Fuzzy data analysis by possibilistic linear models
Fuzzy Sets and Systems - Fuzzy Numbers
Possibilistic linear systems and their application to the linear regression model
Fuzzy Sets and Systems
Evaluation of fuzzy linear regression models
Fuzzy Sets and Systems
Multiobjective fuzzy linear regression analysis for fuzzy input-output data
Fuzzy Sets and Systems
Fuzzy linear regression with fuzzy intervals
Fuzzy Sets and Systems
Properties of certain fuzzy linear regression methods
Fuzzy Sets and Systems
Exponential possibility regression analysis
Fuzzy Sets and Systems - Special issue on fuzzy information processing
A linear regression model using triangular fuzzy number coefficients
Fuzzy Sets and Systems
Support vector fuzzy regression machines
Fuzzy Sets and Systems - Theme: Learning and modeling
Theoretically Optimal Parameter Choices for Support Vector Regression Machines with Noisy Input
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Interval regression analysis by quadratic programming approach
IEEE Transactions on Fuzzy Systems
Linear dependency between ε and the input noise in ε-support vector regression
IEEE Transactions on Neural Networks
Information Sciences: an International Journal
A revisited approach to linear fuzzy regression using trapezoidal fuzzy intervals
Information Sciences: an International Journal
A novel nonlinear programming approach for estimating CAPM beta of an asset using fuzzy regression
Expert Systems with Applications: An International Journal
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Fuzzy linear regression (FLR) model can be thought of as a fuzzy variation of classical linear regression model. It has been widely studied and applied in diverse fields. When noise exists in data, it is a very meaningful topic to reveal the dependency between the parameter h (i.e. the threshold value used to measure degree of fit) in FLR model and the input noise. In this paper, the FLR model is first extended to its regularized version, i.e. regularized fuzzy linear regression (RFLR) model, so as to enhance its generalization capability; then RFLR model is explained as the corresponding equivalent maximum a posteriori (MAP) problem; finally, the general dependency relationship that the parameter h with noisy input should follow is derived. Particular attention is paid to the regression model using non-symmetric fuzzy triangular coefficients. It turns out that with the existence of typical Gaussian noisy input, the parameter h is inversely proportional to the input noise. Our experimental results here also confirm this theoretical claim. Obviously, this theoretical result will be helpful to make a good choice for the parameter h, and to apply FLR techniques effectively in practical applications.