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.     

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.     

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.     

Forecasting time series with genetic fuzzy predictor ensemble

This paper proposes a genetic fuzzy predictor ensemble (GFPE) for the accurate prediction of the future in the chaotic or nonstationary time series. Each fuzzy predictor in the GFPE is built from two design stages, where each stage is performed by different genetic algorithms (GA). The first stage generates a fuzzy rule base that covers as many of training examples as possible. The second stage builds fine-tuned membership functions that make the prediction error as small as possible. These two design stages are repeated independently upon the different partition combinations of input-output variables. The prediction error will be reduced further by invoking the GFPE that combines multiple fuzzy predictors by an equal prediction error weighting method. Applications to both the Mackey-Glass chaotic time series and the nonstationary foreign currency exchange rate prediction problem are presented. The prediction accuracy of the proposed method is compared with that of other fuzzy and neural network predictors in terms of the root mean squared error (RMSE)     

An adaptive fuzzy information retrieval model to improve response time perceived by e-commerce clients

In this paper, an adaptive fuzzy logic-based information retrieval model is presented to enable users retrieve exact and specific information they sort after. The proposed IR model takes into consideration the limited bandwidth between ISP and its users; and the characteristics (processor speed, memory size, resolution, availability of anti-virus, etc.) of clients’ devices in ensuring that a customer has a fruitful and eventful session while conducting business online. The model was designed using unified modelling language and implemented using Borland JBuilder. A performance evaluation of the proposed information retrieval system using two evaluation measures was conducted. The experimental result indicated that the model has an acceptable performance.     

Temperature prediction using fuzzy time series

A drawback of traditional forecasting methods is that they can not deal with forecasting problems in which the historical data are represented by linguistic values. Using fuzzy time series to deal with forecasting problems can overcome this drawback. In this paper, we propose a new fuzzy time series model called the two-factors time-variant fuzzy time series model to deal with forecasting problems. Based on the proposed model, we develop two algorithms for temperature prediction. Both algorithms have the advantage of obtaining good forecasting results.     

Financial time series forecasting with a bio-inspired fuzzy model

In general, times series forecasting is considered as a highly complex problem, which is particularly true for financial time series. In this paper, a fuzzy model evolved through a bio-inspired algorithm is proposed to produce accurate models for the prediction of these time series. The performance of this model is compared to that of a group of state-of-the-art statistical models. A thorough experimental study is designed and carry out in order to assess the merits of the proposal. The experimental results allow us to state that our proposal forecasts consistently outperform the other considered methods.     

An approach to the linguistic summarization of time series using a fuzzy quantifier driven aggregation

We extend our previous work on the linguistic summarization of time series data meant as the linguistic summarization of trends, i.e. consecutive parts of the time series, which may be viewed as exhibiting a uniform behavior under an assumed (degree of) granulation, and identified with straight line segments of a piecewise linear approximation of the time series. We characterize the trends by the dynamics of change, duration, and variability. A linguistic summary of a time series is then viewed to be related to a linguistic quantifier driven aggregation of trends. We primarily employ for this purpose the classic Zadeh's calculus of linguistically quantified propositions, which is presumably the most straightforward and intuitively appealing, using the classic minimum operation and mentioning other t‐norms. We also outline the use of the Sugeno and Choquet integrals proposed in our previous papers. We show an application to the absolute performance type analysis of time series data on daily quotations of an investment fund over an 8‐year period, by presenting first an analysis of characteristic features of quotations, under various (degrees of) granulations assumed, and then by listing some more interesting and useful summaries obtained. We propose a convenient presentation of linguistic summaries focused on some characteristic feature exemplified by what happens “almost always,” “very often,” “quite often,” “almost never,” etc. All these analyses are meant to provide means to support a human user to make decisions. © 2010 Wiley Periodicals, Inc.     

A bivariate fuzzy time series model to forecast the TAIEX

Fuzzy time series models have been applied to forecast various domain problems and have been shown to forecast better than other models. Neural networks have been very popular in modeling nonlinear data. In addition, the bivariate models are believed to outperform the univariate models. Hence, this study intends to apply neural networks to fuzzy time series forecasting and to propose bivariate models in order to improve forecasting. The stock index and its corresponding index futures are taken as the inputs to forecast the stock index for the next day. Both in-sample estimation and out-of-sample forecasting are conducted. The proposed models are then compared with univariate models as well as other bivariate models. The empirical results show that one of the proposed models outperforms the many other models.     

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.     

多变量时间序列的模糊决策树挖掘*

针对目前时间序列决策研究方法的一些缺陷,提出了多变量时间序列模糊决策树挖掘方法,并给出了该方法的实验分析。实验结果证明该方法能够找出多变量时间序列子序列的形态与某个序列的后期趋势或状态的决策信息。     

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.     

一种非线性自适应混沌时间序列预测方法

基函数线性叠加的混沌时间序列预测算法不具有动态特性和明确的物理意义。改进的策略使用与混沌序列的非高斯特性相联系的函数作为基函数,使其能解释为表征混沌序列的高阶统计特性。同时,在算法中引入非线性反馈环节,使其具有了动态特性。数值仿真表明,以之为基础的自适应预测算法在一步预测性能和长期预测能力方面都优于常用的线性预测方法和已有的自适应预测算法。     

An approach to adaptive control of fuzzy dynamic systems

This paper discusses adaptive control for a class of fuzzy dynamic models. The adaptive control law is first designed in each local region and then constructed in the global domain. It is shown that the resulting fuzzy adaptive control system is globally stable. Robustness issues of the adaptive control system are also addressed. A simulation example is given for demonstration of the application of the approach     

Bacterially inspired evolving system with an application to time series prediction

This paper explores the synergies between evolutionary computation and synthetic biology, developing an in silico evolutionary system that is inspired by the behavior of bacterial populations living in continuously changing environments. This system creates a 3D environment seeded with a simulated population of bacteria that eat, reproduce, interact with each other and with the environment and eventually die. This provides a 3D framework implementing an evolutionary process. The subject of the evolution is each bacterium's internal process, defining its interactions with the environment. The evolutionary goal is the survival of the population under successive, continuously changing environmental conditions. The key advantage of this bacterial evolutionary system is its decentralized, asynchronous, parallel and self-adapting general-purpose evolutionary process. We describe this system and present the results of an application to the evolution of a bacterial population that learns how to predict the presence or absence of food in the environment by analyzing three input signals from the environment. The resulting populations successfully evolve by continuously improving their fitness under different environmental conditions, demonstrating their adaptability to a fluctuating medium.     

An intuitionistic fuzzy system for time series analysis in plant monitoring and diagnosis

We describe in this paper a proposed new approach for fuzzy inference in intuitionistic fuzzy systems. The new approach combines the outputs of two traditional fuzzy systems to obtain the final conclusion of the intuitionistic fuzzy system. The new method provides an efficient way of calculating the output of an intuitionistic fuzzy system, and as consequence can be applied to real-world problems in many areas of application. We illustrate the new approach with a simple example to motivate the ideas behind this work. We also illustrate the new approach for fuzzy inference with a more complicated example of monitoring a non-linear dynamic plant.     

BP神经网络和模糊时间序列组合预测模型及其应用

为了解决非线性的时间序列预测问题,提出了BP神经网络和模糊时间序列相结合的预测模型.利用BP神经网络自学习和模糊集能够更客观反应实际情况,通过对时间序列差分模糊化建立数学模型,BP神经网络进行训练,最后去模糊化还原实际.将这种预测方法应用到矿产资源镍价格中,取得了较好的效果.