  Modeling fuzziness and imprecision in human rating data is a crucial problem
in many research areas, including applied statistics, behavioral, social, and
health sciences. Because of the interplay between cognitive, affective, and
contextual factors, the process of answering survey questions is a complex
task, which can barely be captured by standard (crisp) rating responses. Fuzzy
rating scales have progressively been adopted to overcome some of the
limitations of standard rating scales, including their inability to disentangle
decision uncertainty from individual responses. The aim of this article is to
provide a novel fuzzy scaling procedure which uses Item Response Theory trees
(IRTrees) as a psychometric model for the stage-wise latent response process.
In so doing, fuzziness of rating data is modeled using the overall rater's
pattern of responses instead of being computed using a single-item based
approach. This offers a consistent system for interpreting fuzziness in terms
of individual-based decision uncertainty. A simulation study and two empirical
applications are adopted to assess the characteristics of the proposed model
and provide converging results about its effectiveness in modeling fuzziness
and imprecision in rating data.
