In this paper, we propose a new residual analysis method using Fourier SERIES transform into FUZZY TIME SERIES model for improving the forecast- ing performance. This hybrid model takes advantage of the high predictable power of FUZZY TIME SERIES model and Fourier SERIES transform to t the esti- mated residuals into frequency spectra, select the low-frequency terms, lter out high-frequency terms, and then have well forecasting performance. Two numerical examples are given to show that our proposed model can be applied with the best forecasting performance than the other models.

Parametric TIME SERIES models typically consists of model identification, parameter estimation, model diagnostic checking, and forecasting. However compared with parametric methods, nonparametric TIME SERIES models often provide a very flexible approach to bring out the features of the observed TIME SERIES. This paper suggested a novel FUZZY nonparametric method in TIME SERIES models with FUZZY observations. For this purpose, a FUZZY forward fit kernel-based smoothing method was introduced to estimate FUZZY smooth functions corresponding to each observation. A simple optimization algorithm was also suggested to evaluate optimal bandwidths and autoregressive order. Several common goodness-of-fit criteria were also extended to compare the performance of the proposed FUZZY TIME SERIES method compared to other FUZZY TIME SERIES model based on FUZZY data. Furthermore, the effectiveness of the proposed method was illustrated through two numerical examples including a simulation study. The results indicate that the proposed model performs better than the previous ones in terms of both scatter plot criteria and goodness-of-fit evaluations.

FUZZY TIME SERIES Forecasting (TSF) is an approach for dealing with uncertainty in TIME SERIES data that uses FUZZY logic. The Hesitant FUZZY Set (HFS) theory better emphasizes the chances of capturing fuzziness and uncertainty due to randomness than the classic FUZZY set theory. This study aims to improve the previously identified hesitant FUZZY TSF models by including various degrees of hesitation to improve forecasting performance. The goal is to deal with the issue of identifying a common membership grade when several fuzzification methods are available to fuzzify TIME SERIES data. The proposed method utilizes trapezoidal and bell-shaped FUZZY membership functions for constructing HFSs. Ahesitant FUZZY weighted averaging operator is then applied to the Hesitant FUZZY Elements (HEFs) to create FUZZY logical relations. The suggested technique is employed to forecast enrollment in the University of Alabama and Cancer Incidence Rates (CIRs) in India. The efficiency of the proposed forecasting approach is determined by rigorously comparing it to various computational FUZZY TSF methods in terms of error measurements like Root Mean Square Error (RMSE), Average Forecasting Error (AFE), and Mean Absolute Deviation (Mad). The validity of the proposed forecasting model is verified by using correlation coefficients, coefficients of determination, Tracking Signals (TSs), and Performance Parameters (PPs). The significance of improved accuracy in forecasted results is also confirmed using the two-tailed t-test. The study results revealed that the enhanced hesitant FUZZY TIME SERIES (FTS) model is more effective and accurate in forecasting the university enrolment of Alabama and the CIRs of India.

This study proposes the model for interpolating TIME SERIES to use them to forecast effectively for future. This model is established based on the improved FUZZY clustering analysis problem, which is implemented by the Matlab procedure. The proposed model is illustrated by a data set and tested for many other datasets, especially for 3003 SERIES in M3-Competition data. Comparing to the existing models, the proposed model always gives the best result. We also apply the proposed model in forecasting the salt peak for a coastal province of Vietnam. Examples and applications show the potential of the studied problem.

Since the pioneering work of Zadeh, FUZZY set theory has been applied to a myriad of areas. Song and Chissom introduced the concept of FUZZY TIME SERIES and applied some methods to the enrolments of the University of Alabama. Thereafter we apply FUZZY techniques for system identification and apply statistical techniques to modelling system. An automatic methodology framework that combines FUZZY techniques and statistical techniques for nonparametric residual variance estimation is proposed. The methodology framework is creating regression model by using FUZZY techniques. Identification is performed through learning from examples method introduced by Wang and Mendel algorithm. Delta test residual noise estimation is used in order to select the best subset of inputs as well as the number of linguistic labels for the inputs. An experimental result for chaotic TIME SERIES prediction is compared with statistical model and shows the advantages of the proposed methodology in terms of approximation accuracy, generalization capability and linguistic interpretability.

The conventional FUZZY least-squares TIME SERIES models show undesirable performance when the FUZZY data set involves the outliers. By introducing a strategy to detect the outliers, this paper introduced a method for reducing the influence of outliers on the future predictions. For this purpose, according to the weighted square distance error, an estimation procedure was suggested for determining the exact coefficients in the presence of outliers. The parameters of the FUZZY TIME SERIES model were then estimated using an iterative algorithm. In order to identify the potential outliers of the FUZZY data, a  quality control chart was employed based on the center of gravity criterion of FUZZY data. The defuzzification method was also employed to examine the performance of the proposed method via some  scatter plots. Several common goodness-of-fit criteria used in traditional TIME SERIES models were also extended to compare the performance of the proposed FUZZY TIME SERIES method to an existing method. The effectiveness of the proposed method was illustrated through two numerical examples including a simulation study. The results clearly indicated that the proposed model performs well in terms of the both scatter plot criteria and goodness-of-fit evaluations in cases where the potential outliers exist among the FUZZY data.

Simulation of river flow in order to understand the river yield in the future is one of the important and practical issues in water resource management. In this study, monthly discharge of Taleghan river in Glinak stations at one step proceeding were forecasted using Artificial Intelligent (Artificial Neural Network MLP, ANFIS with Grid Partition and Subtractive Clustering) and TIME SERIES methods. Two inputs including raw discharge data and de-seasonalised discharge data were used for different models. For TIME SERIES models, ARIMA (3,0,0) (0,1,1) were selected as suitable model. The optimum structure in Artificial Intelligence method after pre-processing was determined using input and output data based on trial and error, and then, using the optimum structure, the streamflow discharge was forecasted. After the output of each single model was obtained, the structure of hybrid models were determined. The results showed hybrid methods 3 and 2 have the best application and TIME SERIES model has better results than Artificial Intelligent methods.

FUZZY TIME SERIES have been developed during the last decade to improve the forecast accuracy. Many algorithms have been applied in this approach of forecasting such as high order TIME invariant FUZZY TIME SERIES. In this paper, we present a hybrid algorithm to deal with the forecasting problem based on TIME variant FUZZY TIME SERIES and particle swarm optimization algorithm, as a highly efficient and a new evolutionary computation technique inspired by birds’ flight and communication behaviors. The proposed algorithm determines the length of each interval in the universe of discourse and degree of membership values, simultaneously. Two numerical data sets are selected to illustrate the proposed method and compare the forecasting accuracy with four FUZZY TIME SERIES methods. The results indicate that the proposed algorithm satisfactorily competes well with similar approaches.