Mean-absolute-deviation-based fuzzy linear regression analysis by level sets automatic deduction from data

We propose a fuzzy linear regression technique based on the mean-absolute-deviation. The error between the fuzzy linear regression function and the given data is defined as a fuzzy number based on the extension principle. The fuzzy linear regression function is estimated by the minimization of the sum of the absolute deviations of a level set. Since the minimization problem, has an interval objective function, we introduce an interpretation which can deduce the level set from the data without specifying the levels. Through the repetitive use of this level set estimation, the entire fuzzy linear function, is obtained in the form of a family of level sets