فهرست مطالب jalal chachi

In this article, the hypothesis test and confidence interval for the fuzzy coefficients in the fuzzy weighted regression model with precise inputs and fuzzy outputs are discussed. By applying the weighted estimation method in estimating the coefficients and using the conventional fuzzy hypotheses in the fuzzy environment,, We are trying to determine the distribution of the available estimators, based on the bootstrap method so that we can decide to accept or reject the existing hypotheses. Therefore, at first, the required test statistics are calculated based on the bootstrap method. Then, by comparing the probability value and the given significance level, as in the classical method, the null hypothesis is accepted or rejected. Also, from another point of view, hypothesis testing based on bootstrap confidence intervals is also discussed. At the end, by analyzing a practical example with real data in housing, the approach investigated in hypothesis testing and confidence interval for the coefficients of the fuzzy regression model has been analyzed.

In this regard, in the framework of deep learning and based on inaccurate information obtained from images of retinal layers, an end-to-end network has been trained to analyze and segment retinal layers. The result of this study is the introduction of a kit that can be installed on smartphones, which can be used to easily and simply monitor users' vision.The input of this structure is OCT images of the eye, without the need to extract hand-crafted features as input from the image, and its output is accurate spatial information of the retinal layers. The time required for each scan of OCT input images in this kit is about 10ms, which makes it possible to use such kits in a variety of smartphones easily. This kit, which assesses the health of ocular arteries, is inexpensive and can be used for remote locations or people who are not able to visit specialized eye centers or need frequent and continuous monitoring of their eye health. The ranking results presented in the present article show that the proposed structure has an acceptable performance and is very close to the average opinions of the group of specialist ophthalmologists. The results of evaluations and comparisons are made within the framework of multi-criteria decision-making approach. In order to extract the results in this framework, the TOPSIS algorithm is used in which the weights of the indicators are determined based on the entropy size.

Today, various models with different estimation methods are introduced and used in data modeling. The appropriateness of each method of estimating statistical models in the fit of a dataset is based on a specific goodness-of-fit criterion (or a specific objective function). Also, the goodness-of-fit index of any statistical model (including classical or fuzzy regression models) is defined and formulated according to the structure of that model. Therefore, using and applying only one criterion to compare the goodness-of-fit of a diverse set of statistical models leads to oblique/biased and directional decisions. In fact, such a process leads to prioritization of the models that their objective functions are the same as the evaluation criterion and/or their objective functions are structurally proportional to the evaluation criteria. Therefore, considering only one-criterion to evaluate the goodness-of-fit of the models deprives them of the possibility of a fair and equitable comparison, which is very challenging. Our main goal in this paper is to provide and propose an appropriate framework in the context of multi-criteria decision making to overcome the challenge. In this method, it is possible to aggregate a wide range of evaluation criteria from different point of views to generate a generalized evaluation criterion in order to identify the optimal model.Finally, the proposed approach is employed to rank the fit of 22 different fuzzy regression models.

This article introduces a new method to estimate the least absolutes linear regression modelchr('39')s parameters, which considers optimization problems based on the weighted aggregation operators of ordered least absolute deviations. In the optimization problem, weighted aggregation of orderd fitted least absolute deviations provides data analysis to identify the outliers while considering different fitting functions simultaneously in the modeling problem. Accordingly, this approach is not affected by outlier observations and in any problem proportional to the number of potential outliers selects the best model estimator with the optimal break-down point among a set of other candidate estimators. The performance and the goodness-of-fit of the proposed approach are investigated, analyzed and compared in modeling analytical dataset and a real value dataset in hydrology engineering at the presence of outliers. Based on the results of the sensitivity analysis, the properties of unbiasedness and efficiency of the estimators are obtained.

A novel approach is proposed for the problem of testing statistical hypotheses about the fuzzy mean of a fuzzy random variable.The concept of the (uniformly) most powerful test is extended to the (uniformly) most powerful fuzzy-valued test in which the test function is a fuzzy set representing the degrees of rejection and acceptance of the hypothesis of interest.For this purpose, the concepts of fuzzy test statistic and fuzzy critical value have been defined using the $\alpha$ cuts (levels) of the fuzzy observations and fuzzy parameter.In order to make a decision as a fuzzy test, a well-known method is employed to compare the observed fuzzy test statistic and the fuzzy critical value.In this work, we focus on the case in which the fuzzy data are observations of a normal fuzzy random variable.The proposed approach is general so that it can be applied to other kinds of fuzzy random variables as well.Numerical examples, including a lifetime testing problem, are provided to illustrate the proposed optimal tests

Estimation methods of parameters of fuzzy least-squares regression have very sensitivity to unusual data (e.g. outliers). In the presence of outliers, most of the existing estimation methods of parameters of this kind of models using least-squares approach provide unexpected and unreliable estimators with amounts of errors. Therefore, in this paper a robust least trimmed squares fuzzy regression model is described for modeling for crisp input-fuzzy output variables. In this approach, the constructed target function in model parameter estimation problem in such a way which minimizes the sum of the smallest squared residuals. This method has an algorithm that estimates the optimal values of the parameters based on different selected combinations of good observations of the data set of size . Therefore, this method has the ability of reducing the effects of such a data in estimation of the parameters of the model. Finally, the investigated fuzzy regression model is applied and studied to modeling real-world data set in hydrology which sometimes contains outlier points. In this regard, a comparison study between the proposed method and ordinary least squares fuzzy regression method is considered. The comparison results of the applied study reveal that for this particular data set the proposed method performs better fitting than the well-known ordinary fuzzy least-squares regression model. Also the proposed method identified the points that have bad effect on estimation problem of the parameters.

Using the generalized Hausdorff-metric, two least-absolutes (LA) approaches to multiple fuzzy regression modeling are introduced for the case of crisp input-fuzzy output data. The main advantage of the proposed models is that they are not so sensitive to the outlier data points. The proposed models as well as two common fuzzy least-squares (LS) models are employed in a case study to estimate imperfections of cotton yarn using fiber properties in a reallife data. In order to derive the fuzzy regression models between imperfections of cotton yarn and fiber properties, first, effective variables are selected by the statistical stepwise test. Then, four fuzzy models, including two new LA models and two LS models, are sought to fit the data set.
Finally, two criteria are employed to evaluate the goodness-of-fit of models. Moreover, a predictive ability index is introduced and employed to evaluate the predictability of the models. Using these criteria, a comparative study between the proposed fuzzy least-absolutes regression models and fuzzy least-squares regression models has also been addressed. The comparison results reveal that the LA-fuzzy models perform better than the LS-fuzzy models in imperfections of cotton yarn estimation for the particular data set used in this study.

Robust linear regression is one of the most popular problems in the robust statistics community. The parameters of this method are often estimated via least trimmed squares, which minimizes the sum of the k smallest squared residuals. So, the estimation method in contrast to the common least squares estimation method is very computationally expensive. The main idea of this paper is to propose a new estimation method in partial linear models based on minimizing the sum of the k smallest squared residuals which determines the set of outlier point and provides robust estimators. In this regard, first, difference based method in estimation parameters of partial linear models is introduced. Then the method of obtaining robust difference based estimators in partial linear models is introduced which is based on solving an optimization problem minimizing the sum of the k smallest squared residuals. This method can identify outliers. The simulated example and applied numerical example with real data found the proposed robust difference based estimators in the paper produce highly accurate results in compare to the common difference based estimators in partial linear models.

A novel approach to the problem of regression modeling for fuzzy input-output data is introduced.
In order to estimate the parameters of the model, a distance on the space of interval-valued quantities is employed.
By minimizing the sum of squared errors, a class of regression models is derived based on the interval-valued data obtained from the $alpha$-level sets of fuzzy input-output data.
Then, by integrating the obtained parameters of the interval-valued regression models, the optimal values of parameters for the main fuzzy regression model are estimated.
Numerical examples and comparison studies are given to clarify the proposed procedure, and to show the performance of the proposed procedure with respect to some common methods.

The problem of testing fuzzy hypotheses in the presence of vague data is considered. A new method based on the necessity index of strict dominance (NSD) is suggested. An example hoe to apply the proposed test in statistical quality control is shown.

In this paper، we deal with modeling crisp input-fuzzy output data by constructing a MARS-fuzzy regression model with crisp parameters estimation and fuzzy error terms for the fuzzy data set. The proposed method is a two-phase procedure which applies the MARS technique at phase one and an optimization problem at phase two to estimate the center and fuzziness of the response variable. A realistic application of the proposed method is also presented in a hydrology engineering problem. Empirical results demonstrate that the proposed approach is more efficient and more realistic than some traditional least-squares fuzzy regression models.