fIRTree: An Item Response Theory modeling of fuzzy rating data

TL;DR

This paper introduces a new method called fIRTree that models fuzzy rating data using Item Response Theory, capturing decision uncertainty in survey responses through fuzzy numbers.

Contribution

It presents a novel two-step procedure integrating fuzzy numbers with IRT-based trees to better represent fuzziness in survey ratings.

Findings

Simulation study demonstrating the method's effectiveness

Empirical application validating the approach

Enhanced interpretation of fuzziness as decision uncertainty

Abstract

In this contribution we describe a novel procedure to represent fuzziness in rating scales in terms of fuzzy numbers. Following the rationale of fuzzy conversion scale, we adopted a two-step procedure based on a psychometric model (i.e., Item Response Theory-based tree) to represent the process of answer survey questions. This provides a coherent context where fuzzy numbers, and the related fuzziness, can be interpreted in terms of decision uncertainty that usually affects the rater's response process. We reported results from a simulation study and an empirical application to highlight the characteristics and properties of the proposed approach.