In this article, an approach for fitting a FUZZY LINEAR REGRESSION model based on support vectors is presentedwhen the response variable, model parameters and errors are considered as FUZZY numbers.In this method, the objective function is based on the sum of the absolute values ​​of the distances of the hypothetical points to the non-parallel border hyperplanes. The presented model has good robustness to the presence of outlier data. The proposed model has been compared with some other models based on three goodness of fit indices.

REGRESSION is a statistical technique used in finance, investment, and several other domains to assess the magnitude and precision of the association between a dependent variable (often represented as Y) and a set of other factors (referred to as independent variables). This work introduces a LINEAR programming approach for constructing REGRESSION models for Neutrosophic data. To achieve this objective, we use the least absolute deviation approach to transform the REGRESSION issue into a LINEAR programming problem. Ultimately, the efficacy of the suggested approach in resolving such problems has been shown via the presentation of a concrete illustration.

Statistical REGRESSION analysis is a well-known method for formulating the relationship between the response variable (output) and some explanatory variables (input) using a set of observations based on the assumption of normal distributions. FUZZY LINEAR REGRESSION is the most fundamental method in the field of FUZZY modeling in which the uncertain relationship between target and explanatory variables is estimated, and it has been effectively used repeatedly in a wide variety of real-world applications. In this article, we examine the FUZZY REGRESSION model with the coefficients of Neutrosophic FUZZY numbers. For this, we first write a generalization of the measure of the Diamond distance for these numbers, and then estimate the parameters of the model, which are Neutrosophic triangular FUZZY numbers, using the least square method. We show and finally by citing an example, we express the application of the presented model.

This study is an investigation of FUZZY LINEAR REGRESSION model for crisp/FUZZY input and FUZZY output data. A least absolutes deviations approach to construct such a model is developed by introducing and applying a new metric on the space of FUZZY numbers. The proposed approach, which can deal with both symmetric and non-symmetric FUZZY observations, is compared with several existing models by three goodness of fit criteria. Three well-known data sets including two small data sets as well as a large data set are employed for such comparisons.

FUZZY LINEAR REGRESSION models are used to obtain an appropriate LINEAR relation between a dependent variable and several independent variables in a FUZZY environment. Several methods for evaluating FUZZY coefficients in LINEAR REGRESSION models have been proposed. The first attempts at estimating the parameters of a FUZZY REGRESSION model used mathematical programming methods. In this thesis, we generalize the metric defined by Diamond and use it as a criterion to estimate these parameters. Our method, is not only computationally easy to handle, but, when compared with earlier methods, has a smaller the sum of errors of estimation.

Under the additional assumption that the errors are normally distributed, the Ordinary Least Squares (OLS) method is the maximum likelihood estimator. In this paper, we propose, for a simple REGRESSION, an estimation method alternative to the OLS method based on a so-called Gaussian membership function, one that checks the validity of the verbal explanation suggested by the observer. The FUZZY estimation approach demonstrated here is based on a suitable framework for a natural behavior observed in nature. An application based on a group of MENA countries in 2015 is presented to estimate the employment poverty relationship.

In this paper, we introduce a new mathematical programming approach to estimate the parameters of FUZZY LINEAR REGRESSION with crisp/FUZZY input and FUZZY output. The advantage of this approach is, both of dependent and independent variables are influenced on the objective function. Therefore, this model rectifies some problems about outliers. Also, in this paper we use possibility function in constraints. To compare the performance of the proposed approach with previous methods, three examples are presented. 

The FUZZY LINEAR REGRESSION model with FUZZY input-output data and crisp coefficients is studied in this paper. A LINEAR programming model based on goal programming is proposed to calculate the REGRESSION coefficients. In contrast with most of the previous works, the proposed model takes into account the centers of FUZZY data’s an important feature as well as their spreads in the procedure of constructing the REGRESSION model. Furthermore, the model can deal with both symmetric and non-symmetric triangular FUZZY data as well as trapezoidal FUZZY data which have rarely been considered in the previous works. To show the efficiency of the proposed model, some numerical examples are solved and a simulation study is performed. The computational results are compared with some earlier methods.

This paper proposed an extension for the classical partial univariate REGRESSION model with non-FUZZY inputs and triangular FUZZY output. For this purpose, the popular non-parametric estimator and the conventional arithmetic operations of triangular FUZZY numbers were combined to construct a FUZZY univariate REGRESSION model. Then, a hybrid algorithm was developed to estimate the bandwidth and FUZZY REGRESSION coefficient. Some common goodness-of-fit criteria were also used to examine the performance of the proposed method. The effectiveness of the proposed method was then illustrated through two numerical examples including a simulation study. The proposed method was also compared with several common FUZZY LINEAR REGRESSION models with exact inputs and FUZZY outputs. Compared to the available FUZZY LINEAR REGRESSIONs models, the numerical results clearly indicated that the proposed FUZZY REGRESSION model is capable of exhibiting more accurate performances.