Random Fuzzy Sets as Ill-Perceived Random Variables

Couso, Inés; Dubois, Didier; Sánchez, Luciano

doi:10.1007/978-3-319-08611-8_3

Cited by 1 publication

(1 citation statement)

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“…where the definition ξ y = n i=1 ξ yi has been used for the joint fuzzy set [33]. Further details about fuzzy generalization of likelihood functions, fuzzy random variables, and fuzzy probability space can be found in [14,20,24,33,34].…”

Section: Fuzzy Numbers and Fuzzy Probabilitymentioning

confidence: 99%

Modeling random and non-random decision uncertainty in ratings data: A fuzzy beta model

Calcagnì,

Lombardi

2020

Preprint

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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 nonrandom 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.

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