Fuzzy regression : a scalar variable formation

In reliability, quality control and risk analysis, fuzzy methodologies are more and more involved and inevitably introduced difficulties in seeking fuzzy functional relationship between factors. In this paper, we propose a scalar variable formation of fuzzy regression model based on the credibility measure theoretical foundation. It is expecting our scalar variable treatments on fuzzy regression models will greatly simplify the efforts to seeking fuzzy functional relationship between fuzzy factors. An M-estimator for the regression coefficients is obtained and accordingly the properties and the variance-covariance for the coefficient M-estimators are also investigated in terms of weighted least-squares arguments. Finally, we explore the asymptotic membership function for the coefficient M-estimators.