Papers by Gholamreza Hesamian
Mathematics, Sep 21, 2023
In this paper, an exponential autoregressive model for complex time series data is presented. As ... more In this paper, an exponential autoregressive model for complex time series data is presented. As for estimating the parameters of this nonlinear model, a three-step procedure based on quantile methods is proposed. This quantile-based estimation technique has the benefit of being more robust compared to least/absolute squares. The performance of the introduced exponential autoregressive model is evaluated by means of four established goodness-of-fit criteria. The practical utility of the novel time series model is showcased through a comparative analysis involving simulation studies and real-world data illustrations.
Fuzzy Statistical Inferences Based on Fuzzy Random Variables, 2022
Control and Cybernetics, 2017
Iranian Journal of Fuzzy Systems, Aug 13, 2021
Parametric time series models typically consists of model identification, parameter estimation, m... more 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 providea 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-basedsmoothing 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.
Mathematics
In this paper, a nonlinear time series model is developed for the case when the underlying time s... more 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.
Journal of Computational and Applied Mathematics
Fuzzy Information and Engineering, Mar 1, 2023
During the last decades, several methods have been proposed for Kolmogorov−Smirnov one-sample tes... more During the last decades, several methods have been proposed for Kolmogorov−Smirnov one-sample test based on fuzzy random variables to describe the impression of classical random variables. However, such techniques do not discuss the modeling of imprecise observations and simulation of such data from the distribution of a fuzzy random variable. Moreover, such methods rely on a fuzzy cumulative distribution function with known parameters. In this paper, however, a modified Kolmogorov−Smirnov one-sample test is introduced based on a novel notion of fuzzy random variables which comes down to model fuzziness and randomness in the distribution of population in a frequently used family of probability distributions called location and scale distribution functions. A method of moment estimator was also utilized to estimate the location and scale parameters. Then, a notion of non-fuzzy Kolmogorov−Smirnov one-sample test was developed based on fuzzy hypotheses. Monte Carlo simulation was also employed to evaluate the critical value corresponding to a significance level and the performance of the test using power studies. Comparing the observed test statistics and the given fuzzy significance level, a classical procedure was finally used to accept or reject the null fuzzy hypothesis. Two numerical examples including a simulation study and an applied example were provided to clarify the discussions in this paper. The proposed method was also compared with some existing methods. The goodness-of-fit results demonstrated that the proposed Kolmogorov−Smirnov provides an efficient tool to handle statistical inference fuzzy observations.
Soft Computing, Oct 14, 2020
In this paper, a fuzzy nonlinear univariate regression model with nonfuzzy predictors and fuzzy r... more In this paper, a fuzzy nonlinear univariate regression model with nonfuzzy predictors and fuzzy responses is proposed. For this purpose, both nonlinear parametric and nonparametric methods were utilized. The left and right spreads of unknown fuzzy smooth function were estimated via a popular kernel-based curve-fitting method, while the center was estimated using both parametric and nonparametric curve-fitting methods. In fact, two techniques were suggested and compared in terms of estimating the center of fuzzy smooth function: (1) nonparametric method (similar to the left and right spreads) and (2) parametric method adopted with a common nonlinear regression model called truncated spline regression. Each stage was separately estimated the unknown components were addressed via the conventional statistical regression methods. The proposed method managed to provide a simple and fast estimation/prediction approach for the fuzzy univariate regression analysis for any types of L R-fuzzy numbers. Some common goodness-of-fit criteria were also employed to evaluate the performance of the proposed method. The effectiveness of the developed method was further illustrated through three numerical examples including a simulation study based on a common kernel. The proposed method was also compared with several common fuzzy linear/nonlinear regression models. The numerical evaluations indicated that the proposed parametric method for centers exhibited more accurate results as compared with the nonparametric method. Keywords Fuzzy data • Nonlinear • Goodness-of-fit measure • Spline • Kernel fitting 1 Introduction Regression analysis is a powerful tool for the prediction of the unknown values of the response variables from the known predictors. In real-life problems, such a relationship is usually unknown but can be estimated from a series of observations. Regression-based methods can be classified into linear (including parametric) (
International Journal of Fuzzy Systems, Mar 15, 2019
Exponentially weighted moving average (EWMA) chart is an alternative to Shewhart control charts a... more Exponentially weighted moving average (EWMA) chart is an alternative to Shewhart control charts and can serve as an effective tool for detection of shifts in small persistent process. Notably, existing methods rely on induced imprecise observations of a normal distribution with fuzzy mean and variance. Such techniques did not investigate the statistical properties relevant to a fuzzy EWMA. To overcome this shortcoming, employing a common notion of normal fuzzy random variable with fuzzy mean and non-fuzzy variance could be helpful. This paper first developed a notion of fuzzy EWMA statistic as a natural extension to the classical counterpart. Then, the concept of fuzzy EWMA control limit was introduced and discussed in cases where fuzzy mean and/or non-fuzzy variance was unknown parameters. A degree of violence was also employed to monitor the proposed fuzzy EWMA control chart. Potential applications of the proposed fuzzy EWMA chart were also demonstrated based on a real-life example. The advantages of the proposed method were also discussed in comparison with other existing fuzzy EWMA methods.
Soft Computing
Statistical inference is the process of drawing conclusions about underlying population(s) using ... more Statistical inference is the process of drawing conclusions about underlying population(s) using sample data to either confirm or falsify hypotheses. However, the complexity of real-life problems often makes the underlying statistical models inadequate, as information is often imprecise in many respects. To address this common problem, some papers have been published on modifications and extensions of test concepts by employing tools of fuzzy statistics. In this paper, we present a non-parametric test for the difference between quantiles of two independent populations based on fuzzy random variables. For this purpose, we consider the fuzzy quantile function and its estimation based on $$\alpha $$ α -values of fuzzy random variables. We then provide a fuzzy test based on the fuzzy empirical distribution function for the difference of fuzzy order statistics from these independent populations. We also suggest a specific degree-based criterion to compare the fuzzy test statistics at a s...
Artificial Intelligence Review
Computational and Applied Mathematics
Fuzzy Statistical Inferences Based on Fuzzy Random Variables, 2022
Fuzzy Statistical Inferences Based on Fuzzy Random Variables, 2022
Computational & Applied Mathematics, Aug 18, 2022
Computational and Applied Mathematics
Journal of Advanced Mathematical Modeling, Sep 23, 2021
In this paper, a nonparametric time series model based on fuzzy observations is presented. Fuzzy ... more In this paper, a nonparametric time series model based on fuzzy observations is presented. Fuzzy prediction values are estimated using the generalization of the Nadaraya-Watson method in fuzzy environment. An algorithm for achieving autoregressive order and optimal bandwidth is stated and then criteria are introduced to evaluate the predicted values. In the following the performance of the proposed model is examined and analyzed using real data. The effectiveness of the proposed model is also compared with the other time series models with fuzzy data.
Parametric time series models typically consists of model identification, parameter estimation, m... more 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...
Fuzzy Statistical Inferences Based on Fuzzy Random Variables, 2022
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Papers by Gholamreza Hesamian