Reduction to Least-Squares Estimates in Multiple Fuzzy Regression Analysis

In this paper, we deal with the problem of least-squares multiple regression with fuzzy data. The regression coefficients are assumed to be real (crisp). A formula for solving the regression coefficients in one-variable models is derived. If each independent variable is effective (i.e., its corresponding regression coefficient is nonzero), the multiple regression problem can be replaced with a 0-1 programming problem. Its optimal solution is easily computed. Finally, we also propose effective algorithms to compute the regression coefficients in a general case.