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.     

Using multiplicative neuron model to establish fuzzy logic relationships

Determination of fuzzy logic relationships between observations is quite effective on the forecasting performance of fuzzy time series approaches. In various studies available in the literature, it has been seen that utilizing artificial neural networks for establishing fuzzy relations increase the forecasting accuracy. In this study, a novel high order fuzzy time series forecasting approach in which multiplicative neuron model is used to define fuzzy relations is proposed in order to reach high forecasting level. Also, particle swarm optimization method is utilized to train multiplicative neuron model. In order to show forecasting performance of the proposed method, it is applied to a well-known data Taiwan future exchange and the results produced by the proposed approach is compared to those obtained from other fuzzy time series forecasting models. As a result of the implementation, it is observed that the proposed approach gives the best forecasts for Taiwan future exchange time series.     

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.     

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 hybrid forecasting model for enrollments based on aggregated fuzzy time series and particle swarm optimization

In this paper, a new forecasting model based on two computational methods, fuzzy time series and particle swarm optimization, is presented for academic enrollments. Most of fuzzy time series forecasting methods are based on modeling the global nature of the series behavior in the past data. To improve forecasting accuracy of fuzzy time series, the global information of fuzzy logical relationships is aggregated with the local information of latest fuzzy fluctuation to find the forecasting value in fuzzy time series. After that, a new forecasting model based on fuzzy time series and particle swarm optimization is developed to adjust the lengths of intervals in the universe of discourse. From the empirical study of forecasting enrollments of students of the University of Alabama, the experimental results show that the proposed model gets lower forecasting errors than those of other existing models including both training and testing phases.     

A FCM-based deterministic forecasting model for fuzzy time series

The study of fuzzy time series has increasingly attracted much attention due to its salient capabilities of tackling uncertainty and vagueness inherent in the data collected. A variety of forecasting models including high-order models have been devoted to improving forecasting accuracy. However, the high-order forecasting approach is accompanied by the crucial problem of determining an appropriate order number. Consequently, such a deficiency was recently solved by Li and Cheng [S.-T. Li, Y.-C. Cheng, Deterministic Fuzzy time series model for forecasting enrollments, Computers and Mathematics with Applications 53 (2007) 1904–1920] using a deterministic forecasting method. In this paper, we propose a novel forecasting model to enhance forecasting functionality and allow processing of two-factor forecasting problems. In addition, this model applies fuzzy c-means (FCM) clustering to deal with interval partitioning, which takes the nature of data points into account and produces unequal-sized intervals. Furthermore, in order to cope with the randomness of initially assigned membership degrees of FCM clustering, Monte Carlo simulations are used to justify the reliability of the proposed model. The superior accuracy of the proposed model is demonstrated by experiments comparing it to other existing models using real-world empirical data.     

ARMA(p,q) type high order fuzzy time series forecast method based on fuzzy logic relations

Within classic time series approaches, a time series model can be studied under 3 groups, namely AR (autoregressive model), MA (moving averages model) and ARMA (autoregressive moving averages model). On the other hand, solutions are based mostly on fuzzy AR time series models in the fuzzy time series literature. However, just a few fuzzy ARMA time series models have proposed until now. Fuzzy AR time series models have been divided into two groups named first order and high order models in the literature, highlighting the impact of model degree on forecast performance. However, model structure has been disregarded in these fuzzy AR models. Therefore, it is necessary to eliminate the model specification error arising from not utilizing of MA variables in the fuzzy time series approaches. For this reason, a new high order fuzzy ARMA(p,q) time series solution algorithm based on fuzzy logic group relations including fuzzy MA variables along with fuzzy AR variables has been proposed in this study. The main purpose of this article is to show that the forecast performance can be significantly improved when the deficiency of not utilizing MA variables. The other aim is also to show that the proposed method is better than the other fuzzy ARMA time series models in the literature from the point of forecast performance. Therefore, the new proposed method has been compared regarding forecast performance against some methods commonly used in literature by applying them on gold prices in Turkey, Istanbul Stock Exchange (IMKB) and the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX).     

A computational method of forecasting based on fuzzy time series

In this paper, a computational method of forecasting based on fuzzy time series have been developed to provide improved forecasting results to cope up the situation containing higher uncertainty due to large fluctuations in consecutive year's values in the time series data and having no visualization of trend or periodicity. The proposed model is of order three and uses a time variant difference parameter on current state to forecast the next state. The developed model has been tested on the historical student enrollments, University of Alabama to have comparison with the existing methods and has been implemented for forecasting of a crop production system of lahi crop, containing higher uncertainty. The suitability of the developed model has been examined in comparison with the other models to show its superiority.     

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.     

Forecasting analysis by using fuzzy grey regression model for solving limited time series data

The grey model GM(1,1) is a popular forecasting method when using limited time series data and is successfully applied to management and engineering applications. On the other hand, the reliability and validity of the grey model GM(1,1) have never been discussed. First, without considering other causes when using limited time series data, the forecasting of the grey model GM(1,1) is unreliable, and provide insufficient information to a decision maker. Therefore, for the sake of reliability, the fuzzy set theory was hybridized into the grey model GM(1,1). This resulted in the fuzzy grey regression model, which granulates a concept into a set with membership function, thereby obtaining a possible interval extrapolation. Second, for a newly developed product or a newly developed system, the data collected are limited and rather vague with the result that the grey model GM(1,1) is useless for solving its problem with vague or fuzzy-input values. In this paper the fuzzy grey regression model is verified to show its validity in solving crisp-input data and fuzzy-input data with limited time series data. Finally, two examples for the LCD TV demand are illustrated using the proposed models.     

A decision support system methodology for forecasting of time series based on soft computing

Exponential procedures are widely used as forecasting techniques for inventory control and business planning. A number of modifications to the generalized exponential smoothing (Holt-Winters) approach to forecasting univariate time series is presented, which have been adapted into a tool for decision support systems. This methodology unifies the phases of estimation and model selection into just one optimization framework which permits the identification of robust solutions. This procedure may provide forecasts from different versions of exponential smoothing by fitting the updated formulas of Holt-Winters and selects the best method using a fuzzy multicriteria approach. The elements of the set of local minima of the non-linear programming problems allow us to build the membership functions of the conflicting objectives. It is compared to other forecasting methods on the 111 series from the M-competition.     

A non-linear clustering method for fuzzy time series: Histogram damping partition under the optimized cluster paradox

The aim of this paper is to investigate the problem of finding the efficient number of clusters in fuzzy time series. The clustering process has been discussed in the existing literature, and a number of methods have been suggested. These methods have several drawbacks, especially the lack of cluster shape and quantity optimization. There are two critical dimensions in a fuzzy time series clustering: the selection of a proper interval for fuzzy clusters and the optimization of the membership degrees among the fuzzy cluster set. The existing methods for the interval selection assume that the intended data has a short-tailed distribution, and the cluster intervals are established in identical lengths (e.g. Song and Chissom, 1994; Chen, 1996; Yolcu et al., 2009). However, the time series data (particularly in economic research) is rarely short-tailed and mostly converges to long-tail distribution because of the boom-bust market behavior. This paper proposes a novel clustering method named histogram damping partition (HDP) to define sub-clusters on the standard deviation intervals and truncate the histogram of the data by a constraint based on the coefficient of variation. The HDP approach can be used for many different kinds of fuzzy time series models at the clustering stage.     

基于主成分分析的模糊时间序列模型的平稳化算法

在模糊时间序列模型建立的过程中,对数据的预处理和模糊规则的优化往往是影响模型预测精确度的关键因素.针对上述问题,提出基于主成分分析(PCA)的平稳化算法.首先,对数据进行平稳化检验,并将非平稳的数据进行预处理使其平稳;其次,对论域进行划分并根据模糊关系构建广义的协方差矩阵,由此计算广义协方差矩阵的特征值和特征向量;再次,根据特征值的累计贡献率优化模糊规则,利用优化后模型进行预测;最后,通过实际算例验证新算法的可行性.     

AN ENHANCED DETERMINISTIC FUZZY TIME SERIES FORECASTING MODEL

The study of fuzzy time series has attracted great interest and is expected to expand rapidly. Various forecasting models including high-order models have been proposed to improve forecasting accuracy or reducing computational cost. However, there exist two important issues, namely, rule redundancy and high-order redundancy that have not yet been investigated. This article proposes a novel forecasting model to tackle such issues. It overcomes the major hurdle of determining the k-order in high-order models and is enhanced to allow the handling of multi-factor forecasting problems by removing the overhead of deriving all fuzzy logic relationships beforehand. Two novel performance evaluation metrics are also formally derived for comparing performances of related forecasting models. Experimental results demonstrate that the proposed forecasting model outperforms the existing models in efficiency.     

An improved method for forecasting enrollments based on fuzzy time series and particle swarm optimization

Many forecasting models based on the concept of fuzzy time series have been proposed in the past decades. Two main factors, which are the lengths of intervals and the content of forecast rules, impact the forecasted accuracy of the models. How to find the proper content of the main factors to improve the forecasted accuracy has become an interesting research topic. Some forecasting models, which combined heuristic methods or evolutionary algorithms (such as genetic algorithms and simulated annealing) with the fuzzy time series, have been proposed but their results are not satisfied. In this paper, we use the particle swarm optimization to find the proper content of the main factors. A new hybrid forecasting model which combined particle swarm optimization with fuzzy time series is proposed to improve the forecasted accuracy. The experimental results of forecasting enrollments of students of the University of Alabama show that the new model is better than any existing models, and it can get better quality solutions based on the first-order and the high-order fuzzy time series, respectively.     

Soft Computing Techniques for Classification of Voiced/Unvoiced Phonemes

A method that uses fuzzy logic to classify two simple speech features for the automatic classification of voiced and unvoiced phonemes is proposed. In addition, two variants, in which soft computing techniques are used to enhance the performance of fuzzy logic by tuning the parameters of the membership functions, are also presented. The three methods, manually constructed fuzzy logic (VUFL), fuzzy logic optimized with genetic algorithm (VUFL-GA), and fuzzy logic with optimized particle swarm optimization (VUFL-PSO), are implemented and then evaluated using the TIMIT speech corpus. Performance is evaluated using the TIMIT database in both clean and noisy environments. Four different noise types from the AURORA database—babble, white, restaurant, and car noise—at six different signal-to-noise ratios (SNRs) are used. In all cases, the optimized fuzzy logic methods (VUFLGA and VUFL-PSO) outperformed manual fuzzy logic (VUFL). The proposed method and variants are suitable for applications featuring the presence of highly noisy environments. In addition, classification accuracy by gender is also studied.     

Air quality prediction by neuro-fuzzy modeling approach

This paper proposes an air quality prediction system based on the neuro-fuzzy network approach. Historical time series data are employed to derive a set of fuzzy rules, or equivalently a neuro-fuzzy network, for forecasting air pollutant concentrations and environmental factors in the future. Due to the uncertainty of the involved impact factors, fuzzy elements are added to the forecasting system. First of all, training data are partitioned into fuzzy clusters whose membership functions are characterized by the estimated means and variances. From these fuzzy clusters, fuzzy rules are extracted and a four-layer fuzzy neural network is constructed. Then genetic, particle swarm optimization, and steepest descent backpropagation algorithms are applied to train the network. The network outputs, derived through the fuzzy inference process, produce the forecast air pollutant concentrations or air quality indices. Our proposed approach has the following advantages: (1) Adding fuzzy elements can more appropriately deal with the uncertainty of the impact factors involved; (2) The distribution of training data can be described properly by fuzzy clusters with statistical means and variances; (3) Fuzzy rules are extracted automatically from the training data, instead of being supplied manually by human experts; (4) The obtained fuzzy rules are of high quality, and their parameters can be optimized effectively.     

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。     

Power quality time series data mining using S-transform and fuzzy expert system

This paper presents a new approach for power quality time series data mining using S-transform based fuzzy expert system (FES). Initially the power signal time series disturbance data are pre-processed through an advanced signal processing tool such as S-transform and various statistical features are extracted, which are used as inputs to the fuzzy expert system for power quality event detection. The proposed expert system uses a data mining approach for assigning a certainty factor for each classification rule, thereby providing robustness to the rule in the presence of noise. Further to provide a very high degree of accuracy in pattern classification, both the Gaussian and trapezoidal membership functions of the concerned fuzzy sets are optimized using a fuzzy logic based adaptive particle swarm optimization (PSO) technique. The proposed hybrid PSO-fuzzy expert system (PSOFES) provides accurate classification rates even under noisy conditions compared to the existing techniques, which show the efficacy and robustness of the proposed algorithm for power quality time series data mining.     

基于自相关函数的模糊时间序列优化算法

针对模糊时间序列模型中模糊推理规则的优化问题, 提出一种时间序列的自相关理论与模糊时间序列相结合的算法. 首先考查数据平稳化; 然后运用传统的数据模糊化方法得到模糊集, 进而建立模糊规则, 并运用自相关函数理论对模糊规则进行优化; 最后通过对Alabama 大学注册人数的预测验证了所提出算法的有效性.