Fuzzy Time Series: An Application to Tourism Demand Forecasting

This paper proposes a novel optimized model based on the combination of the fuzzy time series (FTS) method and Jacobi polynomials for predicting the behavior of fiber-reinforced polymer (FRP)-confined concrete under compression loads. In this model, the stress-strain curves are approximated by Jacobi polynomials. Then, the FTS method is used to develop a nonlinear relationship between the coefficients of Jacobi polynomials and the specimen features. Moreover, another FTS model is developed to predict the ultimate stress and the ultimate strain of FRP-confined concrete. A comparative analysis is performed to demonstrate the effectiveness of the proposed model. As compared with the well-known design-oriented models applied to 69 experiments, the root mean square error is decreased more than 50% by the proposed model. Also, the effects of input features on the physical behavior of the specimens as described by the proposed model are consistent with the relevant theories and experiments.

Rice has become the main staple food for almost the entire population of Indonesia. However, in Indonesia, the price of food commodities (rice) often fluctuates in price. Due to the rapid fluctuation of rice prices and the uncertainty in the future, it is necessary to forecast rice prices. This study aims to predict the price of rice in the city of Mataram using the Holt double exponential smoothing method and the Cheng fuzzy time series. The model's performance is based on Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE) indicators. Forecasting model based on Holt's double exponential smoothing method, the MSE value is 705967.4994 and the MAPE value is 7.91%. On the other hand, based on Cheng's fuzzy time series method, the performance of the forecasting model based on the MSE indicator is 566312.340 and based on the MAPE value of 6.75%. Based on these results, Cheng's fuzzy time series method is more accurate than Holt's double exponential smoothing method. Keywords: Double Exponential Smoothing Holt, Fuzzy Time Series Cheng, Rice Price, MAPE, MSE

A new approach based on artificial neural networks for high order multivariate fuzzy time series

Short-term load forecasting method based on fuzzy time series, seasonality and long memory process

The primary objective of this study is to evaluate the accuracy of different forecasting models for monthly wind farm electricity production. This study compares the effectiveness of three forecasting models: Autoregressive Integrated Moving Average (ARIMA), Seasonal ARIMA (SARIMA), and Support Vector Regression (SVR). This study utilizes data from two wind farms located in Poland—‘Gizałki’ and ‘Łęki Dukielskie’—to exclude the possibility of biased results due to specific characteristics of a single farm and to allow for a more comprehensive comparison of the effectiveness of both time series analysis methods. Model parameterization was optimized through a grid search based on the Mean Absolute Percentage Error (MAPE). The performance of the best models was evaluated using Mean Bias Error (MBE), MAPE, Mean Absolute Error (MAE), and R2Score. For the Gizałki farm, the ARIMA model outperformed SARIMA and SVR, while for the Łęki Dukielskie farm, SARIMA proved to be the most accurate, highlighting the importance of optimizing seasonal parameters. The SVR method demonstrated the lowest effectiveness for both datasets. The results indicate that the ARIMA and SARIMA models are effective for forecasting wind farm energy production. However, their performance is influenced by the specificity of the data and seasonal patterns. The study provides an in-depth analysis of the results and offers suggestions for future research, such as extending the data to include multidimensional time series. Our findings have practical implications for enhancing the accuracy of wind farm energy forecasts, which can significantly improve operational efficiency and planning.

Forecasting the amount of Pneumonia patients could help medical practitioners to prepare the required medicines, aid-workers, or even prevent it by sharing knowledge to parents, elders, and smokers. This problem poses great concerns on the lives of many people, therefore, adequate accuracy is required in forecasting. Fuzzy Time Series (FTS) is an alternative way to forecast data. By using ARIMA and Holt’s Exponential Smoothing, there are some problems that are difficult to obtain the best model. Using our FTS method, we modified the Cheng algorithm by using higher order (using two or more historical data) to make the accuracy better by seeing the Mean Absolute Percentage Error (MAPE). Data was selected from the amount of Pneumonia Patients in Jakarta from 2008 to 2018. We use R to carryout ARIMA and Holt’s Exponential Smoothing. Forecasting’s accuracy will decrease if the timeframe between these occurrences is lengthy. As a result of this, we made use of 5 periods which are January until May 2019. The result obtained was compared against ARIMA and Holt’s Exponential Smoothing, as well as the MAPE are 9.70%, 16.85%, and 18.55% respectively.

To ensure the sustainable growth of coal production, it is necessary to analyse the growth, to ground the plans and management decisions on effective diagnostics and prediction of current and future situation at the coal production. This study presents a application of fuzzy time series forecasting methods, The new technique is applied to forecasting the coal production data using a fuzzy approach. For testing the methodology, statistical data on the coal production from 1980- to 2019. The Sturges rule is proposed to use as the universe of discourse. The intervals of variation of such indicators as growth rate are calculated when applying the approach to all defined fuzzy sets. The ARIMA model algorithm was applied by using the R - software to find the forecasted values. The forecasting results, obtained by the fuzzy time series method, are supposed to have more accuracy rate than time series model.

Background: One forecasting method that is often used is time series forecasting. The development of applied mathematics has encouraged new mathematical findings that led to the birth of new branches of mathematics, one of which is fuzzy. Purpose: The objectives of the study, namely forecasting, fuzzy set, time series, fuzzy time series, fuzzy time series Singh, interval ratio and measurement of accuracy level. Method: This research method applies Chen's fuzzy time series in the section of determining the universe of talk you to the fuzzification of historical data and in the part of forecasting results obtained through a heuristic approach by building three forecasting rules, namely Rule 2.1, Rule 2.2, and Rule 2.3 to obtain better results and affect very small AFER values. As well as making modifications to the interval partition section using interval ratios to be able to reflect data variations. Results: Based on the calculation of AFER values for order 2, order 3, and order 4 respectively obtained at 1.06389%, 0.689368%, and 0.711947%. Therefore, it can be said, Singh's fuzzy time series forecasting method based on the ratio of 3rd-order intervals is better than that of 2nd-order and 4th-order. Conclusion: Based on the results of research and discussion that has been carried out, it can be concluded that Singh's fuzzy time series forecasting method has the same algorithm as fuzzy time series forecasting. Singh's fuzzy time series forecasting method based on interval ratios applies fuzzy time series and Singh forecasting. Singh's fuzzy time series forecasting modification accuracy rate based on interval ratios produces excellent forecasting values according to evaluator average forecasting error rate (AFER).

During the last decades, air pollution has become a serious environmental hazard. Its impact on public health and safety, as well as on the ecosystem, has been dramatic. Forecasting the levels of air pollution to maintain the climatic conditions and environmental protection becomes crucial for government authorities to develop strategies for the prevention of pollution. This study aims to evaluate the atmospheric air pollution of the city of Zahleh located in the geographic zone of Bekaa. The study aims to determine a relationship between variations in ambient particulate concentrations during a short time. The data was collected from June 2017 to June 2018. In order to predict the Air Quality Index (AQI), Naïve, Exponential Smoothing, TBATS (a forecasting method to model time series data), and Seasonal Autoregressive Integrated Moving Average (SARIMA) models were implemented. The performance of these models for predicting air quality is measured using the Mean Absolute Error (MAE), the Root Mean Square Error (RMSE), and the Relative Error (RE). SARIMA model is the most accurate in prediction of AQI (RMSE = 38.04, MAE = 22.52 and RE = 0.16). The results reveal that SARIMA can be applied to cities like Zahleh to assess the level of air pollution and to prevent harmful impacts on health. Furthermore, the authorities responsible for controlling the air quality may use this model to measure the level of air pollution in the nearest future and establish a mechanism to identify the high peaks of air pollution.

Triple exponential smoothing is one of the prominent linear models for seasonal time series forecasting. Fuzzy time series forecasting is originated as a new advent for forecasting the data which is imprecise and vague. In this work, we proposed a methodology using both triple exponential smoothing and fuzzy time series. It has the advantage of modelling aspects in linear and non-linear setup. Empirical results with real-world data sets show that the hybrid model is an efficient one based on forecasting accuracy than the component models used individually.KeywordsFuzzy time seriesHybridTriple exponential smoothing

Fuzzy time series (FTS) is a method of making educated guesses by using fuzzy intervals, which correspond to time series clusters. It is also useful for data noise reduction and is based on rule-based forecasting. The aim of this article is to develop a vector autoregressive fuzzy integrated logical forecasting (VAR-FILF) model for time charter rates of Panamax and Handymax bulk carriers. Results are tested by using Chen's FTS method (cFTS), bivariate cFTS (Bi-cFTS) method and conventional time series methods, and the accuracy of the VAR-FILF method is found to be higher than these methods. In addition, the length of intervals affects the forecasting result and the accuracy of forecasting. Therefore, this study proposes the fuzzy C-means clustering method for the structuring of the fuzzy length of intervals of the FTS forecasting process.

Background: Malaria remains a significant public health problem in India, particularly in endemic states such as Karnataka. Accurate forecasting of malaria incidence is essential for strengthening surveillance systems, optimizing resource allocation and enabling timely preventive interventions. Objective: This study aimed to analyze the temporal pattern of malaria cases in Karnataka State, India and to develop an appropriate Seasonal Autoregressive Integrated Moving Average (SARIMA) model for forecasting future monthly malaria incidence. Methods: A retrospective time series analysis was conducted using monthly malaria case data from January 2020 to August 2025 obtained from the National Centre for Vector Borne Diseases Control (NCVBDC), Government of India. The Box–Jenkins methodology was applied for model development. Data preprocessing included logarithmic transformation and seasonal and non-seasonal differencing to achieve stationary. Model identification was guided by autocorrelation function (ACF) and partial autocorrelation function (PACF) plots. Competing SARIMA models were estimated using maximum likelihood estimation and evaluated using Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and Bayesian Information Criterion (BIC). Residual diagnostics were assessed using the Ljung–Box Q test. Results: The malaria time series demonstrated a clear increasing trend with pronounced seasonal variation. Among the candidate models, the SARIMA (2,1,0) (0,1,1) ₁₂ model showed the best overall performance, with the lowest RMSE (29.413), MAE (18.279), MAPE (40.437) and normalized BIC (7.054). The Ljung–Box Q test indicated no residual autocorrelation (p = 0.77). Twelve-month forecasts (September 2025–August 2026) revealed marked seasonal peaks, with forecasted values ranging from 43 to 461 cases. Conclusion: The SARIMA (2,1,0) (0,1,1) ₁₂ model effectively captured the trend and seasonal dynamics of malaria transmission in Karnataka. SARIMA based forecasting offers a practical and reliable tool for malaria surveillance and can support evidence-based planning and timely public health interventions. Keywords: Malaria, Time series analysis, SARIMA, Forecasting, Karnataka, Public health

IntroductionRabies, a deadly zoonotic viral disease, accounts for over 50,000 fatalities globally each year. This disease predominantly plagues developing nations, with Thailand being no exception. In the current global landscape, concerted efforts are being mobilized to curb human mortalities attributed to animal-transmitted rabies. For strategic allocation and optimization of resources, sophisticated and accurate forecasting of rabies incidents is imperative. This research aims to determine temporal patterns, and seasonal fluctuations, and project the incidence of canine rabies throughout Thailand, using various time series techniques.MethodsMonthly total laboratory-confirmed rabies cases data from January 2013 to December 2022 (full dataset) were split into the training dataset (January 2013 to December 2021) and the test dataset (January to December 2022). Time series models including Seasonal Autoregressive Integrated Moving Average (SARIMA), Neural Network Autoregression (NNAR), Error Trend Seasonality (ETS), the Trigonometric Exponential Smoothing State-Space Model with Box-Cox transformation, ARMA errors, Trend and Seasonal components (TBATS), and Seasonal and Trend Decomposition using Loess (STL) were used to analyze the training dataset and the full dataset. The forecast values obtained from the time series models applied to the training dataset were compared with the actual values from the test dataset to determine their predictive performance. Furthermore, the forecast projections from January 2023 to December 2025 were generated from models applied to the full dataset.ResultsThe findings revealed a total of 4,678 confirmed canine rabies cases during the study duration, with apparent seasonality in the data. Among the models tested with the test dataset, TBATS exhibited superior predictive accuracy, closely trailed by the SARIMA model. Based on the full dataset, TBATS projections suggest an annual average of approximately 285 canine rabies cases for the years 2023 to 2025, translating to a monthly average of 23 cases (range: 18–30). In contrast, SARIMA projections averaged 277 cases annually (range: 208–214).DiscussionThis research offers a new perspective on disease forecasting through advanced time series methodologies. The results should be taken into consideration when planning and conducting rabies surveillance, prevention, and control activities.

About the research of fuzzy time series model are proposed by Song and Chissom(1993). There are many researchers have proposed many different methods and models. Example the p-order fuzzy time series model FAR(p), the p-order fuzzy time series model with fuzzy trend, and the p-order fuzzy seasonal time series model FSAR(p)s. But, about a fuzzy time series has shown a tendency to increase or decrease over a particular period and also to follow a seasonal pattern, FASRI(p, d)×(P, D)(subscript s) that is no any paper to research this topic. In this research, we want to study the FASRI(p, d)×(P, D)(subscript s) model of fuzzy time series. First, we make testing for the fuzzy trend of fuzzy time series by the rule of Liaw(2000) proposed. If the fuzzy time series with fuzzy trend, we make a differencing for the original time series, then make testing for the fuzzy seasonal of the new fuzzy time series by the rule of Liaw(2000) proposed. If the new fuzzy time series with fuzzy seasonal. It is told us the fuzzy time series simultaneous with fuzzy trend and fuzzy seasonal. We must consider the fuzzy time series simultaneous with fuzzy trend and fuzzy seasonal at the model construction. Finally, we use two relevant instances verify our propose method.

Forecasting activities play an important role in our daily life. In recent years, fuzzy time series (FTS) methods were developed to deal with forecasting problems. FTS attracted researchers because of its ability to predict the future values in some critical situations where most standard forecasting models are doubtfully applicable or produce bad fittings. However, some critical issues in FTS are still open; these issues are often subjective and affect the accuracy of forecasting. In this paper, we focus on improving the accuracy of FTS forecasting methods. The new method integrates the fuzzy clustering and genetic algorithm with FTS to reduce subjectivity and improve its accuracy. In the new method, the genetic algorithm is responsible for selecting the proper model. Also, the fuzzy clustering algorithm is responsible for fuzzifying the historical data, based on its membership degrees to each cluster, and using these memberships to defuzzify the results. This method provides better forecasting accuracy when compared with other extant researches.