Vedide Rezan Uslu

Forecasting in high order fuzzy times series by using neural networks to define fuzzy relations

A given observation in time series does not only depend on preceding one but also previous ones in general. Therefore, high order fuzzy time series approach might obtain better forecasts than does first order fuzzy time series approach. Defining fuzzy relation in high order fuzzy time series approach are more complicated than that in first order fuzzy time series approach. A new proposed approach, which uses feed forward neural networks to define fuzzy relation in high order fuzzy time series, is introduced in this paper. The new proposed approach is applied to well-known enrollment data for the University of Alabama and obtained results are compared with other methods proposed in the literature. It is found that the proposed method produces better forecasts than the other methods.

A new approach for determining the length of intervals for fuzzy time series

In the implementations of fuzzy time series forecasting, the identification of interval lengths has an important impact on the performance of the procedure. However, the interval length has been chosen arbitrarily in many papers. Huarng developed a new approach which is called ratio-based lengths of intervals in order to identify the length of intervals. In our paper, we propose a new approach which uses a single-variable constrained optimization to determine the ratio for the length of intervals. The proposed approach is applied to the two well-known time series, which are enrollment data at The University of Alabama and inventory demand data. The obtained results are compared to those of other methods. The proposed method produces more accurate predictions for the future values of used time series.

Finding an optimal interval length in high order fuzzy time series

Univariate fuzzy time series approaches which have been widely used in recent years can be divided into two classes, which are called first order and high order models. In the literature, it has been shown that high order fuzzy time series approaches improve the forecasting accuracy. One of the important parts of obtaining high accuracy forecasts in fuzzy time series is that the length of interval is very vital. As mentioned in the first-order models by Egrioglu, Aladag, Basaran, Uslu, and Yolcu (2009), the length of interval also plays very important role in high order models too. In this study, a new approach which uses an optimization technique with a single-variable constraint is proposed to determine an optimal interval length in high order fuzzy time series models. An optimization procedure is used in order to determine optimum length of interval for the best forecasting accuracy, we used optimization procedure. In the optimization process, we used a MATLAB function employing an algorithm based on golden section search and parabolic interpolation. The proposed method was employed to forecast the enrollments of the University of Alabama to show the considerable outperforming results.

A new hybrid approach based on SARIMA and partial high order bivariate fuzzy time series forecasting model

In the literature, there have been many studies using fuzzy time series for the purpose of forecasting. The most studied model is the first order fuzzy time series model. In this model, an observation of fuzzy time series is obtained by using the previous observation. In other words, only the first lagged variable is used when constructing the first order fuzzy time series model. Therefore, this model can not be sufficient for some time series such as seasonal time series which is an important class in time series models. Besides, the time series encountered in real life have not only autoregressive (AR) structure but also moving average (MA) structure. The fuzzy time series models available in the literature are AR structured and are not appropriate for MA structured time series. In this paper, a hybrid approach is proposed in order to analyze seasonal fuzzy time series. The proposed hybrid approach is based on partial high order bivariate fuzzy time series forecasting model which is first introduced in this paper. The order of this model is determined by utilizing Box-Jenkins method. In order to show the efficiency of the proposed hybrid method, real time series are analyzed with this method. The results obtained from the proposed method are compared with the other methods. As a result, it is observed that more accurate results are obtained from the proposed hybrid method.

A new approach based on artificial neural networks for high order multivariate fuzzy time series

Fuzzy time series methods have been recently becoming very popular in forecasting. These methods can be categorized into two subclasses that are univariate and multivariate approaches. It is a known fact that real time series data can actually be affected by many factors. In this case, the using multivariate fuzzy time series forecasting model can be more reasonable in order to get more accurate forecasts. To obtain fuzzy forecasts when multivariate fuzzy time series approach is adopted, the most applied method is using tables of fuzzy relations. However, employing this method is a computationally though task. In this study, we introduce a new method that does not require using fuzzy logic relation tables in order to determine fuzzy relationships. Instead, a feed forward artificial neural network is employed to determine fuzzy relationships. The proposed method is applied to the time series data of the total number of annual car road accidents casualties in Belgium from 1974 to 2004 and a comparison is made between our proposed method and the methods proposed by Jilani and Burney [Jilani, T. A., & Burney, S. M. A. (2008). Multivariate stochastic fuzzy forecasting models. Expert Systems with Applications, 35, 691-700] and Lee et al. [Lee, L.-W., Wang, L.-H., Chen, S.-M., & Leu, Y.-H. (2006). Handling forecasting problems based on two factors high order fuzzy time series. IEEE Transactions on Fuzzy Systems, 14, 468-477].

A new approach based on the optimization of the length of intervals in fuzzy time series

In fuzzy time series analysis, the determination of the interval length is an important issue. In many researches recently done, the length of intervals has been intuitively determined. In order to efficiently determine the length of intervals, two approaches which are based on the average and the distribution have been proposed by Huarng [4]. In this paper, we propose a new method based on the use of a single variable constrained optimization to determine the length of interval. In order to determine optimum length of interval for the best forecasting accuracy, we used a MATLAB function which is employing an algorithm based on golden section search and parabolic interpolation. Mean square error is used as a measure of forecasting accuracy so the objective function value is mean square error value for forecasted observations. The proposed method was employed to forecast the enrollments of the University of Alabama to show the considerable outperforming results.

Time-series forecasting with a novel fuzzy time-series approach: an example for Istanbul stock market

Artificial intelligence procedures such as artificial neural networks (ANNs), genetic algorithms and particle swarm optimization and other procedures such as fuzzy clustering have been successfully used in the various stages of different fuzzy time-series forecasting approaches. Fuzzy clustering, genetic algorithm and particle swarm optimization are generally used in the fuzzification stage, and this simplifies the applicability of this stage and makes the fuzzy time-series approach more systematic. ANNs have also been applied successfully in the fuzzy relationship determination stage. In this study, we propose a new hybrid fuzzy time-series approach in which fuzzy c-means clustering procedure is employed in the fuzzification stage and feed-forward neural networks are used in the fuzzy relationship determination stage. This study also includes an empirical analysis pertaining to the forecasting of Index 100 for the stocks and bonds exchange market of Istanbul.

A modified genetic algorithm for forecasting fuzzy time series

Fuzzy time series approaches are used when observations of time series contain uncertainty. Moreover, these approaches do not require the assumptions needed for traditional time series approaches. Generally, fuzzy time series methods consist of three stages, namely, fuzzification, determination of fuzzy relations, and defuzzification. Artificial intelligence algorithms are frequently used in these stages with genetic algorithms being the most popular of these algorithms owing to their rich operators and good performance. However, the mutation operator of a GA may cause some negative results in the solution set. Thus, we propose a modified genetic algorithm to find optimal interval lengths and control the effects of the mutation operator. The results of applying our new approach to real datasets show superior forecasting performance when compared with those obtained by other techniques.

A fuzzy time series approach based on weights determined by the number of recurrences of fuzzy relations

Fuzzy time series approaches, which do not require the strict assumptions of traditional time series approaches, generally consist of three stages. These are called as the fuzzification of crisp time series observations, the identification of fuzzy relationships and the defuzzification. All of these stages play a very important role on the forecasting performance of the model. Although there are many studies contributing to the stages of fuzzification and determining fuzzy relationships, the number of the studies about the defuzzification stage, which is very important at least as much as the others, is limited. None of them considered the number of recurrence of the fuzzy relationships in the stage of defuzzification. However it is very reasonable to take into account since fuzzy relations and their recurrence number are reflected the nature of the time series. Then the information obtained from the fuzzy relationships can be used in the defuzzification stage. In this study, we take into account the recurrence number of the fuzzy relations in the stage of defuzzification. Then this new approach has been applied to the real data sets which are often used in other studies in literature. The results are compared to the ones obtained from other techniques. Thus it is concluded that the results present superior forecasts performance.

Robust learning algorithm for multiplicative neuron model artificial neural networks

A new robust learning algorithm was proposed for multiplicative neuron model (MNM).The proposed method gives successful results even when data sets have outliers.There is no a robust learning algorithm in the literature for MNM.The performance of proposed method was supported with real time series data.A simulation study was performed to show the performance of the proposed method. The two most commonly used types of artificial neural networks (ANNs) are the multilayer feed-forward and multiplicative neuron model ANNs. In the literature, although there is a robust learning algorithm for the former, there is no such algorithm for the latter. Because of its multiplicative structure, the performance of multiplicative neuron model ANNs is affected negatively when the dataset has outliers. On this issue, a robust learning algorithm for the multiplicative neuron model ANNs is proposed that uses Hubers loss function as fitness function. The training of the multiplicative neuron model is performed using particle swarm optimization. One principle advantage of this algorithm is that the parameter of the scale estimator, which is an important factor affecting the value of Hubers loss function, is also estimated with the proposed algorithm. To evaluate the performance of the proposed method, it is applied to two well-known real world time series datasets, and also a simulation study is performed. The algorithm has superior performance both when it is applied to real world time series datasets and the simulation study when compared with other ANNs reported in the literature. Another of its advantages is that, for datasets with outliers, the results are very close to the results obtained from the original datasets. In other words, we demonstrate that the algorithm is unaffected by outliers and has a robust structure.