Narrow Results

Song et al.[3] proposed a new fuzzy time series model by means of defining some new operations on fuzzy numbers. They presented the new model in the form of two theorems, which indicate that the value of F(t) at t+1 can be related to its previous ones by means of forward and backward linguistic difference, as a necessary condition for the homogeneous fuzzy time series. In this note, we prove that it is also a sufficient condition for the homogeneous fuzzy time series.

Many models and techniques have been proposed by researchers to improve forecasting accuracy using fuzzy time series. However, very few studies have tackled problems that involve inverse fuzzy function into fuzzy time series forecasting. In this paper, we modify inverse fuzzy function by considering new factor value in establishing the forecasting model without any probabilistic approaches. The proposed model was evaluated by comparing its performance with inverse and noninverse fuzzy time series models in forecasting the yearly enrollment data of several universities, such as Alabama University, Universiti Teknologi Malaysia (UTM), and QiongZhou University; the yearly car accidents in Belgium; and the monthly Turkish spot gold price. The results suggest that the proposed model has potential to improve the forecasting accuracy compared to the existing inverse and non-inverse fuzzy time series models. This paper contributes to providing the better future forecast values using the systematic rules.

The study of fuzzy time series models have been extensively used to improve the accuracy rates in forecasting problems. In this paper, we present a new type 2 fuzzy time series forecasting model based on three-factors fuzzy logical relationship groups. The proposed method uses a new technique to define partitions the universe of discourse into different length of intervals for different factors. Also, the proposed method fuzzifies the historical data sets of the main factors, second factors and third factors to their maximum membership grades obtained by their corresponding triangular fuzzy sets and construct the fuzzy logical relationship groups which is based on the three-factors to enhance in the forecasting accuracy rates. This paper introduces a new defuzzification technique based on their frequency occurrences of fuzzy logical relationships in fuzzy logical relationship groups. The fitness of the propose method is verified in the forecasting of Bombay Stock Exchange (BSE) Sensex historical data and compare in terms of root mean square and average forecasting errors which indicates that the proposed method produce more accurate forecasted output over the existing models in fuzzy time series.

Prediction of river discharge is important for water resources management. Engineers have developed many physical and mathematical models for prediction of river discharge. The fact that physical hydrological models are site specific and include many parameters, has led researchers to work on mathematical black-box models. In this study, the fuzzy time series (FTS) method was used in the prediction of river discharge. The proposed method, which is employed for the first time in hydrology, allows to fast decision-making mechanism. The proposed algorithm, FTS, is used along with continuous wavelet transform (CWT) method to improve prediction performance. CWT, can be used as pre-treatment technique, is able decompose concerned time series into several bands at different scales which allows to predict much more homogeneous series rather than complex flow discharge series. By considering various statistical success criteria, the wavelet transformed time series (WFTS) method performed quite high accurate predictions compared to the classical fuzzy time series method. Combining FTS with wavelet transform opens a new window in the fuzzy time series method applications that has ability to improve the prediction performance.

Fuzzy time series has been applied to forecast various domain problems because of its capability to deal with vagueness and incompleteness inherent in data. However, most existing fuzzy time series models cannot cope with multi-attribute time series and remain too subjective in the partition of the universe of discourse. Moreover, these models do not consider the trend factor and the corresponding external time series, which are highly relevant to target series. In the current paper, a heuristic bivariate model is proposed to improve forecasting accuracy, and the proposed model applies fuzzy c-means clustering algorithm to process multi-attribute fuzzy time series and to partition the universe of discourse. Meanwhile, the trend predictors are extracted in the training phase and utilized to select the order of fuzzy relations in the testing phase. Finally, the proper full use of the external series to assist forecasting is discussed. The performance of the proposed model is tested using actual time series including the enrollments at the University of Alabama, the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) and a sensor dataset. The experimental results show that the proposed model can be utilized for multi-attribute time series and significantly improves the average MAER to 1.19% when compared with other forecasting models.

Foreign exchange rate (forex) forecasting has been the subject of several rigorous investigations due to its importance in evaluating the benefits and risks of the international business environments. Many methods have been researched with the ultimate goal being to increase the reliability and efficiency of the forecasting method. However as the data are inherently dynamic and complex, the development of accurate forecasting method remains a challenging task if not a formidable one. This paper proposes a new weight of the fuzzy time series model for a daily forecast of the exchange rate market. Through this method, the weights are assigned to the fuzzy relationships based on a probability approach. This can be implemented to carry out the frequently recurring fuzzy logical relationship (FLR) in the fuzzy logical group (FLG). The US dollar to the Malaysian Ringgit (MYR) exchange rates are used as an example and the efficiency of the proposed method is compared with the methods proposed by Yu and Cheng et al. The result shows that the proposed method has enhanced the accuracy and efficiency of the daily exchange rate forecasting opportunities.

Various methods have been presented to investigate the length of data interval and partition number of universe of discourse in fuzzy time series to achieve high level forecasting accuracy. However, the interval length is still an issue and thus, influencing the forecasting accuracy. This paper proposes a new approach using the average inter-quartile range to improve the interval length and subsequently the partition number of universe of discourse. Moreover, in forecasting method, the first-differencing data is also considered to obtain better forecast. The enrollment data of Alabama University is used as an example and the efficiency of the proposed method is compared with the previous methods. The result shows that the proposed method improves the accuracy and efficiency of the yearly enrollment forecasting opportunities.

To forecast the non-stationary data is quite difficult when compared with the stationary data time series. Because their variances are not constant and not stable like the second data type. This paper presents the implementation of fuzzy time series (FTS) into the non-stationary time series data forecasting, such as, the electricity load demand, the exchange rates, the enrollment university and others. These data forecasts are derived by implementing of the weightage and linguistic out-sample methods. The result shows that the FTS can be applied in improving the accuracy and efficiency of these non-stationary data forecasting opportunities.

Numerous fuzzy time series (FTS) forecasting methods have been proposed in scientific literature and has achieved growing attention in practice. Most of them are based on modeling fuzzy relationships(FRs) of the past data. In this paper, a new hybrid forecasting model based on the concept of time-variant FR group (TV-FRG), particle swarm optimization technique (PSO) and refinement technique in the defuzzization stage is presented to forecast the enrolments of the University and the stock market. PSO technique is utilized to adjust for obtaining the effective length of each interval in the universe of discourse for the forecasting model. Most of the existing forecasting models simply ignore the repeated FRs without any proper justification or accept the number of recurrence of the FRs without considering the appearance history of these FRs in the grouping FRs process. Therefore, the appearance history of the fuzzy sets on the right-hand side of the FRs is considered to establish the FR groups, called the TV-FRGs. Furthermore, the high-order TV-FRGs are used in order to obtain more accurate forecasting results in the defuzzication stage. To calculate these high-order TV-FRGs values, a refined defuzzication technique is developed, and incorporated in the proposed model. To verify the effectiveness of the proposed model, two numerical simulations are examined with the case of University enrollments and Taiwan futures exchange (TAIFEX). The experimental results show that the proposed model achieves good forecasting results compared to other existing forecasting models based on the high-order FTS. These promising results bring a significant meaning for the future work on the development of FTS and PSO algorithm in real-world forecasting applications.

In forecasting the fuzzy time series data, several authors took grades of membership 1, 0.5 and 0 for linguistic interval corresponding to fuzzy set. In this paper, we have proposed high-order approach for forecasting the fuzzy time series data by using the grade of membership value defined for each datum corresponding to triangular fuzzy sets and fuzzify the historical data by triangular fuzzy sets which have their maximum membership values. Also, we establish high-order fuzzy logical relationship groups and give a new technique for defuzzification process, by which we can compute the forecasted value in a more efficient way with lower value of MSE. For verifying the suitability of proposed method, we illustrate time series data of student enrollments at the University of Alabama, USA, and crop (Lahi) production of Pantnagar farm, G. B. Pant University of Agriculture and Technology, Pantnagar, India. The forecasting accuracy rate of proposed high-order forecasting method is better than those of existing methods and the forecasted production is much closer to the actual production.

Forecasting for time series has always been of interest to statisticians and data scientists because it offers a lot of benefits in reality. This study proposes the fuzzy time series model which can both interpolate historical data, and forecast effectively for the future with the important contributions. First, we build the universal set based on the percentage of the original data variation, and divide it to clusters with the suitable number by the developed automatic algorithm. Next, the new fuzzy relationship between each element in series and the obtained clusters is established. The bigger the variation is, the more the clusters are divided. Finally, combining the two above improvements, we propose the new principle to forecast for the future. The experiments on many well-known data sets, including 3003 series of M3-competition data show that the proposed model has shown the outstanding advantage in comparing to the existing ones. Because the proposed model is established by the Matlab procedure, it can apply effectively for real series.

In electrical power management, load forecasting accuracy is an indispensable factor which influences the decision making and planning of power companies in the future. Previous research has explored various forecasting models to resolve this issue, ranging from linear and non-linear regression to artificial intelligence algorithm. However, the absolute percentage error has yet to significantly improve using these models. Through this paper, the fuzzy time series (FTS) model was suggested to obtain better forecasted values and increases the forecasting accuracy. This accuracy could be obtained by using effective length of intervals of the discourse universe. The yearly dataset of Taiwan regional electric load was used for this empirical study and the reliability of the proposed model was compared with other previous models. The results indicated that the mean absolute percentage error (MAPE) of the proposed model (FTS) is smaller than MAPE obtained from those previous models.

Intuitionistic fuzzy set plays a vital role in data analysis and decision-making problems. In this paper, we propose an enhanced and versatile method of forecasting using the concept of intuitionistic fuzzy time series (FTS) based on their score function. The developed method has been presented in the form of simple computational steps of forecasting instead of complicated max–min compositions operator of intuitionistic fuzzy sets to compute the relational matrix $R$. Also, the proposed method is based on the maximum score and minimum accuracy function of intuitionistic fuzzy numbers (IFNs) to fuzzify the historical time series data. Further intuitionistic fuzzy logical relationship groups are defined and also provide a forecasted value and lies in an interval and is more appropriate rather than a crisp value. Furthermore, the proposed method has been implemented on the historical student enrollments data of University of Alabama and obtains the forecasted values which have been compared with the existing methods to show its superiority. The suitability of the proposed model has also been examined to forecast the movement of share market price of State Bank of India (SBI) at Bombay Stock Exchange (BSE). The results of the comparison of MSE and MAPE indicate that the proposed method produces more accurate forecasting results.

Present study proposes a method for fuzzy time series forecasting based on difference parameters. The developed method has been presented in a form of simple computational algorithm. It utilizes various difference parameters being implemented on current state for forecasting the next state values to accommodate the possible vagueness in the data in an efficient way. The developed model has been simulated on the historical student enrollments data of University of Alabama and the obtained forecasted values have been compared with the existing methods to show its superiority. Further, the developed model has also been implemented in forecasting the movement of market prices of share of State Bank of India (SBI) at Bombay Stock Exchange (BSE), India.

Intuitionistic fuzzy sets (IFSs) are well established as a tool to handle the hesitation in the decision system. In this research paper, fuzzy sets induced by IFS are used to develop a fuzzy time series forecasting model to incorporate degree of hesitation (nondeterminacy). To improve the forecasting accuracy, induced fuzzy sets are used to establish fuzzy logical relations. To verify the performance of the proposed model, it is implemented on one of the benchmarking time series data. Further, developed forecasting method is also tested and validated by applying it on a financial time series data. In order to show the accuracy in forecasting, the method is compared with other forecasting methods using different error measures.

In this paper, a method is proposed to deal with factors affecting the fuzzy time series forecasting. A new fuzzification process is used by considering all the fuzzy sets with nonzero membership values corresponding to the data points. A strong alpha-cut based method is presented to select appropriate fuzzy logical relationships that carry importance in analyzing the trend of time series. Further, a unique defuzzification approach based on weights is proposed to get crisp variation. This obtained variation is finally converted to the forecasted value. The presented method is tested on the benchmark enrolment dataset of Alabama University and seven datasets of the Taiwan Capitalization Weighted Stock Index. On comparing the results, it is observed that the presented method performs better than the existing methods. Also, the statistical measures indicate the good forecasting results of the presented method.

In fuzzy time series forecasting, the weight of fuzzy logical relationships and the midpoint of interval values are extensively used in the product of defuzzified matrix and the transpose of the weight matrix into the final forecast model. An improved forecast can be achieved through this model. Additionally, because of its excellent performance, successful applications can be widely achieved by exploiting real life data such as enrollment, stock indices and exchange rates for example. However, the improvement of mean square error is still not significant when the midpoint and the weight values are strictly increased in both of the matrixes. In order to reduce the mean square error, a reversal model in which the weight elements are reversed in the transpose matrix is proposed in this paper. Moreover, a theorem is also proposed to justify this reversal model and the annual data of electricity load by regions of Taiwan from 1981 to 2000 is examined as further evidence. The result indicate a consistently significant advantage in the proposed reversal model, i.e. the mean square error is smaller than the non-reversal model for each region.

Fuzzy time series has been implemented for data prediction in the various sectors, such as education, finance-economic, energy, traffic accident, others. Moreover, many proposed models have been presented to improve the forecasting accuracy. However, the interval-length adjustment and the out-sample forecast procedure are still issues in fuzzy time series forecasting, where both issues are yet clearly investigated in the previous studies. In this paper, a new adjustment of the interval-length and the partition number of the data set is proposed. Additionally, the determining of the out-sample forecast is also discussed. The yearly oil production (OP) and oil consumption (OC) of Malaysia and Indonesia from 1965 to 2012 are examined to evaluate the performance of fuzzy time series and the probabilistic time series models. The result indicates that the fuzzy time series model is better than the probabilistic models, such as regression time series, exponential smoothing in terms of the forecasting accuracy. This paper thus highlights the effect of the proposed interval length in reducing the forecasting error significantly, as well as the main differences between the fuzzy and probabilistic time series models.

This paper investigates the influence of a novel scheme for the forecasting energy supplies and accidents happen in nuclear plants. The historical data of energy supplies of the nuclear plants of Taiwan area are conducted.