scholarly journals Comparison of the fuzzy regression analysis and the least squares regression method to the electrical load estimation

2002 ◽  
Author(s):  
W. Zalewski
Keyword(s):  
Regression Analysis ◽  
Least Squares ◽  
Regression Method ◽  
Fuzzy Regression ◽  
Load Estimation ◽  
Least Squares Regression ◽  
Electrical Load ◽  
Fuzzy Regression Analysis

FUZZY ROBUST REGRESSION ANALYSIS BASED ON THE RANKING OF FUZZY SETS

2008 ◽  
Vol 16 (05) ◽  
pp. 663-681 ◽  
Author(s):  
KAMİLE ŞANLI KULA ◽  
AYŞEN APAYDIN
Keyword(s):  
Regression Analysis ◽  
Least Squares ◽  
Fuzzy Sets ◽  
Robust Regression ◽  
Least Squares Method ◽  
Fuzzy Regression ◽  
Least Squares Regression ◽  
Fuzzy Linear Regression ◽  
Data Set ◽  
Independent Variables

Since fuzzy linear regression was introduced by Tanaka et al., fuzzy regression analysis has been widely studied and applied in various areas. Diamond proposed the fuzzy least squares method to eliminate disadvantages in the Tanaka et al method. In this paper, we propose a modified fuzzy least squares regression analysis. When independent variables are crisp, the dependent variable is a fuzzy number and outliers are present in the data set. In the proposed method, the residuals are ranked as the comparison of fuzzy sets, and the weight matrix is defined by the membership function of the residuals. To illustrate how the proposed method is applied, two examples are discussed and compared in methods from the literature. Results from the numerical examples using the proposed method give good solutions.

AN LP-BASED APPROACH TO OUTLIERS DETECTION IN FUZZY REGRESSION ANALYSIS

2007 ◽  
Vol 15 (04) ◽  
pp. 441-456 ◽  
Author(s):  
EBRAHIM NASRABADI ◽  
S. MEHDI HASHEMI ◽  
MEHDI GHATEE
Keyword(s):  
Linear Programming ◽  
Regression Analysis ◽  
Least Squares ◽  
Regression Models ◽  
Fuzzy Regression ◽  
Data Set ◽  
Numerical Examples ◽  
New Model ◽  
Fuzzy Regression Analysis ◽  
Outliers Detection

When the outliers exist in the data set, fuzzy regression gives incorrect results. A few number of researchers considered this problem and proposed linear-programming-based methods and fuzzy least-squares methods to deal with the outliers problem. In this paper, we develop a new model along with a linear-programming-based approach for computation of fuzzy regression models. The problem of outliers is modeled with this approach. Two examples are illustrated to compare the performance of proposed approach with those given in literature. Results from numerical examples show that our approach gives good solutions.

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