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 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.     

基于二阶马尔可夫模型的模糊时间序列预测

针对当前模糊时间序列模型存在的缺乏有效论域划分方法和模糊关系前件多为一阶的现状,提出了基于二阶马尔可夫模型的模糊时间序列预测方法。应用模糊C均值聚类方法,获得序列中元素的隶属度;引入二阶马尔可夫模型中的转移概率矩阵表示模糊关系,更新了传统的模糊关系表示和运算;预测待求元素在各个模糊聚类的隶属度,并利用重心法去模糊化。将该模型运用到移动3G网络的性能预测中,与传统模糊时间序列预测方法相比,其准确性有了较大提高。     

Statistical fuzzy interval neural networks for currency exchange rate time series prediction

In this paper, the statistical fuzzy interval neural network with statistical interval input and output values is proposed to perform statistical fuzzy knowledge discovery and the currency exchange rate prediction. Time series data sets are grouped into time series data granules with statistical intervals. The statistical interval data sets including week-based averages, maximum errors of estimate and standard deviations are used to train the fuzzy interval neural network to discover fuzzy IF-THEN rules. The output of the fuzzy interval neural network is an interval value with certain percent confidence. Simulations are completed in terms of the exchange rates between US Dollar and other three currencies (Japanese Yen, British Pound and Hong Kong Dollar). The simulation results show that the fuzzy interval neural network can provide more tolerant prediction results.     

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。     

Determination of temporal information granules to improve forecasting in fuzzy time series

Partitioning the universe of discourse and determining intervals containing useful temporal information and coming with better interpretability are critical for forecasting in fuzzy time series. In the existing literature, researchers seldom consider the effect of time variable when they partition the universe of discourse. As a result, and there is a lack of interpretability of the resulting temporal intervals. In this paper, we take the temporal information into account to partition the universe of discourse into intervals with unequal length. As a result, the performance improves forecasting quality. First, time variable is involved in partitioning the universe through Gath–Geva clustering-based time series segmentation and obtain the prototypes of data, then determine suitable intervals according to the prototypes by means of information granules. An effective method of partitioning and determining intervals is proposed. We show that these intervals carry well-defined semantics. To verify the effectiveness of the approach, we apply the proposed method to forecast enrollment of students of Alabama University and the Taiwan Stock Exchange Capitalization Weighted Stock Index. The experimental results show that the partitioning with temporal information can greatly improve accuracy of forecasting. Furthermore, the proposed method is not sensitive to its parameters.     

多粒度时间序列下粒度决策的演化模型研究

目前,粗糙集理论大多数的研究应用都停留在静态表的基础上,但在实际中决策信息表的数据是在不停的增加更新当中,静态的方法在处理不停增加和变换的数据时有着很明显的局限性。在经典粗糙集理论的基础上,引入多粒度时间序列,对决策信息系统划分后,研究各个粒所产生的决策间的相互关联性,建立相关的粒度决策演化模型,并通过实例验证同源演化的有效可行性。     

模糊规则模型的粒度性能指标评估方法

模糊规则模型广泛应用于许多领域,而现有的模糊规则模型主要使用基于数值形式的性能评估指标,忽略了对于模糊集合本身的评价,因此提出了一种模糊规则模型性能评估的新方法。该方法可以有效地评估模糊规则模型输出结果的非数值（粒度）性质。不同于通常使用的数值型性能指标（比如均方误差（MSE））,该方法通过信息粒的特征来表征模型输出的粒度结果的质量,并将该指标使用在模糊模型的性能优化中。信息粒性能采用（数据的）覆盖率和（信息粒自身的）特异性两个基本指标得以量化,并通过使用粒子群优化实现了粒度输出质量（表示为覆盖率和特异性的乘积）的最大化。此外,该方法还优化了模糊聚类形成的信息粒的分布。实验结果表明该指标对于模糊规则模型性能评估的有效性。     

A new approach to obtain K-means initial clustering center based on fuzzy granular computing

The traditional K-means is very sensitive to initial clustering centers and the clustering result will wave follow the different initial input. To remove this sensitivity, a new method is proposed to get initial clustering centers. This method is as follows： provide a normalized distance function d（di,dj） in the fuzzy granularity space of data objects, then use the function to do a initial clustering work to these data objects who has a less distance than granularity dλ, then get the initial clustering centers. Approved by the test, this method has such advantages on increasing the rate of accuracy and reducing the program times.     

嵌入局部模型的SOM网络对混沌时间序列预测研究

针对混沌时间序列特征空间多变性的特点，在SOM自组织神经网络中嵌入局部线性回归模型，用于混沌时间序列的预测，该方法融合了局部线性预测的优点以及SOM网络数据快速聚类能力，可视化特征识别性质和拓扑保留映射特点，既可减少运算时间和存储空间，又能适应混沌时间序列的多变特征，取得了较高的预测精度。     

A novel method for constructing the optimal hierarchical structure based on fuzzy granular space

Granular computing serves as a general framework for complex problem solving in broad scopes and at various levels. The granularity was constructed via many ways, however, for complex systems there remain two challenges including determining a reasonable granularity and extracting the hierarchical information. In this paper, a new method is presented for constructing the optimal hierarchical structure based on fuzzy granular space. Firstly, the inter-class deviations and intra-class deviations were introduced, whose properties were investigated in depth and approved mathematically. Secondly, the fuzzy hierarchical evaluation index is developed, followed with a novel model for extracting the global optimal hierarchical structure established. An algorithm is then proposed, which reliably constructs the multi-level structure of complex system. Finally, to reduce the complexity, the granular signatures are extracted according to the nearest-to-center principle; with the use of the signatures, a classifier is designed for verifying our method. The validation of this method is approved by an application to the H1N1 influenza virus system. The theories and methodologies on granular computing presented here are helpful for capturing the structural information of complex system, especially for data mining and knowledge discovery.     

基于模糊粒度计算的文本聚类研究

典型的文本聚类算法是一种硬划分,但是实际上由于中文文本的多样性和大量性更适合进行软划分,模糊集理论的提出为这种软划分提供了有力的分析工具。传统的模糊聚类方法大都是通过对隶属度的矩阵逐步迭代得到模糊等价矩阵或模糊划分的方法实现聚类,这个过程需要大量的存储空间。基于模糊粒度计算的文本聚类算法是在文档集合的模糊粒度空间上给定一个归一化的距离函数d（d_i,d_j）,对距离小于粒度d_λ的文本进行动态聚类。通过实验证明此方法在解决文本聚类问题时具有降低计算复杂度和空间复杂度,适于大量文本的聚类处理。     

A novel high-order weighted fuzzy time series model and its application in nonlinear time series prediction

Conventional time series forecast models can hardly develop the inherent rules of complex non-linear dynamic systems because the strict assumptions they need cannot always be met in reality, whereas fuzzy time series (FTS) techniques can be used even the records of times series have uncertainty and instability since they do not need strict assumptions. In previous study of FTS, the process of aggregating the past observations and assigning proper weights of fuzzy logical relationship groups are ignored, which may lead to poor forecasting accuracy since they are important aspects in time series prediction and analysis where determination of future trends depends only on past observations. In this paper, a novel high-order FTS model is constructed to make time series forecasting. Specifically, by applying the harmony search intelligence algorithm, the optimal lengths of intervals are tuned. Moreover, regularly increasing monotonic quantifiers are employed on fuzzy sets to obtain the weights of ordered weighted aggregation. Simultaneously, the weights of right-hand side of fuzzy logical relationship groups are explored to compensate the presence of bias in the prediction. In the part of empirical analysis, the developed model was applied to predict three well-known time series: numbers of enrollment of Alabama University, TAIEX and electricity load demand of New South Wales and the results obtained were compared with several counterparts, including some old and recently developed models. Experimental results demonstrate that the developed model cannot only achieve higher accuracy of prediction, but also capture the fuzzy features and characters.     

基于动态模糊粒神经网络算法的负荷辨识

针对电力负荷的时变、变结构和非线性等特点,提出一种动态模糊粒神经网络算法.该算法采用粒计算商空间理论和模糊神经网络技术对电力负荷进行建模.将椭圆基函数和模糊ζ-完备性作为在线参数分配机制,避免了初始化选择的随机性.根据模糊规则和输入变量的重要性,对每条规则的输入变量宽度实施在线自适应调整,从而实现了负荷参数和结构同时辨识.实验结果表明了所提出方法的可行性和有效性.     

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.     

两种时间序列模型在客流量预测上的比较

模糊时间序列模型和季节模型都是基于时间序列的模型,为了探讨在时间序列表现出一定的周期性时,哪种模型的预测效果会更好,分别利用模糊时间序列模型和季节模型对南京某商场的客流量进行预测,计算并比较两种方法下的相对误差值和RMSE（Root Mean Square Error）值,发现季节模型的相对误差值图形的平滑度要优于模糊时间序列模型,季节模型的RMSE值小于模糊时间序列模型,这表明考虑到数据特征的模型有更好的预测结果。     

基于商空间的气象时间序列数据挖掘研究

论文从一种新的角度,针对气象时间序列的特点,在商空间粒度计算理论框架下,采用多种粒度,从不同的层次分析复杂的气象数据信息,利用商空间的合成技术,和多侧面递进算法进行综合信息处理。并提出了一种灰色模型GM(1,1)与构造性机器学习方法(交叉覆盖算法)结合的模型对气象时间序列进行数据挖掘(产量预测)。最后,通过该模型在真实数据上的实验(冬小麦产量预测),取得了令人满意的结果。     

基于条件互信息的多维时间序列图模型

在多维时间序列的图模型中引入信息论方法, 提出了多维时间序列中各分量之间直接线性联系存在性的互信息检验．定义了线性条件互信息图, 图中的结点表示多维时间序列的分量, 结点间的边表示各分量之间存在的直接线性相依关系．提出了分量之间条件线性联系存在性的信息论检验方法．图中边的存在性用基于线性条件互信息的统计量检验, 统计量的显著性用置换检验决定．应用到实例中的结果表明本文的方法能迅速准确的捕捉各分量之间的直接线性联系.     

基于遗传算法和模糊决策树的时间序列预测模型

股票价格预测总是投资者和技术分析者感兴趣的一个主题.然而,决定买卖股票的最好时间仍然是困难的,因为有很多因素可能影响股票价格.通过改进模糊决策树建立了一个新型金融时间序列数据预测模型.该预测模型融合数据聚类技术,模糊决策树及遗传算法来构建基于历史数据和技术指标的一个决策系统.提出的GAFDT模型在与各种股票的其它方法相比较时有平均预测准确率为0.82的最好绩效.