Pedotransfer functions are the predictive models of a certain soil property from other easily, routinely, or cheaply measured properties. The common approach for fitting the pedotransfer functions is the use of the conventional statistical Regression method. Such an approach is heavily based on the crisp obervations and also the crisp relations among variables. In the modeling natural systems, like soil, we are dealing with imprecise observations and the vague relations among the variables. Therefore, we need an appropriate algorithm for modeling such a Fuzzy structures. In the present study, the Fuzzy Regression approach was used in order to fit some chemical and physical pedotransfer functions. The optimum Regression models with the Fuzzy coefficients were obtained for modeling pedotransfer functions. Sensivity analysis was carried out by using the credibility level. The results indicated that the Fuzzy Regression might be cOflsidered,as a suitable alternative or a complement to the statistical Regression, whenever a relationship between variables is imprecise and generally when dealing with the errors due to a vaguness in Regression models.

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.

In this paper, we consider the issue of data classification in which the response (dependent) variable is two (or multi) valued and the predictor (independent) variables are ordinary variables. The errors could be nonprecise and random. In this case, the response variable is also a Fuzzy random variable. Based on this and logistic Regression, we formulate a model and find the estimation of the coefficients using the least squares method. We will describe the results with an example of one independent random variable. Finally, we provide recurrence relations for the estimation of parameters. This relation can be used in machine learning and big data classification.

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 a-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.

Statistical significance determines whether the relationship between two or more variables is caused by factors other than chance and randomness. Statistical hypothesis testing is a method by which statistical significance is determined. By introducing Fuzzy Regression, several approaches were presented to estimate parameters of such the models. Now, most researches have conducted on the estimation method and little attention has been paid to the properties of estimators,, confidence intervals and significance tests. The main idea here is to investigate the significance of estimated parameters in an applied study with Fuzzy-valued real data in the framework of Fuzzy Regression modeling using $m$-estimators. For this purpose, by accessing the water and sewage data source of Ahvaz city, the required variables were first introduced. Since $m$-estimators use an algorithm based on reweighted method, we are looking to determine the weight of the users in terms of the consumption pattern, that is, the weight of high consumption users and low consumption users is determined. Now, the company can first identify and classify the consumption patterns of each user based on the determined weights, and then deal with the stepped pricing of each cubic meter of water for each user. This idea requires providing a significant model of Fuzzy Regression. Since $m$-estimators of Fuzzy Regression model do not have a closed form, bootstrap is used to present the numerical indices of the estimators, confidence intervals and the significance test of the model. By analyzing the results and keeping significant parameters a suitable model was introduced.

Groundwater has always been considered as one of the main sources of drinking, agriculture, and industrial water, especially in arid and semi-arid regions. Investigating groundwater level changes in any region has an important role in planning sustainable water resources management. Continuous decline of groundwater level has been observed worldwide in the past half-century. Groundwater is the most important and the only source of freshwater in Neyshabour plain. Unallowable discharges of the groundwater resources and the reduction of recharge factors have caused about 200 million cubic meters deficit in Neyshabour aquifer. Therefore, estimating groundwater is vitally important for the management of water resources.

Both traditional and Fuzzy Regression analyses have demonstrated the significant characteristics of the least-squares methodology as a method for parameter estimation.} The presence of outliers in the sample and/or minor variations in the dataset might impact the behaviour and characteristics of the least-squares estimators (LSE)‎. ‎In contrast‎, ‎robust approaches provide estimators of the parameters that are resilient to the aforementioned unfavourable effects‎. ‎This study aims to expand upon the Theil-Sen estimator in Fuzzy Regression analysis‎, ‎with the objective of obtaining consistent findings even when outliers are present‎. ‎\rd{ We demonstrate the effectiveness of the suggested technique through simulation experiments and real-world examples‎, ‎comparing it to commonly used Fuzzy Regression models‎. ‎The applicative examples are based on hydrology and atmospheric environment datasets‎. ‎We also show the sensitivity analysis of the estimated parameters using a Monte-Carlo simulation study‎, ‎demonstrating the effectiveness of the suggested estimators in comparison to other established approaches in the field of Fuzzy Regression analysis‎. ‎The results showed that the Theil-Sen estimator (TSE) is very effective in cases where there are outliers‎, ‎and the calculation error is smaller compared to other methods.

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.

Pedomodels have become a popular topic in soil science and environmental research. They are predictive functions of certain soil properties based on other easily or cheaply measured properties. The common method for fitting pedomodels is to use classical Regression analysis, based on the assumptions of data crispness and deterministic relations among variables. In modeling natural systems such as soil system, in which the above assumptions are not held true, prediction is influential and we must therefore attempt to analyze the behavior and structure of such systems more realistically. In this paper we consider Fuzzy least squares Regression as a means of fitting pedomodels. The theoretical and practical considerations are illustrated by developing some examples of real pedomodels.

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.