A computational method of forecasting based on high-order fuzzy time series

This paper presents a computational method of forecasting based on high-order fuzzy time series. The developed computational method provides a better approach to overcome the drawback of existing high-order fuzzy time series models. Its simplicity lies with the use of differences in consecutive values of various orders as forecasting parameter and a w-step fuzzy predictor in place of complicated computations of fuzzy logical relations. The objective of the present study is to examine the suitability of various high-order fuzzy time series models in forecasting. The general suitability of the developed method has been tested by implementing it in the forecasting of student enrollments of the University of Alabama and in the forecasting of crop (Lahi) production, a case of high uncertainty in time series data. The results obtained have been compared in terms of average error of forecast to show superiority of the proposed model.     

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.     

Handling forecasting problems based on two-factors high-order fuzzy time series

In our daily life, people often use forecasting techniques to predict weather, economy, population growth, stock, etc. However, in the real world, an event can be affected by many factors. Therefore, if we consider more factors for prediction, then we can get better forecasting results. In recent years, many researchers used fuzzy time series to handle prediction problems. In this paper, we present a new method to predict temperature and the Taiwan Futures Exchange (TAIFEX), based on the two-factors high-order fuzzy time series. The proposed method constructs two-factors high-order fuzzy logical relationships based on the historical data to increase the forecasting accuracy rate. The proposed method gets a higher forecasting accuracy rate than the existing methods.     

A high-order fuzzy time series forecasting model for internet stock trading

Recently, many fuzzy time series models have already been used to solve nonlinear and complexity issues. However, first-order fuzzy time series models have proven to be insufficient for solving these problems. For this reason, many researchers proposed high-order fuzzy time series models and focused on three main issues: fuzzification, fuzzy logical relationships, and defuzzification. This paper presents a novel high-order fuzzy time series model which overcomes the drawback mentioned above. First, it uses entropy-based partitioning to more accurately define the linguistic intervals in the fuzzification procedure. Second, it applies an artificial neural network to compute the complicated fuzzy logical relationships. Third, it uses the adaptive expectation model to adjust the forecasting during the defuzzification procedure. To evaluate the proposed model, we used datasets from both the Taiwanese stock index from 2000 to 2003 and from the student enrollment records of the University of Alabama. The results of our study show that the proposed model is able to obtain an accurate forecast without encountering conventional fuzzy time series issues.     

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.     

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。     

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.     

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.     

一种新的模糊时间序列模型的预测方法

针对目前在模糊时间序列模型中论域划分及数据模糊化方法存在的问题,首先提出了基于模糊聚类算法(FCM)的具有可调参数的模糊时间序列论域的非等分划分方法;然后,在数据模糊化时通过距离客观地定义了模糊集,并利用最小标准误差(RMSE)确定最优的预测结果和聚类数;最后,通过 Alabama 大学注册人数的预测表明了所提出算法的有效性.     

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.     

Deterministic fuzzy time series model for forecasting enrollments

The fuzzy time series has recently received increasing attention because of its capability of dealing with vague and incomplete data. There have been a variety of models developed to either improve forecasting accuracy or reduce computation overhead. However, the issues of controlling uncertainty in forecasting, effectively partitioning intervals, and consistently achieving forecasting accuracy with different interval lengths have been rarely investigated. This paper proposes a novel deterministic forecasting model to manage these crucial issues. In addition, an important parameter, the maximum length of subsequence in a fuzzy time series resulting in a certain state, is deterministically quantified. Experimental results using the University of Alabama’s enrollment data demonstrate that the proposed forecasting model outperforms the existing models in terms of accuracy, robustness, and reliability. Moreover, the forecasting model adheres to the consistency principle that a shorter interval length leads to more accurate results.     

Fuzzy time series forecasting based on axiomatic fuzzy set theory

Neural Computing and Applications - In fuzzy time series, a way of representing their original numeric data through a collection of fuzzy sets plays a pivotal role and impacts the prediction...     

A new deep intuitionistic fuzzy time series forecasting method based on long short-term memory

The Journal of Supercomputing - In recent years, deep artificial neural networks can have better forecasting performance than many other artificial neural networks. The long short-term memory...     

A computational intelligence-based forecasting system for telecommunications time series

In this work a computational intelligence-based approach is proposed for forecasting outgoing telephone calls in a University Campus. A modified Takagi-Sugeno-Kang fuzzy neural system is presented, where the consequent parts of the fuzzy rules are neural networks with an internal recurrence, thus introducing the dynamics to the overall system. The proposed model, entitled Locally Recurrent Neurofuzzy Forecasting System (LR-NFFS), is compared to well-established forecasting models, where its particular characteristics are highlighted.     

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 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 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.     

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。     

青霉素发酵过程中的Type-2模糊预测方法

根据模糊时间序列的模型和算法,本文利用Type-2型模糊隶属度的"宽带"效应具有处理更多信息的特点,给出了基于Type-2模糊时间序列的预测方法,克服了Type-1模糊时间序列模型只用到一个变量进行预测的缺点.避免了只有部分观测值在预测中用到,提高了青霉素发酵过程生物质浓度预测的准确性,实现青霉素发酵过程生物质浓度的测量.     

Recurrent type-1 fuzzy functions approach for time series forecasting

Forecasting the future values of a time series is a common research topic and is studied using probabilistic and non-probabilistic methods. For probabilistic methods, the autoregressive integrated moving average and exponential smoothing methods are commonly used, whereas for non-probabilistic methods, artificial neural networks and fuzzy inference systems (FIS) are commonly used. There are numerous FIS methods. While most of these methods are rule-based, there are a few methods that do not require rules, such as the type-1 fuzzy function (T1FF) approach. While it is possible to encounter a method such as an autoregressive (AR) model integrated with a T1FF, no method that includes T1FF and the moving average (MA) model in one algorithm has yet been proposed. The aim of this study is to improve forecasting by taking the disturbance terms into account. The input dataset is organized using the following variables. First, the lagged values of the time series are used for the AR model. Second, a fuzzy c-means clustering algorithm is used to cluster the inputs. Third, for the MA, the residuals of fuzzy functions are used. Hence, AR, MA, and the degree of memberships of the objects are included in the input dataset. Because the objective function is not derivative, particle swarm optimization is preferable for solving it. The results on several datasets show that the proposed method outperforms most of the methods in literature.