  Modeling human ratings data subject to raters' decision uncertainty is an
attractive problem in applied statistics. In view of the complex interplay
between emotion and decision making in rating processes, final raters' choices
seldom reflect the true underlying raters' responses. Rather, they are
imprecisely observed in the sense that they are subject to a non-random
component of uncertainty, namely the decision uncertainty. The purpose of this
article is to illustrate a statistical approach to analyse ratings data which
integrates both random and non-random components of the rating process. In
particular, beta fuzzy numbers are used to model raters' non-random decision
uncertainty and a variable dispersion beta linear model is instead adopted to
model the random counterpart of rating responses. The main idea is to quantify
characteristics of latent and non-fuzzy rating responses by means of random
observations subject to fuzziness. To do so, a fuzzy version of the
Expectation-Maximization algorithm is adopted to both estimate model's
parameters and compute their standard errors. Finally, the characteristics of
the proposed fuzzy beta model are investigated by means of a simulation study
as well as two case studies from behavioral and social contexts.
