Instrumental variables estimation of fuzzy regression models

Linear regression models with fuzzy independent variables and crisp parameters are considered in this paper. The constant term may be fuzzy. It is determined using calculus of variations. Sometimes linear regression models do not satisfy the conditions under which the least squares estimator should be consistent. It is known from econometrics that in some cases instrumental variables can be used to find a consistent estimator for such models. In this paper, an instrumental variables estimator of a linear fuzzy regression model is constructed and consistency of the estimator is established.