Algorithm 1017

2021 ◽  
Vol 47 (3) ◽  
pp. 1-18
Author(s):  
Pavel Škrabánek ◽  
Natália Martínková
Keyword(s):  
Linear Regression ◽  
Goodness Of Fit ◽  
Fuzzy Numbers ◽  
Linear Models ◽  
Total Error ◽  
Estimation Method ◽  
Fuzzy Regression ◽  
Model Parameters ◽  
Statistical Regression ◽  
Fuzzy Linear Regression

Fuzzy regression provides an alternative to statistical regression when the model is indefinite, the relationships between model parameters are vague, the sample size is low, or the data are hierarchically structured. Such cases allow to consider the choice of a regression model based on the fuzzy set theory. In fuzzyreg, we implement fuzzy linear regression methods that differ in the expectations of observational data types, outlier handling, and parameter estimation method. We provide a wrapper function that prepares data for fitting fuzzy linear models with the respective methods from a syntax established in R for fitting regression models. The function fuzzylm thus provides a novel functionality for R through standardized operations with fuzzy numbers. Additional functions allow for conversion of real-value variables to be fuzzy numbers, printing, summarizing, model plotting, and calculation of model predictions from new data using supporting functions that perform arithmetic operations with triangular fuzzy numbers. Goodness of fit and total error of the fit measures allow model comparisons. The package contains a dataset named bats with measurements of temperatures of hibernating bats and the mean annual surface temperature reflecting the climate at the sampling sites. The predictions from fuzzy linear models fitted to this dataset correspond well to the observed biological phenomenon. Fuzzy linear regression has great potential in predictive modeling where the data structure prevents statistical analysis and the modeled process exhibits inherent fuzziness.

Fuzzy C-Regression Models

2013 ◽  
Vol 278-280 ◽  
pp. 1323-1326
Author(s):  
Yan Hua Yu ◽  
Li Xia Song ◽  
Kun Lun Zhang
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Linear Models ◽  
Least Squares Method ◽  
Least Square Method ◽  
Least Square ◽  
Estimation Methods ◽  
Statistical Regression ◽  
Fuzzy Linear Regression ◽  
Fuzzy Degree

Fuzzy linear regression has been extensively studied since its inception symbolized by the work of Tanaka et al. in 1982. As one of the main estimation methods, fuzzy least squares approach is appealing because it corresponds, to some extent, to the well known statistical regression analysis. In this article, a restricted least squares method is proposed to fit fuzzy linear models with crisp inputs and symmetric fuzzy output. The paper puts forward a kind of fuzzy linear regression model based on structured element, This model has precise input data and fuzzy output data, Gives the regression coefficient and the fuzzy degree function determination method by using the least square method, studies the imitation degree question between the observed value and the forecast value.

RIDGE REGRESSION PROCEDURES FOR FUZZY MODELS USING TRIANGULAR FUZZY NUMBERS

2004 ◽  
Vol 12 (02) ◽  
pp. 145-159 ◽  
Author(s):  
DUG HUN HONG ◽  
CHANGHA HWANG
Keyword(s):  
Nonlinear Regression ◽  
Ridge Regression ◽  
Fuzzy Numbers ◽  
Linear Models ◽  
Estimation Method ◽  
Feature Space ◽  
Triangular Fuzzy Numbers ◽  
Fuzzy Linear Regression ◽  
Data Set ◽  
Nonlinear Regression Models

This paper presents a new method of estimating fuzzy multivariable linear and nonlinear regression models using triangular fuzzy numbers. This estimation method is obtained by implementing a dual version of the ridge regression procedure for linear models. It allows us to perform fuzzy nonlinear regression by constructing a fuzzy linear regression in a high dimensional feature space for the data set with crisp inputs and fuzzy output. Experimental results are then presented, which indicate the performance of this algorithm.

scholarly journals A Learn Of Fuzzy Regression Model and its Applications

2019 ◽  
Vol 8 (2) ◽  
pp. 2967-2971
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Fuzzy Numbers ◽  
Fuzzy Regression ◽  
Regression Coefficients ◽  
Fuzzy Linear Regression ◽  
Fuzzy Regression Model ◽  
Fuzzy Linear Regression Model

Many statistics report shown in fuzzy module into clear problems using the centroid system, consequently we will research the usual linear regression model which is modified from the fuzzy linear regression model. The models enter and generate fuzzy numbers, and the regression coefficients are clear numbers. Hybrid algorithms are considered to fit the fuzzy regression model. So that the validity and quality of the suggested methods can be guaranteed. Therefore,the parameter estimation and have an impact on evaluation situated on knowledge deletion. By way of the gain knowledge of example and evaluation with other model, it may be concluded that the model in this paper is utilized without difficulty and better.

scholarly journals Relating Hydro-Meteorological Variables to Water Table in an Unconfined Aquifer via Fuzzy Linear Regression

Environments ◽  
2021 ◽  
Vol 8 (2) ◽  
pp. 9
Author(s):  
Christopher Papadopoulos ◽  
Mike Spiliotis ◽  
Ioannis Gkiougkis ◽  
Fotios Pliakas ◽  
Basil Papadopoulos
Keyword(s):  
Linear Regression ◽  
Potential Evapotranspiration ◽  
Unconfined Aquifer ◽  
Fuzzy Regression ◽  
Meteorological Variables ◽  
Total Width ◽  
Fuzzy Linear Regression ◽  
Central Value ◽  
Triangular Numbers ◽  
Term Response

This study aims to assess the short-term response of groundwater to the main hydro-meteorological variables of drought in a coastal unconfined aquifer. For this purpose, a multiple fuzzy linear regression-based methodology is implemented in order to relate rainfall, streamflow and the potential evapotranspiration to groundwater. Fuzzy regression analysis is recommended when there is a lack of data. The uncertainty of the system is incorporated into the regression coefficients which, in this study, are considered to be fuzzy symmetrical triangular numbers. Two objective functions are used producing a fuzzy band in which all the observed data must be included. The first objective function, based on Tanaka’s model, minimizes the total width of the produced fuzzy band. The second one includes the first while additionally minimizing the distance between the central value of the fuzzy output of the model and the observed value. Validity of the model is checked through suitability measures. The present methodology is applied at the east part of the Nestos River Delta in the Prefecture of Xanthi (Greece), where the observed values of the depth of groundwater level of four wells are examined.

scholarly journals Fuzzy Linear Regression of Rainfall-Altitude Relationship

Proceedings ◽  
2018 ◽  
Vol 2 (11) ◽  
pp. 636
Author(s):  
Christos Tzimopoulos ◽  
Christos Evangelides ◽  
Christos Vrekos ◽  
Nikiforos Samarinas
Keyword(s):  
Linear Regression ◽  
Rainfall Data ◽  
Fuzzy Regression ◽  
Annual Rainfall ◽  
Fuzzy Linear Regression ◽  
Error Terms ◽  
Classical Linear Regression ◽  
The One ◽  
The Relationship ◽  
Imprecise Parameters

Classical linear regression has been used to measure the relationship between rainfall data and altitude in different meteorological stations, in order to evaluate a linear relation. The values of rainfall are supposed as dependent variables and the values of elevation of each station as independent variables. It has long been known that a classical statistical relationship exists between annual rainfall and the station elevation which in many cases is linear as the one examined in this article. However classical linear regression makes rigid assumptions about the statistical properties of the model, accepting the error terms as random variables, and the violation of this assumption could affect the validity of the classical linear regression. Fuzzy regression assumes ambiguous and imprecise parameters and data. For this reason it may be more effective than classical regression. In this paper we evaluate the relationship between annual rainfall data and the elevation of each station in Thessaly’s meteorological stations, using fuzzy linear regression with trapezoidal membership functions. In this possibilistic model the dependent measured elevations are crisp, and the independent observed rainfall values as well as the parameters of the model are fuzzy.

Regularized Regression for Reserving and Mortality Models

2018 ◽  
Vol 13 (2) ◽  
Author(s):  
Gary Venter
Keyword(s):  
Goodness Of Fit ◽  
Linear Models ◽  
Model Parameters ◽  
Regularized Regression ◽  
Linear Modeling ◽  
Estimation Errors ◽  
Smooth Curves ◽  
Lower Estimation ◽  
Mortality Models ◽  
Loss Reserving

Abstract Bayesian regularization, a relatively new method for estimating model parameters, shrinks estimates towards the overall mean by shrinking the parameters. It has been proven to lower estimation and prediction variances from those of MLE for linear models, such as regression or GLM. It has a goodness-of-fit measure, and can readily be applied using available software. This can be used for any type of actuarial linear modeling, but it is slightly more complicated for mortality and loss reserving models that use row, column, and diagonal effects for array data. These are called age-period-cohort, or APC models by statisticians. The problem is that the row, column and diagonal effects are not what should be shrunk. These models can easily become over-parameterized, and actuaries often reduce parameters with smooth curves or cubic splines. We discuss an alternative smoothing method that uses regularization, with its reduction in estimation errors, and illustrate both its classical and Bayesian forms and their application to APC modeling. Typical actuarial models and some generalizations are used as examples.

scholarly journals Boscovich Fuzzy Regression Line

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 685
Author(s):  
Pavel Škrabánek ◽  
Jaroslav Marek ◽  
Alena Pozdílková
Keyword(s):  
Fuzzy Numbers ◽  
Linear Time ◽  
Regression Line ◽  
Fuzzy Regression ◽  
Linear Regression Method ◽  
Triangular Fuzzy Numbers ◽  
Fuzzy Linear Regression ◽  
Regression Methods ◽  
Dependent Variables ◽  
Real Value

We introduce a new fuzzy linear regression method. The method is capable of approximating fuzzy relationships between an independent and a dependent variable. The independent and dependent variables are expected to be a real value and triangular fuzzy numbers, respectively. We demonstrate on twenty datasets that the method is reliable, and it is less sensitive to outliers, compare with possibilistic-based fuzzy regression methods. Unlike other commonly used fuzzy regression methods, the presented method is simple for implementation and it has linear time-complexity. The method guarantees non-negativity of model parameter spreads.

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