scholarly journals On Optimal and Asymptotic Properties of a Fuzzy L2 Estimator

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1956
Author(s):  
Jin Hee Yoon ◽  
Przemyslaw Grzegorzewski
Keyword(s):  
Regression Model ◽  
Asymptotic Properties ◽  
Asymptotic Relative Efficiency ◽  
Confidence Regions ◽  
Fuzzy Regression ◽  
Monte Carlo Simulation Study ◽  
Fuzzy Input ◽  
Fuzzy Regression Model ◽  
Algebraic Properties ◽  
Best Linear Unbiased

A fuzzy least squares estimator in the multiple with fuzzy-input–fuzzy-output linear regression model is considered. The paper provides a formula for the L2 estimator of the fuzzy regression model. This paper proposes several operations for fuzzy numbers and fuzzy matrices with fuzzy components and discussed some algebraic properties that are needed to use for proving theorems. Using the proposed operations, the formula for the variance, provided and this paper, proves that the estimators have several important optimal properties and asymptotic properties: they are Best Linear Unbiased Estimator (BLUE), asymptotic normality and strong consistency. The confidence regions of the coefficient parameters and the asymptotic relative efficiency (ARE) are also discussed. In addition, several examples are provided including a Monte Carlo simulation study showing the validity of the proposed theorems.

Fuzzy Regression Model Based on Geometric Centroid and Incentre Points and Application to Performance Evaluation

2020 ◽  
Vol 28 (02) ◽  
pp. 269-288
Author(s):  
Yanbing Gong ◽  
Lin Xiang ◽  
Gaofeng Liu
Keyword(s):  
Regression Model ◽  
Least Squares ◽  
Least Squares Method ◽  
Estimation Error ◽  
Triangular Fuzzy Number ◽  
Fuzzy Regression ◽  
Distance Method ◽  
Fuzzy Input ◽  
Fuzzy Regression Model ◽  
Fuzzy Linear Regression Model

Fuzzy regression model is developed to construct the relationship between independent variable and dependent variable in a fuzzy environment. In order to increase the explanatory performance of fuzzy regression model, the least-squares method usually is applied to determine the numeric coefficients based on the concept of distance. In this paper, we consider the fuzzy linear regression model with fuzzy input, fuzzy output and crisp parameters and introduce a new distance based on the geometric centroid and incentre points (GCIP) of triangular fuzzy number, merge least-squares method with the new GCIP distance and propose least-squares GCIP distance method. Finally, an example of employee job performance is given to illustrate the effectiveness and feasibility of the method. Comparisons with existing methods show that total estimation error using the same distance criterion, the explanatory performance of the GCIP method is satisfactory, and the calculation is relatively simple.

scholarly journals FUZZY PRINCIPAL COMPONENT REGRESSION (FPCR) FOR FUZZY INPUT AND OUTPUT DATA

2006 ◽  
Vol 14 (01) ◽  
pp. 87-100 ◽  
Author(s):  
JIH-JENG HUANG ◽  
GWO-HSHIUNG TZENG ◽  
CHORNG-SHYONG ONG
Keyword(s):  
Principal Component Analysis ◽  
Regression Model ◽  
Principal Component Regression ◽  
Principal Component ◽  
Fuzzy Regression ◽  
Output Data ◽  
Input And Output ◽  
Fuzzy Input ◽  
Fuzzy Regression Model ◽  
Component Scores

Although fuzzy regression is widely employed to solve many problems in practice, what seems to be lacking is the problem of multicollinearity. In this paper, the fuzzy centers principal component analysis is proposed to first derive the fuzzy principal component scores. Then the fuzzy principal component regression (FPCR) is formed to overcome the problem of multicollinearity in the fuzzy regression model. In addition, a numerical example is used to demonstrate the proposed method and compare with other methods. On the basis of the results, we can conclude that the proposed method can provide a correct fuzzy regression model and avoid the problem of multicollinearity.

scholarly journals Quadrilateral Interval Type-2 Fuzzy Regression Analysis for Data Outlier Detection

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Pingping Gao ◽  
Yabin Gao
Keyword(s):  
Regression Analysis ◽  
Regression Model ◽  
Outlier Detection ◽  
Euclidean Distance ◽  
Fuzzy Numbers ◽  
Fuzzy Regression ◽  
Fuzzy Regression Analysis ◽  
Fuzzy Regression Model ◽  
Interval Type

This paper presents a fuzzy regression analysis method based on a general quadrilateral interval type-2 fuzzy numbers, regarding the data outlier detection. The Euclidean distance for the general quadrilateral interval type-2 fuzzy numbers is provided. In the sense of Euclidean distance, some parameter estimation laws of the type-2 fuzzy linear regression model are designed. Then, the data outlier detection-oriented parameter estimation method is proposed using the data deletion-based type-2 fuzzy regression model. Moreover, based on the fuzzy regression model, by using the root mean squared error method, an impact evaluation rule is designed for detecting data outlier. An example is finally provided to validate the presented methods.

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