Y(t)(t = . . , 0, 1, 2 . . ), a subset of R, be the universe of discourse on which fuzzy sets fi (t) (i = 1,2 ‌ ) are defined and if F(t) is a collection of f1 t , f2 t , ‌ , then F(t) is called a fuzzy time series on Y(t) (t . . ., 0, 1,2 . ..). Here, F(t) is viewed as a linguistic variable and fi (t) represents possible linguistic values of F(t). Definition 2: Fuzzy logic relationship(FLR) If F(t) is caused by F(t-1) only, the relationship between F(t) and F(t-1) can be expressed by F(t −
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