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Component Models for Fuzzy Data

Published online by Cambridge University Press:  01 January 2025

Renato Coppi ,
Paolo Giordani  and
Pierpaolo D’Urso
Renato Coppi
Affiliation:
Università degli Studi di Roma “La Sapienza”
Paolo Giordani*
Affiliation:
Università degli Studi di Roma “La Sapienza”
Pierpaolo D’Urso
Affiliation:
Università degli Studi del Molise
*
Requests for reprints should be sent to Paolo Giordani, Dipartimento di Statistica, Probabilità e Statistiche applicate, Università degli Studi di Roma ‘La Sapienza,’ P.le A. Moro, 5-00185 Roma, Italy. E-mail: paolo.giordani@uniroma1.it
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Abstract

The fuzzy perspective in statistical analysis is first illustrated with reference to the “Informational Paradigm" allowing us to deal with different types of uncertainties related to the various informational ingredients (data, model, assumptions). The fuzzy empirical data are then introduced, referring to J LR fuzzy variables as observed on I observation units. Each observation is characterized by its center and its left and right spreads (LR1 fuzzy number) or by its left and right “centers" and its left and right spreads (LR2 fuzzy number). Two types of component models for LR1 and LR2 fuzzy data are proposed. The estimation of the parameters of these models is based on a Least Squares approach, exploiting an appropriately introduced distance measure for fuzzy data. A simulation study is carried out in order to assess the efficacy of the suggested models as compared with traditional Principal Component Analysis on the centers and with existing methods for fuzzy and interval valued data. An application to real fuzzy data is finally performed.

Keywords

informational paradigmfuzzy datadistance measure for fuzzy dataprincipal component analysisleast squares approach
Type
Original Paper
Information
Psychometrika , Volume 71 , Issue 4 , December 2006 , pp. 733 - 761
Copyright
Copyright © 2007 The Psychometric Society

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Footnotes

We would like to express our gratitude to the Editor, the Associate Editor, and the Referees whose comments and suggestions improved significantly the quality of the paper.

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