Summary: This study is an investigation of fuzzy linear regression models for crisp/fuzzy input and fuzzy output data. A least absolutes deviations approach to construct such models is developed by introducing and applying a new metric on the space of fuzzy numbers. The proposed approach, which can deal with both symmetric and non-symmetric fuzzy observations, is compared with several existing models by three goodness of fit criteria. Three well-known data sets including two small data sets as well as a large data set are employed for such comparisons.