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Multi-attribute fuzzy time series method based on fuzzy clustering
Abstract
Traditional time series methods can predict the seasonal problem, but fail to forecast the problems with linguistic value. An alternative forecasting method such as fuzzy time series is utilized to deal with these kinds of problems. Two shortcomings of the existing fuzzy time series forecasting methods are that they lack persuasiveness in determining universe of discourse and the length of intervals, and that they lack objective method for multiple-attribute fuzzy time series. This paper introduces a novel multiple-attribute fuzzy time series method based on fuzzy clustering. The methods of fuzzy clustering are integrated in the processes of fuzzy time series to partition datasets objectively and enable processing of multiple attributes. For verification, this paper uses two datasets: (1) the yearly data on enrollments at the University of Alabama, and (2) the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) futures. The forecasting results show that the proposed method can forecast not only one-attribute but also multiple-attribute data effectively and outperform the listing methods.
... Joshi and Kumar [15] and Gangwar and Kumar [16] used IFSs, utilizing the time series forecasting approach to integrate the degree of hesitation in fuzzy logical links and provide a few time series forecasting models [17]. Some researchers selected data from the University of Alabama's student enrollment and the market prices of SBI shares [18,19] that could be solved using intuitionistic fuzzy time series forecasting. These methods represent distinct ways for computing the forecasting of IFS time series, after which they may be compare to each other using calculated errors. ...
... MSE and AFE from University of Albama's admissions. ErrorCheng et al.[18] Yolcu et al.[39] ...
The literature frequently uses fuzzy inference methods for time series forecasting. In business and other situations, it is frequently necessary to forecast numerous time series. The q-Rung orthopair fuzzy set is a beneficial and competent tool to address ambiguity. In this research, a computational forecasting method based on q-Rung orthopair fuzzy time series has been created to deliver better prediction results to deal with situations containing higher uncertainty caused by large fluctuations in consecutive years' values in time series data and with no visualization of trend or periodicity. The main objective of this article is to handle time series forecasting with the usage of q-Rung orthopair fuzzy sets for things like floods, admission of students, number of patients, etc. After this, people can then manage issues that will arise in the future. Previously, there was a gap in determining the forecasting of data whose entire value of membership and non-membership exceeded 1. To fill this kind of gap, we used q-Rung orthopair fuzzy sets in time series forecasting. We also used numerous algebraic components for the q-Rung orthopair fuzzy time series, which has a union, max-min composition, cartesian product, and algorithm that are useful to calculate the method of data forecasting. Moreover, we also defined the algorithm and proposed MATLAB code that facilitates the execution of mathematical calculations, design, analysis, and optimization (structural and mathematical), and gives results with speed, correctness, and precision. At the end, we tested the model using historical student enrollment data and the annual peak discharge at Guddu Barrage. Furthermore, we calculated the error to get an idea of to what extent this method is suitable.
... It has been demonstrated that SARIMA can provide a sufficient modeling approach for weather forecasting. Depending on the data type, SARIMA can generate multiple potential forecasting models [18,42,43], but generating one SARIMA model is also feasible. Our case study is similar to the study conducted by Dimri et al. (2020), where the authors found that SARIMA (0,1,1) (0,1,1)12 was the most appropriate model for precipitation forecasting in Uttarakhand, India. ...
... Additionally, SARIMA requires a substantial amount of data, with a minimum of 50 values, and optimally around 100 values [43]. However, it may be difficult to obtain this amount of data in some cases due to uncertainties or a lack of measurement tools. ...
The study aimed to forecast and monitor drought over degraded land based on monthly precipitation using the Seasonal Autoregressive Integrated Moving Average (SARIMA) approach. Several statistical parameters to select the most appropriate model were applied. The results indicate that the SARIMA (1,1,1) (0,1,1)12 is the most suitable for 1981 to 2019 CHIRPS time-series data. The combination of precipitation data and this approved model will subsequently be applied to compute, assess, and predict the severity of drought in the study area. The forecasting performance of the generated SARIMA model was evaluated according to the mean absolute percentage error (15%), which indicated that the proposed model showed high performance in forecasting drought. The forecasting trends showed adequate results, fitting well with the historical tendencies of drought events.
... In this section, we evaluate proposed forecasting model in education domain on enrolments data of University of Alabama and compared the obtained results with previous prediction models [3,[31][32][33][34][35] to demonstrate the performance of our method. The obtained forecasting results from the proposed model which are shown in Table 7. o visualize, Figure 4 illustrates the first-order fuzzy time series forecasting model and contrasts it with actual enrollments and other existing models. ...
In recent years, numerous fuzzy time series (FTS) forecasting models have been developed to address complex and incomplete problems. However, the accuracy of these models is specific to the problem at hand and varies across datasets. Despite claims of superiority over traditional statistical and single machine learning-based models, achieving improved forecasting accuracy remains a formidable challenge. In FTS models, the lengths of intervals and fuzzy relationship groups are considered crucial factors influencing forecasting accuracy. Hence, this study introduces an FTS forecasting model based on the graph-based clustering technique. The clustering algorithm, utilized during the fuzzification stage, enables the derivation of unequal interval lengths. The proposed model is applied to forecast two numerical datasets: enrollment data from the University of Alabama and the datasets of Gas prices RON95 in Vietnam. Comparisons of forecasting results between the proposed model and others are conducted for enrollment forecasts at the University of Alabama. The findings reveal that the proposed model achieves higher forecasting accuracy across all orders of fuzzy relationships when compared to its counterparts
... Jiang et al. [27] derived the formula used to predict wind speed. Prior to this, the majority of the researchers used his proposed approach using data from the University of Alabama [28,29]. They compared the mistakes of each result with one another after determining the conclusion to determine the best planned technique. ...
This article presents a higher-order circular intuitionistic fuzzy time series forecasting method for predicting the stock change index, which is shown to be an improvement over traditional time series forecasting methods. The method is based on the principles of circular intuitionistic fuzzy set theory. It uses both positive and negative membership values and a circular radius to handle uncertainty and imprecision in the data. The circularity of the time series is also taken into consideration, leading to more accurate and robust forecasts. The higher-order forecasting capability of this method provides more comprehensive predictions compared to previous methods. One of the key challenges we face when using the amount featured as a case study in our article to project the future value of ratings is the influence of the stock market index. Through rigorous experiments and comparison with traditional time series forecasting methods, the results of the study demonstrate that the proposed higher-order circular intuitionistic fuzzy time series forecasting method is a superior approach for predicting the stock change index.
... Song and Chissom used time-invariant and time-variant methods in forecasting. As a result, several fuzzy time series (FTS) methods have been developed, including Chen [3,4], Chen and Hsu [5], weighted [6], backpropagation [7], multiple-attribute [8], percentage change [9], and the Markov chain [10]. ...
Fuzzy time series (FTS) is one of the forecasting methods that has been developed until now. The fuzzy time series is a forecasting method that uses the concept of fuzzy logic, which Song and Chissom first introduced. The fuzzy time series (FTS) Markov chain uses the Markov chain in defuzzification. The determination of the length of the interval in the fuzzy time series plays an important role in forming a fuzzy logic relationship (FLR), and this FLR will be used to determine the forecasting value. One method that can be used to determine the interval length is average-based. However, several studies use partitioning based on frequency density to obtain the optimal interval length to get better forecasting accuracy. This study combines the fuzzy time series Markov chain, Average-based fuzzy time series, and Fuzzy time series based on frequency density partitioning to become average-based fuzzy time series Markov chain based on the Frequency Density Partition which conducts redivided intervals based on frequency density in the average-based fuzzy time series Markov chain method. This method is implemented in forecasting the Indonesian Islamic stock index (ISSI) for the selected period. The calculation of the accuracy level using the mean square error (MSE) and the mean average percentage error (MAPE) shows that the fuzzy Markov chain-based fuzzy time series based on the frequency density partition has a high level of accuracy in forecasting.
... Among these methods various fuzzy (granular) approaches return good results, see Cheng et al (2008); D'Urso and Maharaj (2009) (2020); Guo et al (2020). In particular, the method proposed in Izakian et al (2015) is worth considering. ...
Creating the proper player profile in training is crucial for athlete development. Although there is a great number of studies concerning this subject, there is no solution that would allow to model it in a convenient way. Applying fuzzy modelling clustering can be useful in this field. Moreover, the application of sophisticated acquisition techniques, like motion capture systems, allow ones to obtain accurate data corresponding to athlete’s movement in the form of a multivariate time series. In this study, the authors undertook the task of clustering the most important at the stage of training tennis strokes such as: Forehand, backhand, and volley. They were represented as trajectories of the tennis racket based on four retro-reflective markers attached to it. The Fuzzy C -Means algorithm, which utilizes the dynamic time warping-based distance to cluster analysis of tennis strokes, has been applied with success to group various kinds of movement of tennis players. The comprehensive analysis included numerous separate tennis moves and their groups. Various analyses depending on their number have been thoroughly carried out. The obtained results allowed creation of the reference stroke model,which can be used for further examination of the tennis players’performance.
... One of the most famous fuzzy-based clustering method used in many forecasting models is fuzzy C-Means (FCM). FCM partitioning is exploited in [56][57][58][59][60][61][62][63]. Although these studies adopt the FCM partitioning method, the FLR are generated differently. ...
Time series forecasting is a powerful tool in planning and decision making, from traditional statistical models to soft computing and artificial intelligence approaches several methods have been developed to generate increasingly accurate forecasts. Fuzzy Time Series (FTS) methods have been introduced in the early 1990’s to handle data uncertainty and to undercome the statistical assumptions of linearity. Many studies have been reporting their good accuracy, simplicity, potential for interpretability and reduced computational complexity. This paper presents a tutorial for FTS methods. First, a review of the relevant literature is made, offering a foundation on the main concepts and FTS-based models for different time series and different types of forecasts. Then, the current challenges and possible solutions, are discussed alongside a timeline of the research developed in this area by the authors that aims at filling some of these gaps. Finally, a tutorial on the pyFTS library is presented. PyFTS is an open and free library coded in Python programming language that was developed by the MINDS Lab (Laboratory of Machine Intelligence and Data Science) and, also provides a set of transformation functions for pre-processing time series and a set of metrics and databases for benchmarking, in addition to implementing several FTS models in the literature.
... A new model aggregating both the global information and the local information was proposed by Huang et al. [15]. Some other methods of partitioning the UD based on information granules [16,17], ant colony optimization and auto-regression [18], fuzzy clustering [19,20], rough-fuzzy [21,22], etc., were proposed. ...
Forecasting methods based on fuzzy time series have been examined intensively during the last few years. Three main factors which affect the accuracy of those forecasting methods are the length of intervals, the way of establishing fuzzy logical relationship groups, and defuzzification techniques. Many researchers focus on studying the methods of optimizing the length of intervals to improve forecasting accuracies by utilizing various optimization techniques. In line with that research trend, this paper proposes a hybrid algorithm combining particle swarm optimization with the simulated annealing technique (PSO-SA) to optimize the length of intervals to improve forecasting accuracies. The experimental results on the datasets of the "enrolments of the University of Al-abama," "killed in car road accidents in Belgium," and the "spot gold in Turkey" have shown; that the proposed forecasting model is more effective than their counterparts.
... As science develops, there are several models of fuzzy time series was proposed to obtain optimal forecasting results. Some of them are models proposed by Chen (1996), Singh (2007, and Cheng (2008). These models have different ways of defuzzification to get the forecast value. ...
... They cannot capture the structure of non-linear relationships due to the assumptions based only on linear relationships among timelagged variables [1]. They fail to predict the problems with linguistic values [2], [3] and fail to have high accuracy in complex problems. They require a large amount of data, and they are time-consuming [4]. ...
Forecasting the future trends is of utmost importance for managers and decision makers in different sectors. Scholars thus have introduced various techniques to the service industry aiming at employing a prediction model with ultimate accuracy and high efficiency. The literature proves that adaptive neuro-fuzzy inference systems (ANFIS) are the most efficiency models. However, the literature lacks reports on how ANFIS parameters may affect the accuracy of the system. Employing tourist arrival records to Cyprus between 2015 and 2019, this study has developed an ANFIS system to evaluate the accuracy performance of different prediction models with varied number of inputs and number or type of membership functions. Results show that the forecasting accuracy of a model with four inputs and four membership functions when the type of membership functions is Gaussian is relatively better than other models. In other words, it can be concluded that the forecast model with four inputs and four Gaussian membership functions is ultimate with the most accurate prediction record with reference to MAE, RMSE, and MAPE. The results of this study may be significant for senior managers and decision-makers of the tourism industry.
... This study proposes a new fuzzy time series model using the Fuzzy K-Medoids clustering algorithm in the fuzzification step of FTS to minimize the negative effects of outliers and abnormal observations on the forecasting performance of fuzzy time series models. In order to evaluate the performance of the proposed method in forecasting and prediction of air pollution in comparison to that of the other fuzzy clustering-based FTS models in the literature (Cheng et al., 2008;Egrioglu et al., 2010), air pollution data consisting of weekly SO 2 concentrations measured at 65 monitoring stations in Turkey is used. According to the results of the analyses, it is observed that the proposed method provides successful forecasting results. ...
Air pollution becomes more and more severe and can cause multifaceted harm to the human body. Forecasting the air quality of a country is important to allow the government to make an important approach for air pollution management and prevention. In recent years, a number of methods have been proposed to predict air quality, such as deterministic, statistical, and machine learning. Research activity in the field of air pollution forecasting using artificial neural networks (ANNs) has increased dramatically in recent years. However, these methods have limitations, such as the development of ANN models entails levels of uncertainty given the black-box nature of ANNs. In this regard, fuzzy time series (FTS) models based on the Fuzzy K-Medoid (FKM) clustering algorithm are comprehensively used to monitor environmental pollution quality. FTS models generally have some advantages when compared with other techniques used in forecasting air pollution as they do not require any statistical assumptions on time series data; and they provide successful forecasting results even in situations where the number of observations is small and where data sets include uncertainty, still allowing for generalization. In this paper, Maier et al. (2010) protocol for ANN model development is presented and applied to assess journal papers dealing with air pollution forecasting using ANN models. The majority of the reviewed works are aimed at the long-term forecasting of outdoor PM10, PM2.5, and oxides of nitrogen and ozone. The vast majority of the identified works utilized meteorological and source emissions predictors almost exclusively.
Furthermore, ad-hoc approaches are predominantly used for determining optimal model predictors, appropriate data subsets, and the optimal model structure. Multilayer perceptron and ensemble-type models are predominantly implemented. Overall, the findings highlight the need for developing systematic protocols for developing powerful ANN models.
... k-means clustering algorithm procedure contains the starting with k groups each of which consists of a single random point and then adding a new point to group whose mean new point is nearest. Cheng, Cheng, and Wang (2008), Lai et al. (2009), and Chen and Tanuwijaya (2011) proposed different FTS forecasting methods using different clustering techniques. Zhang and Zhu (2012), Gangwar and Kumar (2012), Egrioglu, Aladag, and Yolcu (2013), and Askari, Montazerin, and Zarandi (2015) proposed k-means clustering, partitioning of intervals, hybrid approach combining fuzzy c-means, and neural networks based fuzzy and multivariate FTS forecasting methods. ...
In the present study, we propose a novel high order weighted fuzzy time series forecasting method using k-mean clustering, weighted fuzzy logical relations and probabilistic fuzzy set. Objective of proposed forecasting method is to handle occurrence of recurrence of fuzzy logical relations and both non-probabilistic and probabilistic uncertainties in assigning membership grades to time series datum. The proposed probabilistic fuzzy set-based forecasting method uses Gaussian probability distribution function to assign probabilities to membership grades. Proposed fuzzy time series forecasting method uses high order weighted fuzzy logical relation in which each fuzzy logical relation uses the weight in ascending order. Superiority of proposed method is shown by implementing it on SBI share price at BSE, India and University of Alabama enrolments. Error measures and statistical parameters e.g. coefficient of correlation, coefficient of determination, performance parameter, evaluation parameter and tracking signal are also used to confirm the outperformance and validity of the proposed probabilistic fuzzy set based forecasting method.
... The concept of fuzzy logic is used in the forecasting of FTS. Song and Chissom introduced the FTS in 1993 [3], and it has since been widely developed, including the Markov method [4], Chen's method [5], Chen and Hsu's method [6], the weighted method [7], the multiple-attribute fuzzy time series method [8], the percentage change method [9], and Markov chain method [10]. ...
COVID-19 is still a pandemic in Indonesia, and Central Java is no exception. New positive cases of COVID-19 in Central Java are being discovered every day. Therefore, researchers try to predict new positive cases in Central Java. Many forecasting methods are currently developing, one of which is fuzzy time series (FTS). FTS has been also developed until now, one of which is a development of the FTS by combining the Markov chain as a defuzzification process. In FTS there is no definite formula to determine the length of the interval, so the researcher uses an average based to determine the length of the interval in the FTS Markov chain. Next, the researcher repartitioned based on the modified frequency density. The results of this study are that forecasting new positive cases of COVID-19 in Central Java using the average based-FTS Markov chain based on a modified frequency density partitioning method has a good level of accuracy, this can be seen from the MAPE value of the method.
... Fuzzy logic is one of the most effective methods for handling uncertainties in dynamic and nonstationary environments [16]. Table 1 lists various hybrid fuzzy models that have been used for predicting time-series [17][18][19][20][21][22]. Fuzzy systems, especially hybrid fuzzy models, have been very promising for solving complex problems, where a model estimates and predicts the similarity between two time-series in uncertain conditions [18,[23][24][25][26][27]. ...
Time-series prediction is associated with non-deterministic pattern analysis for uncertain conditions. It is necessary to develop high-quality prediction methods in real-world applications. Type-2 fuzzy systems can handle high-order uncertainties such as sequential dependencies associated with time series. Precise and reliable prediction can help reasonable strategies and assist the specialists in planning the best policies to model an event in uncertain time series. In this study, a hybrid model (DT2FTW) has been proposed for handling the high-order uncertainties in time-series prediction. This study develops a type-2 fuzzy intelligent system alongside a dynamic time warping algorithm to predict the pattern's similarity in long time-series for time-series prediction. The results have proven that the proposed DT2FTW model could obtain more reliable predictions in global standard benchmarks such as Mackey-Glass time-series, Dow Jones, and NASDAQ time-series. The results have also confirmed that the proposed DT2FTW model has lower error rates than counterpart algorithms in terms of the RMSE, MAE, and MPE. Also, the results confirm the superiority of the proposed model with an average area under the ROC curve (AUC) of 94% with a 95% confidence interval of [92-95] %.
... The direct methods include the commonly used procedures, such as time series model (Mariño et al., 1993;Xu et al., 2012;Zhang et al., 2015) and artificial computation (Kashyap and Panda, 2001;Chi et al., 2011), to forecast ET 0 based on the historical and future weather data. The time series model, a statistical analysis method, requires extensive data of several years, and it can directly use the past trends of changes to predict future changes (Cheng et al., 2008). In contrast, the artificial computation can appropriately simulate and address systems with multiple influencing factors and complex relationships (Gorka et al., 2008;Zhao et al., 2009). ...
Crop evapotranspiration (ETc) plays a fundamental role in agronomic and water resource management. Accurate forecasting of ETc is a major challenge for agricultural researchers and experts. Based on the measured ETc of the Eddy Covariance system and weather forecast data (1–15 d: short and medium-term) in North China, the real-time short (1–7 d) and medium (8–15 d) term ETc forecast models were developed by coupling with the dynamic crop coefficient and modifying the historical threshold. The results demonstrated that compared with the single crop coefficient model recommended by the Food and Agricultural Organization (FAO-56, M1), the M2 model (a modification of the M1 model developed using the dynamic crop coefficient) accurately forecasted the winter wheat and summer maize ETc, with an increased accuracy of 11%. Moreover, the ETc forecasting accuracy using the M2 model for short and medium-term was over 77%, of which the short-term accuracy was higher (greater than84%). The ETc forecasting accuracy increased with the decrease in the forecast period at different growth stages. Further, the short and medium-term accuracies of M3 model (a modification of the M2 model developed by incorporating the historical threshold) were over 81%, of which the accuracy of the 1 d forecast period was approximately 95%, which was 6% higher than that of the M2 model; the root mean square error and the mean absolute error were reduced by 0.1 mm d⁻¹ and 0.11 mm d⁻¹, respectively. Thus, these results indicated that the M3 model, which was developed by integrating the dynamic crop coefficient and the historical empirical threshold, can predict short and medium-term ETc more accurately.
... Huarng (2001) investigated the importance of interval length in FTS forecasting and proposed distribution and average-based heuristic approaches to determine length of intervals. Many researchers (Cheng et al. 2006(Cheng et al. , 2008Huarng and Yu 2006;Chen and Wang 2010) presented numerous techniques to determine the length of intervals for FTS methods using fuzzy clustering, neural network and entropy. Many other researchers (Lee et al. 2008Park et al. 2010;Hsu et al. 2010;Huarng et al. 2011;Singh and Borah 2014;Egrioglu 2014;Chen and Phuong 2017) also optimized length of intervals using particle swarm optimization (PSO) to improve the forecasting accuracy. ...
In this paper, we propose hesitant fuzzy sets-based hybrid time series forecasting method using particle swarm optimization and support vector machine. Length of unequal intervals, weights of intervals and process of defuzzification are major factors that affect the forecasting accuracy of hesitant fuzzy sets-based time series models. The proposed hybrid fuzzy time series forecasting method uses hesitant fuzzy sets which are constructed using fuzzy sets with equal and unequal length intervals. Particle swarm optimization and linear programming are used to optimize length of unequal intervals and weights of equal and unequal intervals. The proposed hybrid method of time series forecasting uses support vector machine for setting input-target pattern for defuzzification. Outperformance of proposed hybrid method of time series forecasting method is revealed by applying it on widely used time series data of enrollments of the University of Alabama, market share price of State Bank of India share at Bombay stock exchange and car sell in Quebec City of Canada. Validity of the proposed hybrid fuzzy time series forecasting method is verified using values of Willmott index and tracking signal.
... Thứ ba, kỹ thuật giải mờ để tính toán các giá trị dự báo rõ. Với yếu tố thứ nhất, các tác giả áp dụng các thuật toán tối ưu để tối ưu độ dài của các khoảng chia tập nền như thuật toán di truyền [8][9][10][11], thuật toán tối ưu bầy đàn [12][13][14][15][16][17], phân cụm [18,19], … Với yếu tố thứ hai, các mô hình chuỗi thời gian mờ bậc cao [6,9,11], mô hình chuỗi thời gian mờ đa nhân tố (thường là hai nhân tố) [18] được đề xuất. Với yếu tố thứ ba, một số cải tiến trong kỹ thuật giải mờ được đề xuất. ...
There are many studies on forecasting models based on fuzzy time series proposed in recent decades. There are many factors affecting the forecasted results that have been studied by many authors such as the techniques of dividing the universe of discourse into sub-intervals, forecasting rules and defuzzification techniques. However, the research results are still limited and do not satisfy users. In this paper, we propose a method to improve the efficiency of the fuzzy time series forecasting model on the basis of combining the swarm optimization algorithm for optimizing the interval length of the universe of discourse and a new efficient defuzzification technique. The proposed forecasting model is applied to forecast the number of students enrolled at the University of Alabama from 1971 to 1992. The experimental results show that the proposed forecasting model is more efficient than the existing models for both first-order and higher-order fuzzy time series forecasting models.
... In some papers, fuzzy clustering algorithms like fuzzy c-means, Gustafson-Kessel are also used for the first step of forecasting algorithms. [8,[22][23][24][25] are some researchers applied FCM, [26] applied Gustafson-Kessel clustering algorithm and used membership values directly for forecasting. For the second step of forecasting algorithm, mostly researchers develop models by using linguistic values to fuzzify the crisp time series according to the index of intervals obtained by UOD partitioning. ...
Fuzzy time series forecasting methods are very popular among researchers for predicting future values as they are not based on the strict assumptions of traditional forecasting methods. Non-stochastic methods of fuzzy time series forecasting are preferred by the researchers over the years because these methods are capable to deal with real life uncertainties and provide significant forecast. There are generally, four factors that determine the performance of the forecasting method (1) number of intervals (NOIs) and length of intervals to partition universe of discourse (UOD), (2) fuzzification rules or feature representation of crisp time series, (3) method of establishing fuzzy logic rule (FLRs), (4) defuzzification rule to get crisp forecasted value. Considering, first two factors to improve the forecasting accuracy, we proposed a modified non-stochastic method of fuzzy time series forecasting in which interval index number and membership value are used as input features to predict future value. We suggested a rounding-off range and large step-size method to find the optimal NOIs and used fuzzy c-means clustering process to divide UOD into intervals of unequal length. We implement two techniques (1) regression by support vector machine and (2) neural network by multilayer perceptron to establish FLRs. To test our proposed method by both techniques we conduct a simulated study on eight widely used real time series and compare the performance with some recently developed models. Two performance measures RSME and SMAPE are used for performance analysis and observed better forecasting accuracy by the proposed model.
... Covariance technique was analyzed in [17]. Among these methods various fuzzy (granular) approaches return good results, see [18]- [25]. In particular, the method proposed in [26] is worth considering. ...
... The accuracy of the third method is higher than that of the first method, but the natural meaning of the division of intervals is not as intuitive as the first two types of methods. The fourth methods are Least Squares Support Vector Machine [17], genetic algorithm [18], [19], Fibonacci sequence [20], clustering algorithm [21]- [23], quantum optimization algorit-hm [24], particle swarm optimization [25], [26], granular com-puting and bio-inspired computing [27]. The basic idea of the fourth method adopts a suitable algorithm for cluster analysis of the sample data and determine the division of each sub-interval. ...
Because the deformation of the slope is affected by the stability of the underground structure, natural factors, and human factors, it is difficult for the traditional prediction model of the slope to accurately predict sudden changes. This paper proposes a method to predict the deformation of high and steep slopes based on the fuzzy time series and Entire Distribution Optimization. The division of the domain is optimized by the Entire Distribution Optimization, and the deformation of high and steep slopes is predicted by the fuzzy time series. The experimental results show that the fuzzy time series has a good predictive effect on the number of mutations, and the Entire Distribution Optimization avoids the one-sidedness of dividing the domain by mean, which improves the accuracy of the deformation forecasting model of the high and steep slope.
... However, when the distribution of the universe of discourse is not uniform, fuzzy time series models may not generate pretty forecasting outcomes. Thus, many studies used clustering techniques to set the distribution of universe discourse from itself and discovered a different fuzzy partition at a different interval length [16], [33], [35], [36], [42]- [44] in order to partition the universe of discourse. Nevertheless, the clustering techniques are difficult in determining an optimal partition number in many cases. ...
Fuzzy Time Series (FTS) models are commonly used in time series forecasting, where they do not require any statistical assumptions on time series data. FTS models can handle data sets with a small number of observations or with uncertainty. This is a general advantage of FTS as compared with other techniques. However, FTS models still have some criticisms, such as the optimal lengths of intervals and the proper weights, which always influence the model accuracy and still have been of many concerns in literature. The work in this paper proposes a novel FTS forecasting model based on a new tree partitioning method (TPM) and Markov chain (MC), called FTSMC-TPM, for determining the optimal partitions of intervals and the proper weights vectors respectively, and this will greatly improve the model accuracy. The efficiency of the FTSMC-TPM model is tested using two types of time series consisting of the air pollution index (API) data, which is collected from Kuala Lumpur, Malaysia and the benchmark data of the University of Alabama enrollment. Three statistical criteria have been used for investigating the accuracy of the proposed model. The results indicate that the FTSMC-TPM model outperforms the existing classic and advanced time series models in terms of forecasting accuracy. In addition, the FTSMC-TPM model shows the ability to successfully deal with forecasting problems to obtain higher model accuracy, which is examined in comparison with the existing models to validate its superiority. Hence, this study demonstrates that the proposed model is more suitable for the accurate prediction of air pollution events as well as for forecasting any type of random time series.
... Huarng [11]'s approaches base on average and rate brought systematicity to the selection of the interval length, but could not guarantee the achievement of the best forecasting performance. For this reason, there are many studies [5,6,8,13,18,25] for the determination of the optimal interval length in a single application by using statistical theory. ...
The approaches of fuzzy time series are used commonly for the analysis of real life time series whose observations include uncertainty. Because of the fact that forecasting methods of fuzzy time series do not need many constraints in the approaches of classic time series, the interest towards this method is increasing. The forecasting methods of fuzzy time series in the literature focus on the models connected to the fuzzy autoregressive (AR) variables. In the models in which the methods of classic time series are used, there are not only autoregressive variables of time series but also moving average (MA) variables of time series. However in the forecasting method of fuzzy time series proposed in the literature, there are no using of MA variables except for only two studies. In this study, by defining a new first-order forecasting model of fuzzy time series which include not only fuzzy AR variables but also MA variables, an analysis of algorithm that depends on artificial neural networks is proposed. The new proposed method is applied to Istanbul Stock Exchange (IMKB) national 100 index time series, gold prices of the Central Bank of the Republic of Turkey and two simulated chaotic time series and compared with the other methods in the literature with regard to forecasting performance.
... The methodological oriented research includes the model improvement by simplifying the calculation method proposed by Chen in [1], optimizing historical data partition intervals [3,17,18,20,21,23,24], applying the high-order fuzzy time series models [2,4,24], applying multi-factor fuzzy time series model [6,34], improving the fuzzy defuzzification techniques [20,21,26,35], ... The application-oriented research includes the problems of the enrollment forecasting [1, 3,4,20,27,29], temperature forecasting [23,24,34], stock forecasting [21,23,24,35,34], tourism demand forecasting [33], car road accident forecasting [26,32], etc. ...
The fuzzy time series (FTS) forecasting models have been studied intensively over the past few years. The existing FTS forecasting models partition the historical data into subintervals and assign the fuzzy sets to them by the human expert's experience. Hieu et al. proposed a linguistic time series by utilizing the hedge algebras quantification to converse the numerical time series data to the linguistic time series. Similar to the FTS forecasting models, the obtained linguistic time series can define the linguistic, logical relationships which are used to establish the linguistic, logical relationship groups and form a linguistic forecasting model. In this paper, we propose a linguistic time series forecasting model based on the linguistic forecasting rules induced from the linguistic, logical relationships instead of the linguistic, logical relationship groups proposed by Hieu. The experimental studies using the historical data of the enrollments of University of Alabama and the daily average temperature data in Taipei show the outperformance of the proposed forecasting models over the counterpart ones. Then, to realize the proposed models in Viet Nam, they are also applied to the forecasting problem of the historical data of the average rice production of Viet Nam from 1990 to 2010.
... Several methods for ET c forecasting have been developed, which can be classified into four main categories: time series model (Marino et al., 1993), grey model (He and Tao, 2014), empirical formula (Kashyap and Panda, 2001), and artificial neural network model (Traore et al., 2016). Time series model is a kind of statistical analysis method, which needs several years of data, it can directly use the past trends to predict the future (Cheng and Wang, 2008). A grey model (grey differential prediction model) uses a small amount of incomplete information to construct a long-term fuzzy description of the law of development of things (Yuan et al., 2019). ...
Accurate prediction of crop evapotranspiration (ETc) can provide a scientific basis for improving water use efficiency, rational allocation of water resources, and sustainable management of ecosystems. However, conventional statistical methods have the limited application in some regions, because of the complex relationships (nonlinear, linear, exponential, etc) between ETc and its each driving factor. This paper illustrated the utility of the back-propagation neural network (BP) model for ETc prediction and compared the performance of this model with that of the multiple linear regression technique. Combined with the ETc measured by Eddy Covariance and the meteorological data, three-layer BP models, trained by the Levenberg-Marquardt algorithm, were developed with a 4-10-1 architecture (corresponding to four, ten, and one nodes in the input, hidden, and output layers, respectively). The BP models were trained and validated in the MATLAB environment, with three different combinations of maximum air temperature, minimum air temperature, sunshine hours, crop coefficient (Kc), and precipitation. A high correlation was observed between the values measured by Eddy Covariance and those predicted by BP, with a higher coefficient of determination (0.87) and accuracy (91.44%) than that achieved by the multiple linear regression model (0.79 and 82.96%, respectively). Furthermore, the performance of the BP models could be improved substantially by including the dynamic change of Kc and the effect of precipitation, which suggested that these two factors were crucial variables in modeling ETc by BP approaches. In testing sets, the BP model that considered the dynamic change of Kc was found to be superior to the BP model that considered the crop coefficient recommended by FAO-56, with prediction accuracy increased by 19%. Additionally, the accuracy of the BP prediction models that considered the dynamic change of Kc and the effect of precipitation were higher than 95%. Moreover, the BP prediction model in typical weather with precipitation was superior to the BP model in typical weather with no precipitation. The results obtained would be helpful for obtaining the ETc more consistent with the actual growth status of the crop, thereby providing a scientific basis for improving water management during crop production.
Rising market demands, economic pressures, and technological advancements have spurred researchers to seek ways to enhance business environments and scientific productivity. Predictive science, crucial in this context, has gained prominence due to the rapid progress in information technology and forecasting algorithms. Time series forecasting, widely used in fields like engineering, economics, tourism, and energy, has inherent limitations with classical statistical methods, leading researchers to explore artificial intelligence and fuzzy logic for more accurate predictions. However, despite extensive efforts to improve accuracy, challenges persist. The research introduces a model aimed at surpassing existing methods in time series forecasting accuracy. This approach combines meta-heuristic optimization algorithms and neutrosophic logic to enhance precision in uncertain and complex environments, promising improved forecasting outcomes. The study shows that the performance of the neutrosophic time series modeling approach is highly dependent on the optimal selection of the universe of discourse and its corresponding intervals. This study selects the quantum optimization algorithm (QOA), genetic algorithm (GA), and particle swarm optimization (PSO) to address this weakness. These optimization algorithms improve the performance of the NTS modeling approach by selecting the global universe of discourse and corresponding intervals from the list of locally optimal solutions. The proposed hybrid model (i.e., NTS-QOA model) is verified and validated with datasets of university enrollment of Alabama (USA), Taiwan futures exchange (TAIFEX) index, and Taiwan Stock Exchange Corporation (TSEC) weighted index. Various experimental results signified the efficiency of the proposed model over existing benchmark models in terms of average forecasting error rate (AFER). This value using the proposed NTS QOA, NTS GA, and NTS PSO method on the university dataset is 0.166, 0.167, 0.164, on the TAIFEX dataset, is 0.081, 0.081, and 0.081, and on the TSEC dataset is 0.09, 0.09, and 0.09, respectively.
Produk Domestik Regional Bruto (PDRB) merupakan salah satu indikator perekonomian. Jawa Barat merupakan provinsi dengan jumlah PDRB terbesar ketiga di Indonesia. Berdasarkan data dari Badan Pusat Statistik, sektor industri pengolahan merupakan sektor terbesar yang menyokong PDRB Jawa Barat. Sektor Industri Pengolahan menyokong 42% dari PDRB Jawa Barat. Pada Tahun 2001 jumlah Unit Industri di Jawa barat ada sebanyak 201.953 yang terdiri dari 198.478 Industri Kecil dan Menengah (IKM) dan 3475 Industri Besar (IB). Pada tahun 2021 jumlah unit usaha di Jawa barat mencapai 216.671, artinya terdapat penambahan unit usaha yang cukup banyak dalam 20 tahun yaitu sebanyak 14.718 unit usaha. Pembangunan industri di Jawa barat berkembang sangat pesat. Pembangunan industri ini memberikan dampak positif dan dampak negatif. Perkembangan Industri di Jawa Barat perlu dikendalikan dengan kebijakan yang tepat. Data perkiraan jumlah unit industri di masa yang akan dapat menjadi acuan bagi pemerintah dalam menentukan kebijakan yang tepat. Pada penelitian ini akan dilakukan peramalan menggunakan fuzzy time series untuk memprediksi jumlah unit industri di Jawa Barat. Model fuzzy time series yang digunakan adalah model cheng dan akurasi hasil prediksi akan dihitung menggunakan nilai MAPE. Berdasarkan hasil peramalan menggunakan metode fuzzy time series dengan model cheng, diperoleh prediksi jumlah unit industri tahun 2023 sebesar 215.200. Menurut prediksi jumlah unit industri di Jawa Barat akan berkurang sebanyak 1.471 unit jika dibandingkan tahun sebelumnya. Selanjutnya tingkat akurasi hasil peramalan data jumlah industri menggunakan metode fuzzy time series dengan model cheng menunjukan hasil prediksi yang sangat akurat dengan eror berdasarkan nilai MAPE adalah sebesar 0,442327%.
Computational methods for time series forecasting have always an edge over conventional methods of forecasting due to their easy implementation and prominent characteristics of coping with large amount of time series data. Many computational methods for fuzzy time series (FTS) forecasting have been developed in past using fuzzy set, intuitionistic fuzzy set (IFS), and hesitant fuzzy set (HFS) for incorporating uncertainty, non-determinism, and hesitation in time series forecasting. Since probabilistic fuzzy set (PFS) incorporates both probabilistic and non-probabilistic uncertainties simultaneously, we have proposed PFS and particle swarm optimization (PSO) based computational method for FTS forecasting. First, we have developed a PFS based computational method for FTS forecasting and then it is integrated with PSO to enhance the accuracy in forecasted outputs. Unlike other PSO based for FTS forecasting method, PSO is used to optimize both number of partitions and length of intervals. Three diversified time series data of enrolments of the University of Alabama, market price of State Bank of India (SBI) share at Bombay stock exchange (BSE) India, and death cases due to COVID-19 in India are used to compare the performance of PFS based computational method of FTS forecasting before and after its integration with PSO in terms of root mean square error (RMSE). After integration of PFS based computational method with PSO, accuracy in the forecasted outputs is increased significantly and its performance is found better than many other existing FTS forecasting methods. Goodness of the proposed FTS forecasting method is also tested using tracking signal and Willmott index.
z Yoksullukla mücadele etmede başarılı olmak için yoksulluğun iyi şekilde tanımlanmış olması, yoksulluk ölçüm kriterlerinin iyi belirlenmiş olması gerekmektedir. Özellikle son zamanlarda yapılan çalışmalarda, yoksulluk sadece gelir yetersizliği olarak tanımlanmamakta, yoksulluk çok boyutlu bir sorun olarak tanımlanmaktadır. Yoksulluk göstergeleri üzerine yapılan bu güncel araştırmalarda ise tüm boyutlar eşit öneme sahip olarak ele alınmaktadır. Halbuki yoksulluğu oluşturan boyutların bu problem üzerine etkileri eşit değildir. Bu çalışmada yoksulluk kavramını oluşturan boyutların önem düzeyleri uzman görüşleri dikkate alınarak hesaplanmıştır. Ağırlıkların bilimsel hesaplamasını geliştirmek için Bulanık LMAW modeli kullanılmıştır. Çok boyutlu yoksulluk endeksinin sağlık, eğitim ve yaşam standardı üç boyutu ve onlara ait göstergelerinin ağırlığı, ilgili uzmanlarla yapılan görüşmeye dayanarak hesaplanmıştır. Araştırma, yaşam standardı boyutunun ve onun temel göstergelerinden olan içme suyunun çok boyutlu yoksulluğun belirlenmesinde önemli ağırlıkta olduklarını göstermektedir. Bu ağırlık düzeyleri kullanılarak yoksulluk göstergeleri üzerine yapılan çalışmalarda boyutların ağırlıkları tespit edilebilecek ve çözüm önerileri daha etkili olacaktır. Abstract In order to be successful in combating poverty, poverty must be well defined and poverty measurement criteria must be well defined. Especially in recent studies, poverty is not only defined as an income deficiency, but poverty is defined as a multidimensional problem. In these current studies on poverty indicators, all dimensions are considered with equal importance. However, the effects of the dimensions of poverty on this problem are not equal. In this study, the importance levels of the dimensions constituting the concept of poverty were calculated by taking into account the expert opinions. The Fuzzy LMAW model was used to improve the scientific calculation of weights. The three dimensions of the multidimensional poverty index on health, education and living standards and the weight of their indicators were calculated on the basis of an interview with relevant experts. The research shows that the dimension of living standard and drinking water, which is one of its basic indicators, have an important weight in determining multidimensional poverty. By using these weight levels, the weights of the dimensions will be determined in the studies on poverty indicators and the solution proposals will be more effective.
This paper proposes a method for aggregating the information contained in sets of Time Series (TS) into a Fuzzy Time Series (FTS). First, an aggregation technique is defined, which is based on the algorithm known as Kernel Density Estimation (KDE) which reconstructs the probabilistic density function of a set of points, in this case a TS. Second, to operate with FTS, an algebraic framework is created based on Zadeh's extension principle and as a result of operating with FTS, a new FTS is obtained, which allows obtaining richer information and operating under conditions of uncertainty. Finally, the operations needed to compute the membership function of any TS in the aggregated FTS are introduced too. As a use case, it is proposed to work with sets of TS in the supply and demand domain, in such a way that information regarding the satisfaction of demand over time can be extracted. The specific application domain chosen will be that of the electricity market, analysing the consumption of buildings and their self-generation of energy to obtain information about the dependence on the electricity grid.
In recent trends, different models are developed by various researchers to improve the accuracy of forecasted values in fuzzy time series. We propose a new model for temperature prediction using intuitionistic fuzzy time series forecasting. In this model, intuitionistic fuzzification based on maximum membership grade value and defuzzification based on multi set,List function concepts are used. The historical data of daily average temperature in Taipei, Taiwan (Central weather bureau 1996) is used to illustrate the proposed method.
Many of decision-making and policy planning processes involve a time-series prediction problem and so this area has extensive literature including a great variety of time-series prediction tools and inferences systems. An important part of these is based on fuzzy sets. However, it is known that fuzzy sets may fail to satisfy or characterize the uncertainty of the data in a comprehensive manner because they cannot depict the neutrality degree of time-series. Another important and decisive deficiency of current inference systems is to based on the univariate structure. However, the time series dealt with in a prediction problem generally interact with other time series. Considering these issues, creating an inference system based on intuitionistic fuzzy sets and multivariate relationships for a time series prediction problem is a requirement even an obligation. With these regards, this study presents a multivariate intuitionistic fuzzy time-series definition and its prediction models and introduces a multivariate intuitionistic fuzzy inference system (M-IFIS). The basic novelty of the article can be expressed as the definition of a multivariate intuitionistic fuzzy time series, as well as the creation of a relevant analysis mechanism, first-time in the literature. Sigma-pi neural network is used as an inference tool in M-IFIS and membership and non-membership values and lagged crisp observations of multivariable time-series are used as inputs of it. In order to reveal the performance of the proposed system, Istanbul Stock Exchange (IEX) and Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) are analysed and the results are evaluated as comprehensive and comparative. All findings reveal the superiority M-IFIS in predictive accuracy.
Time series analysis models, understands, and predicts phenomena from different domains such as meteorology, medicine, and economics. In this context, Fuzzy Time Series has been standing out due to its capacity of using mathematical functions to represent linguistic variables, resulting in interpretative and more accurate models. Several studies aim at improving time series forecasting using fuzzy set theory, however such efforts were executed solely to obtain modeling improvements in the fuzzification stage, disregarding the stochastic and deterministic influences composing time series to assist the modeling process. In an attempt to fill out such gap, this manuscript employs the Empirical Mode Decomposition (EMD) to extract the deterministic influences which are next modeled using fuzzy clustering to improve time series forecasting. EMD reduces the data imprecision and uncertainty thus helping the fuzzy clustering stage that automatically finds an adequate space partitioning to produce the fuzzy sets. We use Fuzzy C-means to generate fuzzy sets with different characteristics, contributing to improvements in the definition of the number of sets, usually barely explored in the fuzzification stage. Our method was assessed using different validation indices while forecasting time series, which has confirmed promising results and supported the interpretability of data ranges along time.
Websites are a virtual window of services in e-government, so the evaluation of websites enables organizations to provide quality online services to beneficiaries. This article aims to design a model that allows the evaluation of any organization's website. The proposed model consists of 7 criteria such as multi-language support for usability, website map for faster access to information, returning to the previous step, canceling the process, links to connect to other organizations, 24/7 accessibility, and a simple menu for better navigation. In order to determine these criteria and to determine their degrees, people who use online services were interviewed. The common views of these people are included as decision makers in the study. “Fuzzy set theory” was applied to model the problem. Fuzzy FUCOM method was used to weight the criteria. As a result of the application with fuzzy FUCOM, 24/7 accessibility was the most important criterion with a weight of 0.2383 among the criteria used in the evaluation of e-government websites, while being able to cancel the transaction was the least important criterion with a weight of 0.0878. The final values of the weight coefficients were obtained with the LINGO 17 software.
Intuitionistic fuzzy time series (IFTS) forecasting models have been proved more ideal than other forecasting models because of their efficient handling of non-stochastic uncertainties with non-determinism. It has also been shown by many researchers that interval length in both fuzzy time series (FTS) and IFTS plays a pivot role and affects accuracy in forecasting. In this paper, we propose a novel method to optimize interval length for enhancing accuracy in IFTS forecasting models. Proposed method optimizes interval length by minimizing mean square errors (MSEs). Objective function considered in this study is an interpolating polynomial which is calculated by Newton divided difference method. Performance and accuracy of proposed method is validated by comparing it with model of Kumar and Gangwar (IEEE Trans Fuzzy Syst 2015:2507582, [1]) and other previous existing FTS and IFTS forecasting models using time series data of University of Alabama enrollments.
In the Islamic finance framework, sukuk has emerged as a rapidly developing structure in recent times. Having emerged in Muslim countries and spreading all over the world, sukuk offers many new fields of study to financial experts who want to work in this area. In
general, sukuk is expressed as a financial concept that covers a number of shopping procedures in order to regulate commercial relations in the early days of Islam. Five of the companies exporting sukuk in our country were dealt within our study. Using the price data of these companies, future prices were estimated. Within the scope of this estimation, out of the correlations between the companies, 3 companies with the best relations were determined and possible future price values were estimated. Fuzzy Logic method is used in the study. Estimates were tested with the help of statistical success criteria of error squares averages and efficiency coefficients. In this study, which is the first to use Fuzzy Logic methods in sukuk data, the
suitability of Fuzzy Logic method was proved once again for financial problems.
Mô hình chuỗi thời gian mờ là một trong những công cụ được sử dụng để giải quyết quá trình phức tạp và không chắc chắn. Trong quá trình thiết lập mô hình chuỗi thời gian mờ, độ chính xác dự báo phụ thuộc vào hai vấn đề chính: (1) Phân khoảng và xác định độ dài khoảng dữ liệu hiệu quả, (2) Thiết lập các mối quan hệ mờ hợp lý cho dự báo. Trong nghiên cứu này, một mô hình dự báo chuỗi thời gian mờ mới sử dụng kỹ thuật phân cụm dựa trên đồ thị để xác định độ dài khoảng khác nhau được đề xuất. Mô hình đề xuất được áp dụng trên hai tập dữ liệu chuỗi thời gian, dữ liệu lịch sử về số lượng tuyển sinh đại học tại Đại học Alabama và dữ liệu về đỉnh muối của một tỉnh ven biển Việt Nam. Kết quả tính toán cho thấy, mô hình đề xuất có độ chính xác dự báo cao hơn các mô hình hiện có khi áp dụng cho hai tập dữ liệu cụ thể.
Fuzzy time series theory is a concept of artificial intelligence that can use to conduct forecasting technique.. This paper discusses the fuzzy logic concept to develop the base of the fuzzy time series with time invariant and time variant methods. There are several methods of fuzzy time series, including Markov Chain method and Chen and Hsu method. The Markov Chain method combines between the fuzzy time series and the Markov Chain. This merger goals to finest opportunity of the use matrix probability transitions. Chen and Hsu method is based on the historical data difference in conducting forecasting. By using Markov Chain and Chen & Hsu methods, it may achieve forecasting outcomes with a low mistakes rate. To clarify each technique and for comparison further, it is given an example of the relevant issue to be resolved by both methods. The consequences acquired can be compared, so it can be concluded which method is better.
Many fuzzy time series (FTS) methods have been developed by the researchers without including non-determinacy caused using single function for both membership and non-membership grades. Optimum length of intervals and inclusion of non- determinacy have been two important key issues for the researchers for long time. In this paper, we propose a novel hybrid FTS forecasting method using particle swarm optimization (PSO) and intuitionistic fuzzy set (IFS). PSO determines optimum length and IFS includes non-determinacy during fuzzification of time series data. To show the applicability and suitability of proposed forecasting method, it is implemented on three time series data of the University of Alabama, State bank of India (SBI) share price at Bombay Stock Exchange (BSE), India and car sells in Quebec. Performance of proposed method is measured using mean square error (MSE). Reduced amount of MSE confirms outperformance of proposed FTS forecasting method over various existing fuzzy set-, IFS-, hesitant-and probabilistic hesitant fuzzy set-based FTS forecasting methods in forecasting the University of Alabama enrollments, SBI share price and car sells in Quebec. Validity of the proposed FTS forecasting method is also verified using tracking signal.
This study proposes a new Fuzzy Time Series (FTS) approach, called as Dynamic Panel Fuzzy Time Series (DPFTS) which combines Dynamic Panel Data Analysis and FTS. The major advantages of proposed approach can be summarized as follows: i) proposed approach is adapted version of traditional fuzzy time series (TFTS) model to time series data having more than two cross-sections such as countries, cities, regions etc, in other words to panel data. Hence, it has the ability of globally determining the fuzzy sets and the fuzzy relations to be represent a large number of time series simultaneously, ii) it can construct FTS models even if time series have very small sample size since panel data are constructed by combining the time and cross-section dimensions. In order to evaluate the performance of proposed approach and compare it with its traditional version, two experiments which compose of a simulation study and a real time examples are conducted. Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE) criteria are chosen for performance comparisons. Experimental results show that proposed approach exhibits considerable good performance in prediction and forecasting.
Based upon the works by Zadeh (1973, 1975), in this paper, a special dynamic process with linguistic values as its observations is defined and studied. This dynamic process is called fuzzy time series. To describe fuzzy time series, fuzzy relational equations are employed as the models. There are two classes of fuzzy time series: time-variant and time-invariant. The definition of fuzzy time series is given, some properties of fuzzy time series are explored, and procedures to develop fuzzy time series models are discussed. Finally, a procedure for using fuzzy time series for foracasting is suggested.
This paper is the continuation of Forecasting enrollments with fuzzy time series — Part I (Fuzzy Sets and Systems54 (1993) 1–10), the development of a first-order time-invariant fuzzy time series model with application to forecasting the enrollment of The Universoty of Alabama. In this paper, we are interested in applying first-order time-variant models in forecasting the enrollment of the same university. In doing so, the difference between time-invariant and time-variant models is discussed. An approach to developing time-variant models is proposed together with a formula to calculate the model. A step-by-step procedure is presented to develop and utilize the time-variant model. To convert the output of the model, a 3-layer backpropagation neural network is applied. Three different defuzzification methods are compared using the same data. Results show that the neural network defuzzification method yields the smallest average forecasting error, and the less complex the model, the better the forecasting results.
There have been a good many methods to forecast university enrollments in the literature. However, none of them could be applied when the historical data are linguistic values. Fuzzy time series is an effective tool to deal with such problems. In this paper, as an application of fuzzy time series in educational research, the forecast of the enrollments of the University of Alabama is carried out. In so doing, a fuzzy time series model is developed using historical data. A complete procedure is proposed which includes: fuzzifying the historical data, developing a fuzzy time series model, and calculating and interpreting the outputs. To evaluate the forecasting model, the robustness of the fuzzy time series model is tested. Advantages and problems of the forecasting method are also discussed.
A variety of researches are examined from the standpoint of information theory. It is shown that the unaided observer is severely limited in terms of the amount of information he can receive, process, and remember. However, it is shown that by the use of various techniques, e.g., use of several stimulus dimensions, recoding, and various mnemonic devices, this informational bottleneck can be broken. 20 references. (PsycINFO Database Record (c) 2006 APA, all rights reserved).
This paper studies the influence of a novel scheme. First-order fuzzy time series models embedded with this novel scheme is then made high-order. To illustrate this high-order model, the forecasting enrollments are conducted. The results are compared with those of Chen's method and those of Song-Chissom method [4]. It is found that the root mean square error of the forecast can be improved from 630.86 for the Chen's method and 624.23 for the Song-Chissom method to 199.32 for the proposed model.
Fuzzy time-series models have been used to model observations, where each one of them contains multiple values. The formulation of fuzzy relationships and the lengths of intervals are considered to be two of the critical factors that affect forecasting results. Unfortunately, the lengths of the intervals were determined during the early stages of forecasting in these models, and they thus often failed to reflect the distribution of observations. This study therefore proposes a refined fuzzy time-series model to further refine the lengths of intervals. This model can refine the lengths of intervals during the formulation of fuzzy relationships, and hence capture the fuzzy relationships more appropriately. As a result, the forecasting results can be improved. Both the stock index and enrollment are used as the targets in the empirical analysis.
A main drawback of existing fuzzy time series forecasting methods is that they lack persuasiveness in determining universe of discourse and the length of intervals. Two approaches are proposed for overcoming the problem, and the proposed approaches are more objective and reasonable to improve the persuasiveness in determining the universe of discourse, length of intervals and membership functions of fuzzy time series. The first approach is using Minimize Entropy Principle Approach (MEPA) to partition the universe of discourse and build membership functions, and the second is using Trapezoid Fuzzification Approach (TFA). Monthly amount data of IT project expenditure of a company are used to evaluate the performance of the proposed approaches. The forecasting accuracies of the proposed approaches are better than those of previous methods.
It appears that stock market index returns exhibit (weak) autocorrelation and there is evidence that volatility in equity markets is inversely related to first order autocorrelation. A prominent theory that can address both the aforementioned stylized facts is the feedback trading theory that relates autocorrelation to individual investor trading patterns. We provide a unified framework to simultaneously investigate market wide feedback trading strategies effects and the presence of volatility-correlation relationships. Our empirical application uses market portfolios from six international markets and employs conditional non-linear in mean and in variance models. Parametric specifications for conditional dependence beyond the mean and variance are also modelled following Hansen's (1994) (Hansen, B.E., 1994. Int. Econ. Rev. 35 (a), 705–730) autoregressive conditional density estimation. For the sample period under investigation (post 1990), our results support the presence of feedback traders and an inverse volatility–correlation relationship in three out of six markets while only two of the series under investigation do not provide evidence of autocorrelation. Our empirical work supports volatility induced sign switches in correlation. We document positive and significant risk premium parameters in three markets while we find that volatility at the market level is enhanced by past movements of the daily range (daily high–low price difference) series.
Most conventional fuzzy time series models (Type 1 models) utilize only one variable in forecasting. Furthermore, only part of the observations in relation to that variable are used. To utilize more of that variable's observations in forecasting, this study proposes the use of a Type 2 fuzzy time series model. In such a Type 2 model, extra observations are used to enrich or to refine the fuzzy relationships obtained from Type 1 models and then to improve forecasting performance. The Taiwan stock index, the TAIEX, is used as the forecasting target. The study period extends over the 2000–2003 period. The TAIEX from January to October in each year is used for the estimation, while that covering November and December is used for forecasting. The empirical analyses show that Type 2 model outperforms Type 1 model.
In [6–9], Song et al. proposed fuzzy time-series models to deal with forecasting problems. In [10], Sullivan and Woodall reviewed the first-order time-invariant fuzzy time series model and the first-order time-variant model proposed by Song and Chissom [6–8], where the models are compared with each other and with a time-invariant Markov model using linguistic labels with probability distributions. In this paper, we propose a new method to forecast university enrollments, where the historical enrollments of the University of Alabama shown in [7,8] are used to illustrate the forecasting process. The average forecasting errors and the time complexity of these methods are compared. The proposed method is more efficient than the ones presented in [7, 8, 10] due to the fact that the proposed method simplifies the arithmetic operation process. Furthermore, the average forecasting error of the proposed method is smaller than the ones presented in [2, 7, 8].
This paper presents a new method to forecast university enrollments based on fuzzy time series. The data of historical enrollments of the University of Alabama shown in Song and Chissom (1993a, 1994) are adopted to illustrate the forecasting process of the proposed method. The robustness of the proposed method is also tested. The proposed method not only can make good forecasts of the university enrollments, but also can make robust forecasts when the historical data are not accurate. The proposed method is more efficient than the one presented in Song and Chissom (1993a) due to the fact that the proposed method uses simplified arithmetic operations rather than the complicated max-min composition operations presented in Song and Chissom (1993a).
This paper investigates the use of a flexible forecasting method based on non-linear Markov modelling and canonical variate analysis, and the use of a prediction algorithm to forecast conditional volatility. We assess the dynamic behaviour of the model by forecasting volatility of a stock index. It is found that the non-linear non-parametric model based on canonical variate analysis forecasts stock index volatility significantly better than the GJR-GARCH(1,1)-t model due to the flexibility in accommodating multiple dynamic patterns in volatility which are not captured by its parametric counterpart.
In this paper, we compare the performance of a daily ARCH type model (which uses daily returns) with the performance of a model based on the daily realized volatility (which uses intraday returns) when the 1-day ahead value-at-risk (VaR) is to be computed. While the VaR specification based on a long memory skewed Student model for the daily realized volatility provides adequate 1-day-ahead VaR forecasts for two stock indexes (the CAC40 and SP500) and two exchange rate returns (the YEN–USD and DEM–USD), it does not really improve on the performance of a VaR model based on the skewed Student APARCH model and estimated using daily data only. Thus both methods seem to be equivalent. This paper also shows that daily returns standardized by the square root of the 1-day-ahead forecast of the daily realized volatility are not normally distributed.
Length of intervals affects forecasting results in fuzzy time series. Unfortunately, the issue of how to determine effective lengths of intervals has not been touched in previous studies. This study proposes distribution- and average-based length to approach this issue. Distribution-based length is the largest length smaller than at least half the first differences of data. Average-based length is set to one half the average of the first differences of data. Empirical analyses show that distribution- and average-based lengths are simple to calculate and can greatly improve forecasting results; in particular, they are superior to the randomly chosen lengths used in previous studies.
By a linguistic variable we mean a variable whose values are words or sentences in a natural or artificial language. For example, Age is a linguistic variable if its values are linguistic rather than numerical, i.e.,young, not young, very young, quite young, old, not very old and not very young, etc., rather than 20, 21,22, 23, In more specific terms, a linguistic variable is characterized by a quintuple (L>, T(L), U,G,M) in which L is the name of the variable; T(L) is the term-set of L, that is, the collection of its linguistic values; U is a universe of discourse; G is a syntactic rule which generates the terms in T(L); and M is a semantic rule which associates with each linguistic value X its meaning, M(X), where M(X) denotes a fuzzy subset of U. The meaning of a linguistic value X is characterized by a compatibility function, c: U → [0,1], which associates with each u in U its compatibility with X. Thus, the compatibility of age 27 with young might be 0.7, while that of 35 might be 0.2. The function of the semantic rule is to relate the compatibilities of the so-called primary terms in a composite linguistic value-e.g., young and old in not very young and not very old-to the compatibility of the composite value. To this end, the hedges such as very, quite, extremely, etc., as well as the connectives and and or are treated as nonlinear operators which modify the meaning of their operands in a specified fashion. The concept of a linguistic variable provides a means of approximate characterization of phenomena which are too complex or too ill-defined to be amenable to description in conventional quantitative terms. In particular, treating Truth as a linguistic variable with values such as true, very true, completely true, not very true, untrue, etc., leads to what is called fuzzy logic. By providing a basis for approximate reasoning, that is, a mode of reasoning which is not exact nor very inexact, such logic may offer a more realistic framework for human reasoning than the traditional two-valued logic. It is shown that probabilities, too, can be treated as linguistic variables with values such as likely, very likely, unlikely, etc. Computation with linguistic probabilities requires the solution of nonlinear programs and leads to results which are imprecise to the same degree as the underlying probabilities. The main applications of the linguistic approach lie in the realm of humanistic systems-especially in the fields of artificial intelligence, linguistics, human decision processes, pattern recognition, psychology, law, medical diagnosis, information retrieval, economics and related areas.
A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
This study proposes weighted models to tackle two issues in fuzzy time series forecasting, namely, recurrence and weighting. It is argued that recurrent fuzzy relationships, which were simply ignored in previous studies, should be considered in forecasting. It is also recommended that different weights be assigned to various fuzzy relationships. In previous studies, these fuzzy relationships were treated as if they were equally important, which might not have properly reflected the importance of each individual fuzzy relationship in forecasting. The weighted models are compared with the local regression models in which weight functions also play an important role. Both models are different by nature, but certain theoretical backgrounds in local regression models are adopted. By using the Taiwan stock index as the forecasting target, the empirical results show that the weighted model outperforms one of the conventional fuzzy time series models.
Song and Chissom first proposed the definitions of fuzzy time series and time-invariant and variant models of fuzzy time series. Chen then proposed arithmetic operations to replace the complex computations in Song and Chissom's models. This study proposes heuristic models by integrating problem-specific heuristic knowledge with Chen's model to improve forecasting. This is because Chen's model was easy to calculate, was straightforward to integrate heuristic knowledge, and forecast better than the others. Both university enrollment and futures index are chosen as the forecasting targets. The empirical analyses show that the heuristic models reflect the fluctuations in fuzzy time series better and provide better overall forecasting results than the previous models.
Fuzzy time series models were introduced by Song and Chissom [Fuzzy Sets and Systems54 (1993) 269–277, 54 (1993) 1–9, 62 (1994) 1–8] to model and forecast processes whose values are described by linguistic variables. Song and Chissom used as an application the forecasting of educational enrollments. This paper reviews the two methods set forth by Song and Chissom, a first-order time-invariant fuzzy time series model and a first-order time variant model. These models are compared with each other and with a time-invariant Markov model using linguistic labels with probability distributions. The results of these methods for the enrollment data are compared with three traditional time series models, a first-order autoregressive (AR(1)) model and two second-order auto-regressive (AR(2)) models, all of which are time-invariant.
In recent years, the innovation and improvement of forecasting techniques have caught more and more attention. Especially, in the fields of financial economics, management planning and control, forecasting provides indispensable information in decision-making process. If we merely use the time series with the closing price array to build a forecasting model, a question that arises is: Can the model exhibit the real case honestly? Since, the daily closing price of a stock index is uncertain and indistinct. A decision for biased future trend may result in the danger of huge lost. Moreover, there are many factors that influence daily closing price, such as trading volume and exchange rate, and so on. In this research, we propose a new approach for a bivariate fuzzy time series analysis and forecasting through fuzzy relation equations. An empirical study on closing price and trading volume of a bivariate fuzzy time series model for Taiwan Weighted Stock Index is constructed. The performance of linguistic forecasting and the comparison with the bivariate ARMA model are also illustrated.
By a linguistic variable we mean a variable whose values are words or sentences in a natural or artificial language. For example, Age is a linguistic variable if its values are linguistic rather than numerical, i.e.,young, not young, very young, quite young, old, not very old and not very young, etc., rather than 20, 21,22, 23, In more specific terms, a linguistic variable is characterized by a quintuple (L>, T(L), U,G,M) in which L is the name of the variable; T(L) is the term-set of L, that is, the collection of its linguistic values; U is a universe of discourse; G is a syntactic rule which generates the terms in T(L); and M is a semantic rule which associates with each linguistic value X its meaning, M(X), where M(X) denotes a fuzzy subset of U. The meaning of a linguistic value X is characterized by a compatibility function, c: U → [0,1], which associates with each u in U its compatibility with X. Thus, the compatibility of age 27 with young might be 0.7, while that of 35 might be 0.2. The function of the semantic rule is to relate the compatibilities of the so-called primary terms in a composite linguistic value-e.g., young and old in not very young and not very old-to the compatibility of the composite value. To this end, the hedges such as very, quite, extremely, etc., as well as the connectives and and or are treated as nonlinear operators which modify the meaning of their operands in a specified fashion. The concept of a linguistic variable provides a means of approximate characterization of phenomena which are too complex or too ill-defined to be amenable to description in conventional quantitative terms. In particular, treating Truth as a linguistic variable with values such as true, very true, completely true, not very true, untrue, etc., leads to what is called fuzzy logic. By providing a basis for approximate reasoning, that is, a mode of reasoning which is not exact nor very inexact, such logic may offer a more realistic framework for human reasoning than the traditional two-valued logic. It is shown that probabilities, too, can be treated as linguistic variables with values such as likely, very likely, unlikely, etc. Computation with linguistic probabilities requires the solution of nonlinear programs and leads to results which are imprecise to the same degree as the underlying probabilities. The main applications of the linguistic approach lie in the realm of humanistic systems-especially in the fields of artificial intelligence, linguistics, human decision processes, pattern recognition, psychology, law, medical diagnosis, information retrieval, economics and related areas.
One of the fundamental tenets of modern science is that a phenomenon cannot be claimed to be well understood until it can be characterized in quantitative terms.l Viewed in this perspective, much of what constitutes the core of scientific knowledge may be regarded as a reservoir of concepts and techniques which can be drawn upon to construct mathematical models of various types of systems and thereby yield quantitative information concerning their behavior.
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.
This study investigates the forecasting scheme of local region
data. In view of the model of Song and Chissom (1993), we find it is
robust for large amounts of data. After implementation for local region
data, in this study, we find it is not so accurate as expected. Hence,
the proposed scheme is tried. This scheme can make the forecasting more
accurate. To illustrate the effect of this proposed scheme, the
forecasting enrollments of Tainan, a small city in Taiwan, are carried
out. It is found that the root mean square error of the forecasting
enrollments can be improved from 443.44 for the Song-Chissom method to
45.69 for the proposed model
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
Disruption in a Tokamak reactor is a sudden loss of confinement that can cause damage to the machine walls and support structures. In this paper, we propose the use of a fuzzy time series (FTS) approach for detection of disruption in Tokamaks. In particular, two-factors FTS models have been exploited for the prediction of the time to disruption in the ASDEX-Upgrade machine. The concept of fuzzy logic is used taking into account that previous techniques make use of expert knowledge for deciding about the onset of a disruption.
Pattern recognition with fuzzy objective function algorithms Time series analysis: Forecasting and control
- J C G P Bezdek
- G M Jenkins
Bezdek, J. C. (1981). Pattern recognition with fuzzy objective function algorithms. NY: Plenum Press. Box, G. P., & Jenkins, G. M. (1976). Time series analysis: Forecasting and control. CA: Holden-day.
A study for second-order modeling of fuzzy time series, presented at IEEE international fuzzy systems conference proceedings
- C C Tsai
- S J Wu
Tsai, C. C., & Wu, S. J. (1999). A study for second-order modeling of
fuzzy time series, presented at IEEE international fuzzy systems
conference proceedings, Seoul, Korea.
The magical number seven, plus or minus two: some limits on our capacity of processing information. The Psychological Review. v63
- Miller