Singh's Fuzzy Time Series Forecasting Modification Based on Interval Ratio

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

n the literature, there have been a good many different forecasting methods related forecasting problems of fuzzy time series. The main issue of fuzzy time series forecasting is the accuracy of the forecasted values. The forecasting accuracy rate is affected by the length of each interval in the universe of discourse. Thus, it is substantial to determine the length of each interval. In this study, new computational method based on class width to determine interval length is proposed and also used coefficient of variation for time series forecasting. After the intervals are formed, the historical time series data set is fuzzified according to fuzzy time series theory. The proposed model has been tested on the student enrollments, University of Alabama and a real life problem of rice production for containing higher uncertainty. This method was compared with existent methods to determine the effectiveness in terms of the mean square error (MSE) and the average forecasting (AFE). The results are shown that the proposed model can achieve a higher forecasting accuracy rate than the existent models.

In this study, the author presents a new model to deal with four major issues of fuzzy time series (FTS) forecasting, viz., determination of effective lengths of intervals (i.e., intervals which are used to fuzzify the numerical values), repeated fuzzy sets, trend associated with fuzzy sets, and defuzzification operation. To resolve the problem of determination of length of intervals, this study suggests the application of an artificial neural network (ANN) based algorithm. After generating the intervals, the historical time series data set is fuzzified based on FTS theory. In part of existing FTS models introduced in the literature, each fuzzy set is given equal importance, which is not effective to solve real time problems. Therefore, in this model, it is recommended to assign weights on the fuzzy sets based on their frequency of occurrences. In the FTS modeling approach, fuzzified time series values are further used to establish the fuzzy logical relations (FLRs). To determine the trends associated with the fuzzy sets in the corresponding FLR, this article also introduces three trend-based conditions. To deal repeated fuzzy sets and trend associated with them, this study proposes a new defuzzification technique. The proposed model is verified and validated with real-world time series data sets. Empirical analyzes signify that the proposed model has the robustness to deal one-factor time series data sets very efficiently than existing FTS models. Experimental results show that the proposed model also outperforms over the conventional statistical models.

Fuzzy time series methods have been applied to social forecasting for over a decade; however, little research has been done to discuss the decision of an optimal fuzzy model for time series. In the paper, we evaluate the forecasting performance of three listed multivariate fuzzy models by comparing forecasting MSE of model. The data obtained from AEROM, Taiwan, includes Taiwan’s exports and foreign exchange rate for models’ test. The algorithm for predictive value of the models has three-stage computation procedure: First, calibrating time series correlation, deciding window base and interval partition; second, solving the static forecasting value of each model; third, comparing the dynamic parameter to impact of the forecasting error. The empirical results indicate that increasing predictor variables has no significant effect on predictive performance of the models; increasing length of interval would not improve the prediction performance of the models. Moreover, Fuzzy model is better for short-term time series forecasting. For forecasting purpose, Heuristic model has best forecasting performance among three fuzzy models. The findings of the paper represent a significant contribution to our understanding of the applicability of fuzzy models to predict.

Fuzzy time series model (FTS) has been widely used to forecast various time series data. When some data are missing, the forecasting accuracy will be greatly reduced. Therefore, a new forecasting method G-FTS is proposed based on the Gaussian mixture model and FTS. First, the distribution of the samples is estimated by using a Gaussian mixture model, the missing data are filled with the estimated distribution, and then a fuzzy time series forecasting is performed. The effectiveness of this method is illustrated by forecasting the monthly inventory data of small and medium-sized industrial enterprises in China. According to the characteristics of industrial data, such as time correlation, fast arrival, and large quantity, a dynamic forecasting method Dynamic-GFTS is proposed. This method is used to forecast the data collected by a textile factory. Simulation results show that Dynamic-GFTS is more effective in actual industrial data.

Time series Forecasting is one of crucial techniques that helps with strategic decision-making and mitigating potential risks –One of which is Weighted fuzzy time series (WFTS). Moreover, the interval length of the WFTS plays a crucial role in its modelization and accuracy in predicting future values. Therefore, this research implements a dual optimization on WFTS, which are (1) Particle Swarm Optimization to find the optimum interval length of the WFTS and (2) a Lagrange quadratic to optimize the weight of the fuzzy interval. In this research, a univariate Average Air Temperature located in Malang is used to perform forecasting model. The dataset is taken from BMKG-Indonesia. This research aims to acquire an optimized interval length on fuzzy time series forecasting, i.e., improving its accuracy by finding the optimal interval length. Based on the result, the proposed dual optimization model outperforms the classical WFTS on forecasting. The proposed model excels based on the evaluation matrix values. It has been noticed also that implementing PSO to find the optimum interval length has improved the accuracy of the classical WFTS. The classical WFTS has MAPE and RMSE of 2.4 and 0.73, respectively, while the proposed dual optimized model has 1.01 and 0.3. This approach identifies the best interval values and provides optimum weights related to each data point, providing solid insights for air temperature forecasting.

The arising air pollution has addressed much attention globally due to its detrimental effects on human health and environment. As an early warning system for air quality control and management, it is important to provide precise information about the future concentrations in pollutants. We present here a time series model in predicting the Air Pollution Index (API) from three different stations; industrial, residential, and sub-urban areas between 2000 and 2009. In this paper, the Box–Jenkins approach of seasonal autoregressive integrated moving average (ARIMA), artificial neural network (ANN), and three models of fuzzy time series (FTS) have been compared by using the mean absolute percentage error, mean absolute error, mean square error, and root mean square error. Although all the methods were used as operational tools, the ANN seemed more accurate in forecasting API. The results showed that FTS (i.e. Chen’s, Yu’s, and Cheng’s) performed inconsistent results since the conventional methods of ARIMA outperformed the performance of FTS. However, consistent results were achieved as the ANNs gave the smallest forecasting error compared to FTS and ARIMA.

The kNN time series forecasting method is based on a very simple idea. kNN forecasting is base on the idea that similar training samples most likely will have similar output values. One has to look for a certain number of nearest neighbors, according to some distance. The first idea that comes to mind when we see the nearest neighbor time series forecasting technique is to weigh the contribution of the different neighbors according to distance to the present observation. The fuzzy version of the nearest neighbor time series forecasting technique implicitly weighs the contribution of the different neighbors to the prediction, using the fuzzy membership of the linguistic terms as a kind of distance to the current observation. The training phase compiles all different scenarios of what has been observed in the time series’ past as a set of fuzzy rules. When we encounter a new situation and need to predict the future outcome, just like in normal fuzzy inference systems, the current observation is fuzzyfied, the set of rules is traversed to see which ones of them are activated (i.e., their antecedents are satisfied) and the outcome of the forecast is defuzzyfied by the common center of gravity rule.KeywordsTime series forecastingFuzzy reasoningAutomatic machine learning

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.

In this paper a hybrid forecasting technique that integrates Cat Swarm optimization Clustering (CSO-C) and Particle Swarm Optimization (PSO) with Fuzzy Time Series (FTS) forecasting is presented. In the three stages of FTS, CSO-C found application at the fuzzification module where its efficient capability in terms of data classification was utilized to neutrally divide the universe of discourse into unequal parts. Then, disambiguated fuzzy relationships were obtained using Fuzzy Set Group (FSG). In the final stage, PSO was adopted for optimization; by tuning weights assigned to fuzzy sets in a rule. This rule is a fuzzy logical relationship induced from FSG. The forecasting results showed that the proposed method outperformed other existing methods; using RMSE and MAPE as performance metrics.

Aims: Sample: To determine the effectiveness of the proposed forecasting method, namely Singh's fuzzy time series based on high order (third order) interval ratios. And find out the forecasting results in January 2022. Study Design: Modification of Singh's fuzzy time series based on interval ratios. Place and Duration of Study: Sample: monthly rainfall data for Semarang City from January 2017 to December 2021. Methodology: The method proposed by the researcher is the Singh fuzzy time series forecasting method based on high order (third order) interval ratios. This research method uses a combination of Chen and Singh's fuzzy time series. Applying Chen's fuzzy time series in the section determining the universe of discourse () to fuzzification which includes determining the universe of discourse, determining interval partitions, forming Fuzzy Logical Relationships and Fuzzy Logical Relationship Groups. Then apply Singh's fuzzy time series to the forecasting part. Finally, calculate the Average Forecasting Error Rate (AFER) to test forecasting performance. In the forecasting part, it is obtained through a heuristic approach by building high order forecasting rules to obtain better results and have an effect on very small AFER values. In the step of determining the interval partition, this research uses the interval ratio method which aims to reflect variations in historical data. Conclusion: Based on the calculation of the AFER value, the AFER for third order is 0.2422%. It can be said that Singh's fuzzy time series forecasting method based on high order (third order) interval ratios on monthly rainfall data for Semarang City from January 2017 to December 2021 is very good. And the rainfall forecast for January 2022 is 196.80 mm3 or into the category of very heavy rain.

Forecasting the demand for public services is often overlooked in border regions, where data-driven management remains limited. However, accurate forecasts are essential for improving service quality and optimizing the use of public facilities. This study aims to predict the number of university student visits to the Regional Library of Timor Tengah Utara (TTU) Regency, an Indonesian border area, using Chen’s fuzzy time series (FTS) model. The dataset consists of monthly records of university student visits from April 2022 to September 2025. The forecasting process involves fuzzification, the establishment of fuzzy logical relationships, and defuzzification to obtain predicted values. The results show that the number of student visits decreased from 240 in April 2022 to 213 in October 2025. The model achieved a Mean Absolute Percentage Error (MAPE) of 35.15%, indicating a fairly good forecasting accuracy. This study extends the application of Chen’s FTS model to library management forecasting in developing and border regions. In the long term, improved forecasting and service planning are expected to enhance library management efficiency and encourage greater student interest in visiting and reading at regional libraries.

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.

Stock Index prediction plays a vital role for investors, resulting in significant benefits. In response to a need to recover prediction performance of fuzzy time-series models, the research work is substituted for fuzzy logical relationships with rule-based procedure to abstract prediction directions from time-series explanations. This research work suggests the originality of fuzzy time-series forecasting models presented with numerous linear regressions and time-series assembled for forecasted market price. Here, some learning algorithms are shown to execute the proposed model, which makes the overall model simple and precise. Hence, this paper establishes a novel fuzzy time-series model based on rough set-rule orientation for predicting stock index, and this study has four contributions to improve forecast accuracy and provide investment point. To work on this paper, various data was collected from TAIEX, BSE, and KOSPI from 2015 to 2020 as experimental dataset.

In recent years, there has been a growing interest in Time Series forecasting. A number of time series forecasting methods have been proposed by various researchers. However, a common trend found in these methods is that they all underperform on a data set that exhibit uneven ups and downs (turbulences). In this paper, a new method based on fuzzy time-series (henceforth FTS) to forecast on the fundament of turbulences in the data set is proposed. The results show that the turbulence based fuzzy time series forecasting is effective, especially, when the available data indicate a high degree of instability. A few benchmark FTS methods are identified from the literature, their limitations and gaps are discussed and it is observed that the proposed method successfully overcome their deficiencies to produce better results. In order to validate the proposed model, a performance comparison with various conventional time series models is also presented.