Optimizing h value for fuzzy linear regression with asymmetric triangular fuzzy coefficients

The parameter h in a fuzzy linear regression model is vital since it influences the degree of the fitting of the estimated fuzzy linear relationship to the given data directly. However, it is usually subjectively pre-selected by a decision-maker as an input to the model in practice. In Liu and Chen (2013), a new concept of system credibility was introduced by combining the system fuzziness with the system membership degree, and a systematic approach was proposed to optimize the h value for fuzzy linear regression analysis using the minimum fuzziness criterion with symmetric triangular fuzzy coefficients. As an extension, in this paper, their approach is extended to asymmetric cases, and the procedure to find the optimal h value to maximize the system credibility of the fuzzy linear regression model with asymmetric triangular fuzzy coefficients is described. Some illustrative examples are given to show the detailed procedure of this approach, and comparative studies are also conducted via the testing data sets. HighlightsA systematic approach is proposed to optimize the h value for fuzzy linear regression with maximum reliability.The h value is suggested not be more than 0.5 for FLR analysis with symmetric or asymmetric TFNs.It is shown that the optimal h value will decrease with the augment of volume of the sample data pairs.It is shown that the system credibility in the asymmetric case will be higher than that in the symmetric case.