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 effective neural network and fuzzy time series-based hybridized model to handle forecasting problems of two factors

Fuzzy time series forecasting method has been applied in several domains, such as stock market price, temperature, sales, crop production and academic enrollments. In this paper, we introduce a model to deal with forecasting problems of two factors. The proposed model is designed using fuzzy time series and artificial neural network. In a fuzzy time series forecasting model, the length of intervals in the universe of discourse always affects the results of forecasting. Therefore, an artificial neural network- based technique is employed for determining the intervals of the historical time series data sets by clustering them into different groups. The historical time series data sets are then fuzzified, and the high-order fuzzy logical relationships are established among fuzzified values based on fuzzy time series method. The paper also introduces some rules for interval weighing to defuzzify the fuzzified time series data sets. From experimental results, it is observed that the proposed model exhibits higher accuracy than those of existing two-factors fuzzy time series models.     

Adaptive-expectation based multi-attribute FTS model for forecasting TAIEX

In recent years, there have been many time series methods proposed for forecasting enrollments, weather, the economy, population growth, and stock price, etc. However, traditional time series, such as ARIMA, expressed by mathematic equations are unable to be easily understood for stock investors. Besides, fuzzy time series can produce fuzzy rules based on linguistic value, which is more reasonable than mathematic equations for investors. Furthermore, from the literature reviews, two shortcomings are found in fuzzy time series methods: (1) they lack persuasiveness in determining the universe of discourse and the linguistic length of intervals, and (2) only one attribute (closing price) is usually considered in forecasting, not multiple attributes (such as closing price, open price, high price, and low price). Therefore, this paper proposes a multiple attribute fuzzy time series (FTS) method, which incorporates a clustering method and adaptive expectation model, to overcome the shortcomings above. In verification, using actual trading data of the Taiwan Stock Index (TAIEX) as experimental datasets, we evaluate the accuracy of the proposed method and compare the performance with the (Chen, 1996 [7], Yu, 2005 [6], and Cheng, Cheng, & Wang, 2008 [20]) methods. The proposed method is superior to the listing methods based on average error percentage (MAER).     

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.     

模糊时间序列建模及股票市场多步预测

首先应用模糊聚类方法将数据分类,以相邻两个聚类中心的中点作为子区间的分界点来划分论域,并以此将时间序列模糊化为模糊时间序列;其次根据证券市场主要量价指标建立了具有多个前件的高阶模糊关系;最后将该模型用于上证股票综合指数和深证股票成分指数的多步预测和涨跌趋势预测。与典型模糊时间序列模型比较,涨跌趋势预测准确率有较大提高,多步预测结果表明模型具有较好的泛化能力。     

Forecasting enrollments using high‐order fuzzy time series and genetic algorithms

In recent years, many researchers have presented different forecasting methods to deal with forecasting problems based on fuzzy time series. When we deal with forecasting problems using fuzzy time series, it is important to decide the length of each interval in the universe of discourse due to the fact that it will affect the forecasting accuracy rate. In this article, we present a new method to deal with the forecasting problems based on high‐order fuzzy time series and genetic algorithms, where the length of each interval in the universe of discourse is tuned by using genetic algorithms, and the historical enrollments of the University of Alabama are used to illustrate the forecasting process of the proposed method. The proposed method can achieve a higher forecasting accuracy rate than the existing methods. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 485–501, 2006.     

An adaptive ordered fuzzy time series with application to FOREX

An adaptive ordered fuzzy time series is proposed that employs an adaptive order selection algorithm for composing the rule structure and partitions the universe of discourse into unequal intervals based on a fast self-organising strategy. The automatic order selection of FTS as well as the adaptive partitioning of each interval in the universe of discourse is shown to greatly affect forecasting accuracy. This strategy is then applied to prediction of FOREX market. Financial markets, such as FOREX, are generally attractive applications of FTS due to their poorly understood model as well as their great deal of uncertainty in terms of quote fluctuations and the behaviours of the humans in the loop. Specifically, since the FOREX market can exhibit different behaviours at different times, the adaptive order selection is executed online to find the best order of the FTS for current prediction. The order selection module uses voting, statistical analytic and emotional decision making agents. Comparison of the proposed method with earlier studies demonstrates improved prediction accuracy at similar computation cost.     

Quick Design of Fuzzy Controllers With Good Interpretability in Mobile Robotics

This paper presents a methodology for the design of fuzzy controllers with good interpretability in mobile robotics. It is composed of a technique to automatically generate a training data set plus an efficient algorithm to learn fuzzy controllers. The proposed approach obtains a highly interpretable knowledge base in a very reduced time, and the designer only has to define the number of membership functions and the universe of discourse of each variable, together with a scoring function. In addition, the learned fuzzy controllers are general because the training set is composed of a number of automatically generated examples that cover the universe of discourse of each variable uniformly and with a predefined precision. The methodology has been applied to the design of a wall-following and moving object following behavior. Several tests in simulated environments using the Nomad 200 robot software and a comparison with another learning method show the performance and advantages of the proposed approach.     

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。     

Predicting daily ozone concentration maxima using fuzzy time series based on a two-stage linguistic partition method

Air pollution is a result of global warming, greenhouse effects, and acid rain. Especially in highly industrialization areas, air pollution has become a major environmental issue. Poor air quality has both acute and chronic effects on human health. The detrimental effects of ambient ozone on human health and the Earth’s ecosystem continue to be a national concern in Taiwan. The pollutant standard index (PSI) has been adopted to assess the degree of air pollution in Taiwan. The standardized daily air quality report provides a simple number on a scale of 0 to 500 related to the health effects of air quality levels. The report focuses on health and the current PSI subindices to reflect measured ozone (O₃) concentrations. Therefore, this study uses the O₃ attribute to evaluate air quality. In an effort to forecast daily maximum ozone concentrations, many researchers have developed daily ozone forecasting models. However, this continuing worldwide environmental problem suggests the need for more accurate models. This paper proposes two new fuzzy time series based on a two-stage linguistic partition method to predict air quality with daily maximum O₃ concentration: Stage 1, use the fuzzy time series based on the cumulative probability distribution approach (CPDA) to partition the universe of discourse into seven intervals; Stage 2, use two linguistic partition methods, the CPDA and the uniform discretion method (UDM), to repartition each interval into three subintervals. To verify the forecasting performance of the proposed methods in detail, the practical collected data is used as and evaluating dataset; five other methodologies (AR, MA, ARMA, Chen’s and Yu’s) are used as comparison models. The proposed methods both show a greatly improved performance in daily maximal ozone concentration prediction accuracy compared with the other 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.     

Modeling fitting-function-based fuzzy time series patterns for evolving stock index forecasting

Fuzzy time series models that have been developed have been widely applied to many applications of forecasting future stock prices or weighted indexes in the financial field. Three interesting problems have been identified in relation to the associated time series methods, as follows: (1) conventional time series models that consider single variables on associated problems only, (2) fuzzy time series models that determine the interval length of the linguistic values subjectively, and (3) selected variables that depend on personal experience and opinion subjectively. In light of the above limitations, this study constitutes a hybrid seven-step procedure that proposes three integrated fuzzy time series models that are based on fitting functions to forecast weighted indexes of the stock market. First, the proposed models employ Pearson correlation coefficients to objectively select important technical indicators. Second, this study utilizes an objective algorithm to determine the lower bound and upper bound of the universe of discourse automatically. Third, the proposed models use the spread-partition algorithm to automatically determine linguistic intervals. Finally, they combine the transformed variables to build three fuzzy time series models using the criterion of the minimal root mean square error (RMSE). Furthermore, this study provides all of the necessary justifying information for using a linear process to select the inputs for the given non-linear data. To further evaluate the performance of the proposed models, the transaction records of TAIEX (Taiwan Stock Exchange Capitalization Weighted Stock Index) and HSI (Hang Seng Indexes) from 1998/01/03 to 2006/12/31 are used to illustrate the methodology with two experimental data sets. Chen’s (Fuzzy Sets Syst. 81:311–319, 1996) model, Yu’s (Physica A 349:609–624, 2005) model, support vector regression (SVR), and partial least square regression (PLSR) are used as models to be compared with the proposed model when given the same data sets. The analytical results show that the proposed models outperform the listed models under the evaluation criteria of the RMSE (in contrast to the forecasting accuracy) for forecasting a weighted stock index in both the Taiwan and Hong Kong stock markets.     

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.     

直觉模糊时间序列建模及应用

针对模糊时间序列对于预测不确定性的控制、有效的分区间隔和不同分区间隔达到一致的预测准确性方面研究的不足,构建了直觉模糊时间序列预测模型。新模型应用直觉模糊??均值聚类算法优化序列区间划分,充分考虑数据点固有的模糊不确定性,较好地反映了系统的特征分布,提高了复杂环境中时间序列的预测性能且允许处理多因子预测问题。最后通过实例验证了所提出方法的有效性和优越性。     

A neurofuzzy scheme to on-line identification in an adaptive–predictive control

A neurofuzzy scheme has been designed to carry out on-line identification, with the aim of being used in an adaptive–predictive dynamic matrix control (DMC) of unconstrained nonlinear systems represented by a transfer function with varying parameters. This scheme supplies to the DMC controller the linear model and the nonlinear output predictions at each sample instant, and is composed of two blocks. The first one makes use of a fuzzy partition of the external variable universe of discourse, which smoothly commutes between several linear models. In the second block, a recurrent linear neuron with interpretable weights performs the identification of the models by means of supervised learning. The resulting identifier has several main advantages: interpretability, learning speed, and robustness against catastrophic forgetting. The proposed controller has been tested both on simulation and on a real laboratory plant, showing a good performance.     

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.     

作物产量预测的粒度分析法

针对作物产量预测,提出基于商空间粒度计算的分析法。在商空间粒度计算理论思想下,分析作物产量序列中粒度的选取,用属性划分方法对论域X进行颗粒化,对属性f取不同的粒度进行颗粒化。通过属性的粒度变化对论域进行划分,得到新的商空间并应用其解决问题,可以降低问题复杂度。通过商空间理论中的分层与合成技术选取大小合适的粒度,能全面获取产量序列中的信息,也更加符合人类智能特点。冬小麦产量预测实验结果也证明这种粒度分析和选取方法是有效的。     

一种新的基于模糊C均值算法的模糊时间序列确定性预测模型

模拟时间序列因为在处理数据采集中固有的不确定性和含糊性方面的显著能力而得到了越来越多的的关注,已经有许多模型致力于改进预测准确性和减少预测的计算开销,然而对于预测不确定性的控制、有效的分区间隔和对于不同的分区间隔达到一致的预测准确性方面研究较少。针对现有预测模型的不足,本文提出了一种新的预测模型,新模型增强了预测的性能并允许处理两因子预测问题。在新模型中,应用模糊均值算法来处理模糊时间序列的区间划分,划分时考虑了数据点的性质,产生不等大小的区间。最后在仿真实验中采用真实的观察数据,仿真实验结果表明本文提出的预测模型在预测准确性方面要优于现有的其他预测模型。     

Ratio-based lengths of intervals to improve fuzzy time series forecasting.

The objective of this study is to explore ways of determining the useful lengths of intervals in fuzzy time series. It is suggested that ratios, instead of equal lengths of intervals, can more properly represent the intervals among observations. Ratio-based lengths of intervals are, therefore, proposed to improve fuzzy time series forecasting. Algebraic growth data, such as enrollments and the stock index, and exponential growth data, such as inventory demand, are chosen as the forecasting targets, before forecasting based on the various lengths of intervals is performed. Furthermore, sensitivity analyses are also carried out for various percentiles. The ratio-based lengths of intervals are found to outperform the effective lengths of intervals, as well as the arbitrary ones in regard to the different statistical measures. The empirical analysis suggests that the ratio-based lengths of intervals can also be used to improve fuzzy time series forecasting.     

Function approximation based on fuzzy rules extracted frompartitioned numerical data

We present an efficient method for extracting fuzzy rules directly from numerical input-output data for function approximation problems. First, we convert a given function approximation problem into a pattern classification problem. This is done by dividing the universe of discourse of the output variable into multiple intervals, each regarded as a class, and then by assigning a class to each of the training data according to the desired value of the output variable. Next, we partition the data of each class in the input space to achieve a higher accuracy in approximation of class regions. Partition terminates according to a given criterion to prevent excessive partition. For class region approximation, we discuss two different types of representations using hyperboxes and ellipsoidal regions, respectively. Based on a selected representation, we then extract fuzzy rules from the approximated class regions. For a given input datum, we convert, or in other words, defuzzify, the resulting vector of the class membership degrees into a single real value. This value represents the final result approximated by the method. We test the presented method on a synthetic nonlinear function approximation problem and a real-world problem in an application to a water purification plant. We also compare the presented method with a method based on neural networks.