Fuzzy least absolute deviations regression based on the ranking of fuzzy numbers

A general fuzzy linear model for fuzzy regression analysis was formulated. Based on both this general model and a fuzzy difference ranking method (P.-T. Chang and E.S. Lee, 1993; 1992), approaches for fuzzy least squares regression and fuzzy least absolute value deviations regression were proposed. The former approach resulted in a nonlinear programming problem while the latter resulted in a linear programming problem. Numerical examples were solved by using the absolute deviations approach to illustrate the problems of conflicting trends and ways to at least partially overcoming these problems. Furthermore, these examples showed that the absolute deviations formulation forms an effective computational tool