Fuzzy Time Series Model Research Articles

Comparison of improved hybrid FTS models for forecasting the urban air quality index

Air pollution data is variable and vulnerable, and it is difficult to capture the changing pattern of air pollution data. In this study, multiple novel hybrid models are proposed which combine fuzzy time series (FTS) with mode decomposition to achieve stationarity and improve the effectiveness of the forecasting process. More specifically, air pollution data are first processed using the mode decomposition technique, and sample entropy is used to recombine the subseries, then, the information granularity is utilized for fuzzification. Complementary ensemble empirical mode decomposition-sample entropy-probabilistic weights FTS (CEEMD-SE-PWFTS) is the model that best captures the variation pattern of air pollution data. The experimental results verified that: Among all the proposed novel models, CEEMD-SE-PWFTS gets the highest forecasting accuracy of Air Quality Index (AQI). Air pollution datasets from five cities in China (Shanghai, Nanjing, Lianyungang, Beijing, and Guangzhou) were used for the tests, and the best MAPE in their prediction results were 2.78%, 3.43%, 5.61%, 3.63% and 2.31% respectively.

Multi-rule combination prediction of compositional data time series based on multivariate fuzzy time series model and its application

Compositional data (CoDa) is a type of relative data reflecting the proportion of different units in an integrated system, which can reveal the internal structure of observed objects and has been widely used to analyze practical economic and management problems. However, the summation constraint limits the prediction of compositional data time series. Especially, with small samples and poor information characteristics of the data set, the difficulties are further exacerbated. Compared with real-valued time series analysis, fuzzy time series (FTS) mainly transforms initial observed data to be different status so that the historical evolution rules can be derived. As a result, forms of initial observed data can be concealed. Correspondingly, this paper aims to establish a multi-rule combination prediction of compositional data based on a multivariate fuzzy time series model, named GA-CoDa-MFTS. Firstly, with the interaction of components, the adjustment rules between components are explored by using the fuzzy logical relationship (FLR). Secondly, the Genetic algorithm (GA) is used to find the optimal weight of the predicted values under different rules and derive the combined predicted values. Finally, the prediction effectiveness of the model is verified by CRMSE and CMAPE through a numerical study.

A fuzzy time series forecasting model with both accuracy and interpretability is used to forecast wind power

Considering the current research focus on the interpretability and efficiency of wind speed prediction models, this research presents a novel prediction model for dynamic non-stationary fuzzy time series. The proposed model aims to effectively improve prediction accuracy and address the issues of low interpretability and excessive data preprocessing. Unlike existing mainstream hybrid systems for wind speed prediction, this model provides detailed explanations for almost every prediction step and eliminates the need for cumbersome data preprocessing steps. To improve the prediction accuracy of the proposed model, this research incorporates non-stationary sets to overcome the limitations of fuzzy time series in adapting to long-term changes. The developed algorithm, SFTSM, dynamically adjusts the fuzzy time series prediction to effectively address long-term prediction challenges. Furthermore, this study introduces an enhanced version of the artificial hummingbird algorithm, called SLG-AHA, to further improve the accuracy and stability of fuzzy time series prediction. Experimental results using data from the Shandong Penglai wind farm in China validate the effectiveness of the proposed model by showcasing its superior prediction accuracy and stability.

Complex multidimensional fuzzy models of monitoring and rehabilitation processes for patients with uneven observation interval

Purpose. The work is devoted to the development of mathematical models and methods of fuzzy modeling of multidimensional time series (CDM) for the processes of monitoring and rehabilitation of patients with uneven intervals between observations. CDM takes into account the system properties and unity of the components of the studied processes by forming combined/complex multidimensional fuzzy models (CFTS). Methodology. The implementation of CFTS models takes into account the intrinsic features of these processes. The peculiarity of CFTS is that uneven intervals of observations, as well as other parameters, reflect the systemic unity of the controlled process, rather than the externally established form of observations, regulations. SFTS generalize models of multidimensional fuzzy time series of order n with m input parameters and one output parameter, i.e., different components may have different order of prehistory n, individual parameters may be measured by different types of data and forms of uncertainty. Findings. The article presents a comprehensive improved structure of CFTS models of order n with m input and one output parameter, which is adapted to the properties of monitoring and rehabilitation processes with uneven observation intervals. To form the SFTS, a step-by-step procedure is proposed that allows forming the composition of parameters. An example of modeling the process of rehabilitation of patients with diabetes based on the SFTS is presented, which demonstrates its differences and effectiveness. The comparative properties of SFTS and FTS models are presented. Originality. The development of CDM models and methods for monitoring and rehabilitation processes at uneven intervals is obtained, and complex SFTS models are formed. The difference between the SFTS is that the component of uneven intervals is represented as other multiparameters m, which can have different order of prehistory n, as well as different types of data and forms of uncertainty. A procedure for the step-by-step formation of the composition of the parameters of SFTS models is proposed. Practical value. SFTS models ensure the implementation of multiparameter monitoring and rehabilitation processes with uneven observation intervals, simplify the structure and reduce the number of relational relations, and eliminate the conflict of product rules in case of ensuring the required accuracy of results. The example of modeling the rehabilitation process for diabetics with such parameters as sugar level, interval between observations, and blood pressure has confirmed the reliability and practical significance of CFTS models.

Bayesian network based probabilistic weighted high-order fuzzy time series forecasting

The present article proposes a probabilistic weighted high-order fuzzy time series (FTS) forecasting model employing Bayesian network (BN) to address complex relationships and uncertainty hidden in time series. As considerable FTS forecasting models considers the fuzzy relationships between precedent moments and the consequent moment as the complex relationships in time series, BN structure learning is utilized to discover and model dependence relationships between each moment in time series. The combination of the fuzzy relationships modeled by fuzzy logical relationships and the dependence relationships modeled by the BN provides a comprehensive establishment and representation of the complex relationships inherent in time series data. The proposed FTS forecasting method calculates the fuzzy-probabilistic weights of each fuzzy logical relationship group using the improved fuzzy empirical probabilities to model both aleatoric and epistemic uncertainty in time series. To this end, the improved fuzzy empirical probabilities are formulated by integrating fuzzy empirical probabilities with the BN to incorporate dependence relationships from the original time series into the FTS forecasting procedure. The efficiency of the proposed forecasting model is validated on fourteen publicly available time series. Experimental results confirm the better performance of the proposed method comparing with nine existing FTS models and six numeric models. Hypothesis tests also validate the robustness and reliability of the proposed method.

Comparison of the Chen and Sinsgh’s Fuzzy Time Series Methods in Forecasting Farmer Exchange Rates in Indonesia

Chen and Singh's Fuzzy Time Series Model is a forecasting method that uses the basi fuzzy logic in the process. The differences in the models are in the fuzzy logic relations. Chen's model uses Fuzzy Logical Relationship Groups. Meanwhile, the Singh model uses only Fuzzy Logical Relationships in the forecasting process. To find out the best model between the two models, forecasting the Farmer's Exchange Rate is carried out. Farmers' exchange rates are the option for observers of agricultural development in assessing the level of welfare of farmers in Indonesia. With changes in farmer exchange rates every month, it is necessary to forecast data in order to obtain an overview for the following month. Research used is applied research where the initial step is to study and analyze the theories related to our research, then colect the necessary data. The data used is data secondary data obtained online from the official website of the Badan Pusat Statistika (BPS). the forecasting results of the two models were compared using MAPE. The results of the comparison of the accuracy of the prediction accuracy of Chen and Singh's fuzzy time series models on farmers' exchange rates obtained Chen's MAPE fuzzy time series values ​​of 0.679% and Singh's fuzzy time series models of 0.354%. This means that the best forecasting model for farmer exchange rates in Indonesia is the Singh model.

Comparison of Gold Price Prediction Techniques Using Long Short Term Memory (LSTM) And Fuzzy Time Series (FTS) Method

Gold is a precious metal that has economic value and is often used as an investment tool. The demand for gold from day to day is increasing, because many know and think that gold can be used as ownership in the form of investment assets that have low risk. Therefore, it is necessary to predict the gold price to avoid losses. This study aims to predict the gold price using a machine learning architecture including deep learning, namely Long Short Term Memory (LSTM) and Fuzzy Time Series (FTS). Several trial processes were carried out in the training process and predict the LSTM and FTS models to get the best results. The data used in this experiment is real data from the period 15 September 2016 – 15 September 2021. The final results obtained from the LSTM method have an RMSE value of training data of 391.95 RMSE, and a value of test data 412.36 RMSE, and the FTS method has an RMSE value of 10449.115791541652

Forecasting of daily new lumpy skin disease cases in Thailand at different stages of the epidemic using fuzzy logic time series, NNAR, and ARIMA methods.

Lumpy skin disease (LSD) is an important transboundary disease affecting cattle in numerous countries in various continents. In Thailand, LSD is regarded as a serious threat to the cattle industry. Disease forecasting can assist authorities in formulating prevention and control policies. Therefore, the objective of this study was to compare the performance of time series models in forecasting a potential LSD epidemic in Thailand using nationwide data. For the forecasting of daily new cases, fuzzy time series (FTS), neural network auto-regressive (NNAR), and auto-regressive integrated moving average (ARIMA) models were applied to various datasets representing the different stages of the epidemic. Non-overlapping sliding and expanding window approaches were also employed to train the forecasting models. The results showed that the FTS outperformed other models in five of the seven validation datasets based on various error metrics. The predictive performance of the NNAR and ARIMA models was comparable, with NNAR outperforming ARIMA in some datasets and vice versa. Furthermore, the performance of models built from sliding and expanding window techniques was different. This is the first study to compare the forecasting abilities of the FTS, NNAR, and ARIMA models across multiple phases of the LSD epidemic. Livestock authorities and decision-makers may incorporate the forecasting techniques demonstrated herein into the LSD surveillance system to enhance its functionality and utility.

A Three-Stage Nonparametric Kernel-Based Time Series Model Based on Fuzzy Data

In this paper, a nonlinear time series model is developed for the case when the underlying time series data are reported by LR fuzzy numbers. To this end, we present a three-stage nonparametric kernel-based estimation procedure for the center as well as the left and right spreads of the unknown nonlinear fuzzy smooth function. In each stage, the nonparametric Nadaraya–Watson estimator is used to evaluate the center and the spreads of the fuzzy smooth function. A hybrid algorithm is proposed to estimate the unknown optimal bandwidths and autoregressive order simultaneously. Various goodness-of-fit measures are utilized for performance assessment of the fuzzy nonlinear kernel-based time series model and for comparative analysis. The practical applicability and superiority of the novel approach in comparison with further fuzzy time series models are demonstrated via a simulation study and some real-life applications.

Forecasting Using Point-valued Time Series and Fuzzy-valued Time Series Models

The point-valued time series (PTS) is simply about one value in each time or period of the data, but when the data have two values at each time, the suitable time series is called the interval-valued time series (ITS). An example of ITS is the daily close and open stock prices. If the time series data are of typed linguistic data, for example, “low increase”, “medium increase” and “high increase”, the time series data are called a fuzzy-valued time series or being well-known as fuzzy time series (FTS). The aim of this study is to compare the PTS and FTS models for forecasting stock prices in the stock market. The stock market is one of the essential investments in the economy. The movement of stock price can be leading or declining which respectively expands or contracts a country’s economy. The movement may also represent the scenario or event happening in a company. Therefore, forecasting stock price movement is highly important since it will assist investors and sellers to make planning in their investment’s decision. Therefore, the objectives of this study are to identify the best forecasting models in point-valued time series (PTS) and fuzzy time series (FTS) based on forecasting measurement error. Eight stock price forecasting models consisting of four models from PTS and four models from FTS. Meanwhile, four forecasting measurement errors were discussed in the analysis as a criterion for choosing the best forecasting model. A set of daily historical data from the Bursa Malaysia website was used as a basis for analysis. The finding shows the simple exponential smoothing model is the best PTS model. In the meantime, the Cheng model based on Sturges’ rule is the best FTS model. However, among these two types of models, the Cheng model is found to be the best model with forecasting measurement errors of 0.0001 (MSFE), 0.0108 (RMSFE) and 1.1918 (MAPFE). The results reveal that besides the PTS model, the FTS model is an alternative model to forecast stock market movement. Moreover, these FTS and PTS models can also be applied to solving other forecasting problems.

Renewable energy generation forecasting in Turkey via intuitionistic fuzzy time series approach

Recently, renewable energy generation (REG) forecasting has become a challenging task for effective energy management. To date, a number of time-series models utilizing physical models, statistical techniques, and artificial intelligence algorithms have been proposed to deal with this problem. Fuzzy time series (FTS) models stand out among these methods since they do not need extensive historical data or some statistical assumptions like the normal distribution. Because intuitionistic fuzzy sets incorporate non-membership values in addition to membership values, they provide more information than conventional fuzzy sets do. In this regard, this paper recommends a hybrid methodology that combines the intuitionistic FTS method with the intuitionistic fuzzy c-means method for REG forecasting of Turkey between the years 2000–2020. According to the empirical results, it can be concluded that the presented integrated model showed good performance in terms of accuracy. The suggested framework is a useful tool not only for REG forecasting but also for other time series forecasting problems.

Comparison Fuzzy Time Series Cheng and Ruey Chyn Tsaur Model for Forecasting Sales at Empat Saudara Store

Trading business is a type of business that focuses on buying goods and reselling them with the aim of making a profit without making changes to the condition of the goods being sold. The problem that often occurs at the Empat Saudara Store is excess or deficiency in the stock of goods owned, where consumer demand is high but goods are insufficient and consumer demand is low but goods are available. One effort to overcome these problems is to make stable sales happen by forecasting to find out future sales. Forecasting is an activity that aims to estimate or predict what will happen in the future by using historical data from the past. The research method used is Fuzzy Time Series (FTS) because this method's forecasting system is to capture patterns from past data and then use it to project future data based on linguistic values. FTS models used are FTS Cheng and FTS Ruey Chyn Tsaur. The five-period forecasting results for FTS Cheng are 200,668.2 , 171,761.5 , 222,412.6 , 214,507.4 , 216,294.3 and for the FTS Ruey Chyn Tsaur model are 198,600 , 229,094.2 , 202,203.05, 230,804.80 ,6. With a MAPE value of the FTS Cheng model of 9.904% and a MAPE value of the FTS Ruey Chyn Tsaur model of 14.01%. From the forecasting results it can be concluded that the FTS Cheng model is better than the FTS Ruey Chyn Tsaur model in predicting sales at the Empat Saudara Store.

Application of the Average Based Fuzzy Time Series Model in Predictions Seeing the Use of Travo Substations

PT PLN expects the delivery of information quickly in predicting the capacity of transformer substations in each region in view of population growth in industrial areas. Unbalanced and overloaded electricity that is not suitable for the capacity of the transformer substation so that the results of this study are more optimal in predicting the usage load at the transformer substation using the methodaverage based fuzzy time series. The application of this method can provide fast and accurate information in accordance with consumer expectations in predicting each need in each area and the number of managed substations. The capacity of the substation can be seen in 1 phase and 3 phase with the percentage of loading quickly and precisely with the current transformer card system. The purpose of the transformer distribution in this study is to look at reducing high voltage to low voltage, so that the voltage used is in accordance with the customer's electrical equipment rating or the load rating used by all consumers in each region. The research methodology is to determine the placement of distribution transformer locations that are not suitable which can affect the end voltage drop on consumers or the drop/drop in consumer line end voltage and view complete data from the specifications of the distribution transformers along with the locations of distribution transformers that can be managed through Development of a mobile device-based Distribution Transformer Recording System at PT PLN. The results of this study in transformer power 100 consumption 99.43, unbalanced 28%, fuzzification A8, FLRG G8, forecasting results 10.69 with a Mape forecast value of 0.57%. Furthermore, power consumption of transformer 50 is 36.70, unbalanced 78%, fuzzification A6, FLRG G6, forecasting results 23.91 with Mape 1.11%. Results with the smallest mape with each travo travo 50 in each usage area 28.43, unbalanced 26%, fuzzification A5, FLRG G5, forecasting results 23.91 with Mape 0.28%. The results of this study can determine the location of the transformer along with unbalance, overload and the estimated amount of power consumption load for the use of transformer substations in an area, especially the ULP PT.PLN area for each region in PT.PLN (Persero) Krueng Geukuh. Then the results of this study can be used as a reference for monitoring population growth with excessive transformer power loads (overload) so that later you can install new transformer substations with a capacity according to the number of customers

Chen’s model to understand the invariant fuzzy time series model through maize production in India

The present study has applied a time-invariant fuzzy time series model for maize Production in India. Most of the time series data is forecasted using AR and ARIMA models but the present study considered the Chen fuzzy time series model to understand fuzzy time series and endeavour to forecast. Generally, fuzzy models are based on uncertainty, non-probabilistic and linguistic variables. The maize production of India during 1951-2020 data was divided into seven subsets. The subsets are equal intervals. Chen's model has used arithmetic operations for fuzzy logic relations and forecasting. The accuracy of the model was measured by Root Mean Square Error (1949.93) and Mean Absolute Percentage Error (25.86). The Chen model will give impetus to the higher-order fuzzy time series model.

Automatic Clustering and Fuzzy Logical Relationship to Predict the Volume of Indonesia Natural Rubber Export

Natural rubber is one of the pillars of Indonesia's export commodities. However, over the last few years, the export value of natural rubber has decreased due to an oversupply of this commodity in the global market. To overcome this problem, it is possible to predict the volume of Indonesia natural rubber exports. Predicted values can also help the government to compile market intelligence for natural rubber commodities periodically. In this study, the prediction of the export volume of natural rubber was carried out using the Automatic Clustering as an interval maker in the Fuzzy Time Series or usually called Automatic Clustering and Fuzzy Logical Relationship (ACFLR). The data used is 51 data per year from 1970 to 2020. The purpose of this study is to predict the volume of Indonesia natural rubber exports and compare the prediction results between the Automatic Clustering and Fuzzy Logical Relationship (ACFLR) and Chen's Fuzzy Time Series. The results showed that there was a significant difference between the two methods, ACFLR got 0.5316% MAPE with and Chen's Fuzzy Time Series model got 8.009%. Show that the ACFLR method performs better than the pure Fuzzy Time Series in predicting volume of Indonesia natural rubber exports.

Establishing the Forecasting Model with Time Series Data Based on Graph and Particle Swarm Optimization

In recent years, a wide variety of fuzzy time series (FTS) forecasting models have been created and recommended to handle the complicated and ambiguous challenges relating to time series data from real-world sources. However, the accuracy of a model is problem-specific and varies across data sets. But a model's precision varies between different data sets and depends on the situation at hand. Even though many models assert that they are better than statistics and a single machine learning-based model, increasing forecasting accuracy is still a challenging task. In the fuzzy time series models, the size of the intervals and the fuzzy relationship groups are thought to be crucial variables that affect the model's forecasting abilities. This study offers a hybrid FTS forecasting model that makes use of both the graph-based clustering technique (GBC) and particle swarm optimization (PSO) for adjusting interval lengths in the universe of discourse (UoD). The suggested model's forecasting results have been compared to those provided by other current models on a dataset of enrollments at the University of Alabama. For all orders of fuzzy relationships, the suggested model outperforms its counterparts in terms of forecasting accuracy.

Establishing the Forecasting Model with Time Series Data Based on Graph and Particle Swarm Optimization

In recent years, a wide variety of fuzzy time series (FTS) forecasting models have been created and recommended to handle the complicated and ambiguous challenges relating to time series data from real-world sources. However, the accuracy of a model is problem-specific and varies across data sets. But a model’s precision varies between different data sets and depends on the situation at hand. Even though many models assert that they are better than statistics and a single machine learning-based model, increasing forecasting accuracy is still a challenging task. In the fuzzy time series models, the size of the intervals and the fuzzy relationship groups are thought to be crucial variables that affect the model’s forecasting abilities. This study offers a hybrid FTS forecasting model that makes use of both the graph-based clustering technique (GBC) and particle swarm optimization (PSO) for adjusting interval lengths in the universe of discourse (UoD). The suggested model’s forecasting results have been compared to those provided by other current models on a dataset of enrollments at the University of Alabama. For all orders of fuzzy relationships, the suggested model outperforms its counterparts in terms of forecasting accuracy.

The Application Of Multi-Sensor Data Fusion Method with Fuzzy Time Series Model to Improve Indoor Water Prediction Accuracy Quality

There is a lot of indoor air pollution, especially from cigarette smoke, wall paint, air fresheners and gas. With this situation, the room uses Air Box WP6003 air quality detection device by transmitting information about air quality through visualization index. This study aims to improve prediction accuracy with fuzzy time series methods processed through 2 naïve and moving average models using forecast transformers and without transformers. The level of prediction accuracy is calculated through several metrics, namely Mean Absolute Percentage Error (MAPE), Sum of Squares Error (SSE), Mean Square Error (MSE), Root Mean Square Error (RMSE) and Mean Absolute Error (MAE). These results can be calculated between the actual value and the predicted value. The data used is 204584 data from 4 parameters including Temperature, TVOC, HCHO and CO2. The test results with the difference from the forecast transformer and without transformer are comparable. Temperature value obtained using naïve with transformer from RMSE of 0.158866 and naïve without transformer of 0.782397, data using moving average with transformer obtained by 0.147546 and moving average without transformer of 0.772570. This can be explained by the error analysis that was tried, where the error rate continued to increase so that the experimental results continued to be far from the actual number. From the test results it can be concluded that the accuracy of air quality prediction using naïve forecast transformer is pretty accurate.

Combining embeddings and fuzzy time series for high-dimensional time series forecasting in internet of energy applications

High-dimensional time series increasingly arise in the Internet of Energy (IoE), given the use of multi-sensor environments and the two way communication between energy consumers and the smart grid. Therefore, methods that are capable of computing high-dimensional time series are of great value in smart building and IoE applications. Fuzzy Time Series (FTS) models stand out as data-driven non-parametric models of easy implementation and high accuracy. Unfortunately, the existing FTS models can be unfeasible if all variables were used to train the model. We present a new methodology named Embedding Fuzzy Time Series (EFTS), by applying a combination of data embedding transformation and FTS methods. The EFTS is an explainable and data-driven approach, which is flexible and adaptable for many smart building and IoE applications. The experimental results with three public datasets show that our methodology outperforms several machine learning based forecasting methods (LSTM, GRU, TCN, RNN, MLP and GBM), and demonstrates the accuracy and parsimony of the EFTS in comparison to the baseline methods and the results previously published in the literature, showing an enhancement greater than 80%. Therefore, EFTS has a great value in high-dimensional time series forecasting in IoE applications.

Forecasting Shallot Prices in West Sumatra Province Using the Fuzzy Time Series Method of the Singh Model and the Cheng Model

Shallots are one of the leading spices that are widely used by humans as food seasoning and traditional medicine. The price of shallots always fluctuates which can affect the buying and selling of consumers and producers. Therefore, forecasting is used as a reference to be able to predict the price of shallots in the future and can provide convenience to the public for the condition of shallot prices in the next period. The forecasting method used is the fuzzy time series (FTS) method. FTS is a method whose forecasting uses data in the form of fuzzy sets sourced from real numbers to the universe set on actual data. Forecasting models used in this study are Singh's FTS model and Cheng's model. The data used is monthly data on shallot prices in West Sumatra Province for the period January 2018 to March 2022. The results obtained in this forecast are the Singh model FTS has a smaller MAPE value of 4.41% with a forecasting accuracy value of 95.59 %. This means that Singh's FTS model is better at predicting the price of shallots in West Sumatra Province.