INTUITIONISTIC FUZZY SETS BASED METHOD FOR FUZZY TIME SERIES FORECASTING

Fuzzy time series models are of great interest in forecasting when the information is imprecise and vague. However, the major problem in fuzzy time series forecasting is the accuracy of the forecasted values. In the present study we propose a hybrid method of forecasting based on fuzzy time series and intuitionistic fuzzy sets. The proposed model is a simplified computational approach that uses the degree of nondeterminacy to establish fuzzy logical relations on time series data. The developed model was implemented on the historical enrollment data for the University of Alabama and the forecasted values were compared with the results of existing methods to show its superiority. The suitability of the proposed method was also examined in forecasting market share prices of the State Bank of India on the Bombay Stock Exchange, India.     

基于区间相似度的模糊时间序列预测算法

针对现有模糊时间序列预测算法无法适应预测中新关系出现的问题,提出了一种基于区间相似度的模糊时间序列预测（ISFTS）算法。首先,在模糊理论的基础上,采用基于均值的方法二次划分论域的区间,在论域区间上定义相应模糊集将历史数据模糊化;然后建立三阶模糊逻辑关系并引入逻辑关系相似度的计算公式,计算未来数据变化趋势值得到预测的模糊值;最后对预测模糊值去模糊化得到预测的确定值。由于ISFTS算法是预测数据变化趋势,克服了目前预测算法的逻辑关系的缺陷。仿真实验结果表明,与同类的预测算法相比,ISFTS算法预测误差更小,在误差相对比(MAPE)、绝对误差均值(MAE)和均方根误差(RMSE)三项指标上均优于同类的对比算法,因此ISFTS算法在时间序列预测中尤其是大数据量情况下的预测具有更强的适应性。     

A high order fuzzy time series forecasting model based on adaptive expectation and artificial neural networks

Many fuzzy time series approaches have been proposed in recent years. These methods include three main phases such as fuzzification, defining fuzzy relationships and, defuzzification. Aladag et al. [2] improved the forecasting accuracy by utilizing feed forward neural networks to determine fuzzy relationships in high order fuzzy time series. Another study for increasing forecasting accuracy was made by Cheng et al. [6]. In their study, they employ adaptive expectation model to adopt forecasts obtained from first order fuzzy time series forecasting model. In this study, we propose a novel high order fuzzy time series method in order to obtain more accurate forecasts. In the proposed method, fuzzy relationships are defined by feed forward neural networks and adaptive expectation model is used for adjusting forecasted values. Unlike the papers of Cheng et al. [6] and Liu et al. [14], forecast adjusting is done by using constraint optimization for weighted parameter. The proposed method is applied to the enrollments of the University of Alabama and the obtained forecasting results compared to those obtained from other approaches are available in the literature. As a result of comparison, it is clearly seen that the proposed method significantly increases the forecasting accuracy.     

A computer program for time series forecasting using single and double exponential smoothing techniques

This paper presents a microcomputer program for time series forecasting. The program has been developed in GW-BASIC for Zenith 150 microcomputers which are IBM PC compatible. It utilizes Single exponential smoothing, Adaptive-response-rate single exponential smoothing, and Brown's double exponential smoothing methods to forecast the future values of a given time series. The program produces plots of the original time series and forecasted series as well as forecasting errors. It computes 90% and 95% confidence intervals for forecasted values and calculates the following statistics: Mean squared error, Mean absolute percentage error, Mean absolute error, Durbin-Watson statistic, and Theil's U statistic.     

Constructing and applying an improved fuzzy time series model: Taking the tourism industry for example

This study develops an improved fuzzy time series models for forecasting short-term series data. The forecasts were obtained by comparing the proposed improved fuzzy time series, Hwang’s fuzzy time series, and heuristic fuzzy time series. The tourism from Taiwan to the United States was used to build the sample sets which were officially published annual data for the period of 1991–2001. The root mean square error and mean absolute percentage error are two criteria to evaluate the forecasting performance. Empirical results show that the proposed fuzzy time series and Hwang’s fuzzy time series are suitable for short-term predictions.     

The modeling of time series based on fuzzy information granules

A lot of research has resulted in many time series models with high precision forecasting realized at the numerical level. However, in the real world, higher numerical precision may not be necessary for the perception, reasoning and decision-making of human. Model of time series with an ability of humans to perceive and process abstract entities (rather than numeric entities) is more adaptable for some problems of decision-making. With this regard, information granules and granular computing play a primordial role. Fox example, if change range (intervals) of stock prices for a certain period in the future is regarded as information granule, constructing model that can forecast change ranges (intervals) of stock prices for a period in the future is better able to help stock investors make reasonable decisions in comparison with those based upon specific forecasting numerical value of stock price. In this paper, we propose a new modeling approach to realize interval prediction, in which the idea of information granules and granular computing is integrated with the classical Chen’s method. The proposed method is to segment an original numeric time series into a collection of time windows first, and then build fuzzy granules expressed as a certain fuzzy set over each time windows by exploiting the principle of justifiable granularity. Finally, fuzzy granular model can be constructed by mining fuzzy logical relationships of adjacent granules. The constructed model can carry out interval prediction by degranulation operation. Two benchmark time series are used to validate the feasibility and effectiveness of the proposed approach. The obtained results demonstrate the effectiveness of the approach. Besides, for modeling and prediction of large-scale time series, the proposed approach exhibit a clear advantage of reducing computation overhead of modeling and simplifying forecasting.     

A high-order fuzzy time series forecasting model for internet stock trading

Recently, many fuzzy time series models have already been used to solve nonlinear and complexity issues. However, first-order fuzzy time series models have proven to be insufficient for solving these problems. For this reason, many researchers proposed high-order fuzzy time series models and focused on three main issues: fuzzification, fuzzy logical relationships, and defuzzification. This paper presents a novel high-order fuzzy time series model which overcomes the drawback mentioned above. First, it uses entropy-based partitioning to more accurately define the linguistic intervals in the fuzzification procedure. Second, it applies an artificial neural network to compute the complicated fuzzy logical relationships. Third, it uses the adaptive expectation model to adjust the forecasting during the defuzzification procedure. To evaluate the proposed model, we used datasets from both the Taiwanese stock index from 2000 to 2003 and from the student enrollment records of the University of Alabama. The results of our study show that the proposed model is able to obtain an accurate forecast without encountering conventional fuzzy time series issues.     

Effective intervals determined by information granules to improve forecasting in fuzzy time series

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, we study how to partition the universe of discourse into intervals with unequal length to improve forecasting quality. First, we calculate the prototypes of data using fuzzy clustering, then form some subsets according to the prototypes. An unequal length partitioning method is proposed. We show that these intervals carry well-defined semantics. To verify the suitability and effectiveness of the approach, we apply the proposed method to forecast enrollment of students of Alabama University and Germany’s DAX stock index monthly values. Empirical results show that the unequal length partitioning can greatly improve forecast accuracy. Further more, the proposed method is very robust and stable for forecasting in fuzzy time series.     

An efficient time series forecasting model based on fuzzy time series

In this paper, we present a new model to handle four major issues of fuzzy time series forecasting, viz., determination of effective length of intervals, handling of fuzzy logical relationships (FLRs), determination of weight for each FLR, and defuzzification of fuzzified time series values. To resolve the problem associated with the determination of length of intervals, this study suggests a new time series data discretization technique. After generating the intervals, the historical time series data set is fuzzified based on fuzzy time series theory. Each fuzzified time series values are then used to create the FLRs. Most of the existing fuzzy time series models simply ignore the repeated FLRs without any proper justification. Since FLRs represent the patterns of historical events as well as reflect the possibility of appearances of these types of patterns in the future. If we simply discard the repeated FLRs, then there may be a chance of information lost. Therefore, in this model, it is recommended to consider the repeated FLRs during forecasting. It is also suggested to assign weights on the FLRs based on their severity rather than their patterns of occurrences. For this purpose, a new technique is incorporated in the model. This technique determines the weight for each FLR based on the index of the fuzzy set associated with the current state of the FLR. To handle these weighted FLRs and to obtain the forecasted results, this study proposes a new defuzzification technique. The proposed model is verified and validated with three different time series data sets. Empirical analyses signify that the proposed model have the robustness to handle one-factor time series data set very efficiently than the conventional fuzzy time series models. Experimental results show that the proposed model also outperforms over the conventional statistical models.     

Partitions based computational method for high-order fuzzy time series forecasting

In this paper, we present a computational method of forecasting based on multiple partitioning and higher order fuzzy time series. The developed computational method provides a better approach to enhance the accuracy in forecasted values. The objective of the present study is to establish the fuzzy logical relations of different order for each forecast. Robustness of the proposed method is also examined in case of external perturbation that causes the fluctuations in time series data. The general suitability of the developed model has been tested by implementing it in forecasting of student enrollments at University of Alabama. Further it has also been implemented in the forecasting the market price of share of State Bank of India (SBI) at Bombay Stock Exchange (BSE), India. In order to show the superiority of the proposed model over few existing models, the results obtained have been compared in terms of mean square and average forecasting errors.     

A computational method of forecasting based on high-order fuzzy time series

This paper presents a computational method of forecasting based on high-order fuzzy time series. The developed computational method provides a better approach to overcome the drawback of existing high-order fuzzy time series models. Its simplicity lies with the use of differences in consecutive values of various orders as forecasting parameter and a w-step fuzzy predictor in place of complicated computations of fuzzy logical relations. The objective of the present study is to examine the suitability of various high-order fuzzy time series models in forecasting. The general suitability of the developed method has been tested by implementing it in the forecasting of student enrollments of the University of Alabama and in the forecasting of crop (Lahi) production, a case of high uncertainty in time series data. The results obtained have been compared in terms of average error of forecast to show superiority of the proposed model.     

A new time invariant fuzzy time series forecasting method based on particle swarm optimization

In the analysis of time invariant fuzzy time series, fuzzy logic group relationships tables have been generally preferred for determination of fuzzy logic relationships. The reason of this is that it is not need to perform complex matrix operations when these tables are used. On the other hand, when fuzzy logic group relationships tables are exploited, membership values of fuzzy sets are ignored. Thus, in defiance of fuzzy set theory, fuzzy sets’ elements with the highest membership value are only considered. This situation causes information loss and decrease in the explanation power of the model. To deal with these problems, a novel time invariant fuzzy time series forecasting approach is proposed in this study. In the proposed method, membership values in the fuzzy relationship matrix are computed by using particle swarm optimization technique. The method suggested in this study is the first method proposed in the literature in which particle swarm optimization algorithm is used to determine fuzzy relations. In addition, in order to increase forecasting accuracy and make the proposed approach more systematic, the fuzzy c-means clustering method is used for fuzzification of time series in the proposed method. The proposed method is applied to well-known time series to show the forecasting performance of the method. These time series are also analyzed by using some other forecasting methods available in the literature. Then, the results obtained from the proposed method are compared to those produced by the other methods. It is observed that the proposed method gives the most accurate forecasts.     

Linguistic time series forecasting using fuzzy recurrent neural network

It is known that one of the most spread forecasting methods is the time series analysis. A weakness of traditional crisp time series forecasting methods is that they process only measurement based numerical information and cannot deal with the perception-based historical data represented by linguistic values. Application of a new class of time series, a fuzzy time series whose values are linguistic values, can overcome the mentioned weakness of traditional forecasting methods. In this paper we propose a fuzzy recurrent neural network (FRNN) based time series forecasting method for solving forecasting problems in which the data can be presented as perceptions and described by fuzzy numbers. The FRNN allows effectively handle fuzzy time series to apply human expertise throughout the forecasting procedure and demonstrates more adequate forecasting results. Recurrent links in FRNN also allow for simplification of the overall network structure (size) and forecasting procedure. Genetic algorithm-based procedure is used for training the FRNN. The effectiveness of the proposed fuzzy time series forecasting method is tested on the benchmark examples.     

A hybrid multi-order fuzzy time series for forecasting stock markets

This paper proposes a hybrid model based on multi-order fuzzy time series, which employs rough sets theory to mine fuzzy logical relationship from time series and an adaptive expectation model to adjust forecasting results, to improve forecasting accuracy. Two empirical stock markets (TAIEX and NASDAQ) are used as empirical databases to verify the forecasting performance of the proposed model, and two other methodologies, proposed earlier by Chen and Yu, are employed as comparison models. Besides, to compare with conventional statistic method, the partial autocorrelation function and autoregressive models are utilized to estimate the time lags periods within the databases. Based on comparison results, the proposed model can effectively improve the forecasting performance and outperforms the listing models. From the empirical study, the conventional statistic method and the proposed model both have revealed that the estimated time lags for the two empirical databases are one lagged period.     

Fuzzy lagged variable selection in fuzzy time series with genetic algorithms

Fuzzy time series forecasting models can be divided into two subclasses which are first order and high order. In high order models, all lagged variables exist in the model according to the model order. Thus, some of these can exist in the model although these lagged variables are not significant in explaining fuzzy relationships. If such lagged variables can be removed from the model, fuzzy relationships will be defined better and it will cause more accurate forecasting results. In this study, a new fuzzy time series forecasting model has been proposed by defining a partial high order fuzzy time series forecasting model in which the selection of fuzzy lagged variables is done by using genetic algorithms. The proposed method is applied to some real life time series and obtained results are compared with those obtained from other methods available in the literature. It is shown that the proposed method has high forecasting accuracy.     

Fuzzy time series forecasting with a novel hybrid approach combining fuzzy c-means and neural networks

In recent years, time series forecasting studies in which fuzzy time series approach is utilized have got more attentions. Various soft computing techniques such as fuzzy clustering, artificial neural networks and genetic algorithms have been used in fuzzy time series method to improve the method. While fuzzy clustering and genetic algorithms are being used for fuzzification, artificial neural networks method is being preferred for using in defining fuzzy relationships. In this study, a hybrid fuzzy time series approach is proposed to reach more accurate forecasts. In the proposed hybrid approach, fuzzy c-means clustering method and artificial neural networks are employed for fuzzification and defining fuzzy relationships, respectively. The enrollment data of University of Alabama is forecasted by using both the proposed method and the other fuzzy time series approaches. As a result of comparison, it is seen that the most accurate forecasts are obtained when the proposed hybrid fuzzy time series approach is used.     

Fuzzy forecasting based on fuzzy time series

This article presents an improved method of fuzzy time series to forecast university enrollments. The historical enrollment data of the University of Alabama were first adopted by Song and Chissom (Song, Q. and Chissom, B. S. (1993). Forecasting enrollment with fuzzy time series-part I, Fuzzy Sets and Systems, 54, 1–9; Song, Q. and Chissom, B. S. (1994). Forecasting enrollment with fuzzy time series-part II, Fuzzy Sets and Systems, 54, 267–277) to illustrate the forecasting process of the fuzzy time series. Later, Chen proposed a simpler method. In this article, we show that our method is as simple as Chen's method but more accurate. In forecasting the enrollment of the University of Alabama, the root mean square percentage error (RMSPE) of our method is 3.1113% while the RMSPE of Chen's method is 4.0516%, which shows that our method is doing much better.     

A multivariate model of fuzzy integrated logical forecasting method (M-FILF) and multiplicative time series clustering: A model of time-varying volatility for dry cargo freight market

The aim of this paper is to improve the fuzzy logical forecasting model (FILF) by utilizing multivariate inference and the partitioning problem for an exponentially distributed time series by using a multiplicative clustering approach. Fuzzy time series (FTS) is a growing study field in computer science and its superiority is indicated frequently. Since the conventional time series analysis requires various pre-conditions, the FTS framework is very useful and convenient for many problems in business practice. This paper particularly investigates pricing problems in the shipping business and price-volatility relationship is the theoretical point of the proposed approach. Both FTS and conventional time series results are comparatively presented in the final section and superiority of the proposed method is explicitly noted.     

A SIMPLE TIME VARIANT METHOD FOR FUZZY TIME SERIES FORECASTING

Forecasting using fuzzy time series models needs computations of fuzzy relations in adjacent observations of time series data. In view of getting better forecasted values, these fuzzy relations have been considered as time invariant and time variant, and have been computed in several ways. However, the complication lies with the various rules developed for obtaining these fuzzy relations and then the defuzzification process. In this article, we propose a simple time variant method for time series forecasting. It uses the difference operator and the values obtained have been used for developing fuzzy rules for forecast. We develop algorithms to forecast enrollments of the University of Alabama and compared them with existing methods. The method has been also implemented to forecast rice production of Pantnagar (farm), India. The computational algorithms of the proposed method are simple and provide higher accuracy in forecasting.     

An integrated fuzzy time series forecasting system

A number of fuzzy time series models have been designed and developed during the last decade. One problem of these models is that they only provide a single-point forecasted value just like the output of the crisp time series methods. In addition, these models are suitable for forecasting stationary or trend time series, but they are not appropriate for forecasting seasonal time series. Hence, the objective of this study is to develop an integrated fuzzy time series forecasting system in which the forecasted value will be a trapezoidal fuzzy number instead of a single-point value. Furthermore, this system can effectively deal with stationary, trend, and seasonal time series and increase the forecasting accuracy. Two numerical data sets are selected to illustrate the proposed method and compare the forecasting accuracy with four fuzzy time series methods. The results of the comparison show that our system can produce more precise forecasted values than those of four methods.