  In several research areas, ratings data and response times have been
successfully used to unfold the stage-wise process through which human raters
provide their responses to questionnaires and social surveys. A limitation of
the standard approach to analyze this type of data is that it requires the use
of independent statistical models. Although this provides an effective way to
simplify the data analysis, it could potentially involve difficulties with
regards to statistical inference and interpretation. In this sense, a joint
analysis could be more effective. In this research article, we describe a way
to jointly analyze ratings and response times by means of fuzzy numbers. A
probabilistic tree model framework has been adopted to fuzzify ratings data and
four-parameter triangular fuzzy numbers have been used in order to integrate
crisp responses and times. Finally, a real case study on psychometric data is
discussed in order to illustrate the proposed methodology. Overall, we provide
initial findings to the problem of using fuzzy numbers as abstract models for
representing ratings data with additional information (i.e., response times).
The results indicate that using fuzzy numbers lead to theoretically sound and
more parsimonious data analysis methods, which limit some statistical issues
that may occur with standard data analysis procedures (e.g., the problem of
multiple hypothesis testing).
