Least-squares estimation in linear regression models with vague concepts

Abstract

The paper is a contribution to parameter estimation in fuzzy regression models with random fuzzy sets. Here models with crisp parameters and fuzzy observations of the variables are investigated. This type of regression models may be understood as an extension of the ordinary single equation linear regression models by integrating additionally the physical vagueness of the involved items. So the significance of these regression models is to improve the empirical meaningfulness of the relationship between the items by a more sensitive attention to the fundamental adequacy problem of measurement. Concerning the parameter estimation the ordinary least-squares method is extended. The existence of estimators by the suggested method is shown, and some of their stochastic properties are surveyed.