CUB models: a preliminary fuzzy approach to heterogeneity

TL;DR

This paper introduces a fuzzy extension to CUB models to better handle heterogeneity and uncertainty in ordinal data, demonstrated through a university survey case study.

Contribution

It combines fuzzy set theory with CUB models, providing a novel way to interpret heterogeneity as an uncertainty measure in questionnaire analysis.

Findings

Fuzzy CUB models effectively capture heterogeneity in ordinal data.

The approach offers a new interpretation of the CUB uncertainty parameter.

Application to a university survey illustrates practical utility.

Abstract

In line with the increasing attention paid to deal with uncertainty in ordinal data models, we propose to combine Fuzzy models with \cub models within questionnaire analysis. In particular, the focus will be on \cub models' uncertainty parameter and its interpretation as a preliminary measure of heterogeneity, by introducing membership, non-membership and uncertainty functions in the more general framework of Intuitionistic Fuzzy Sets. Our proposal is discussed on the basis of the Evaluation of Orientation Services survey collected at University of Naples Federico II.