Asymptotic properties of least squares estimation with fuzzy observations

Abstract

This paper deals with the asymptotic properties of the least squares estimators for fuzzy linear regression models with fuzzy triangular input–output and random error terms. The asymptotic normality and strong consistency of the fuzzy least squares estimator (FLSE) are investigated; a confidence region based on a class of FLSEs is proposed; the asymptotic relative efficiency of FLSEs with respect to the crisp least squares estimators is also provided and a numerical example is given. Some simulation results are also presented to illustrate the behavior of FLSEs.