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.
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Coppi, R., Giordani, P. & D’Urso, P. Component Models for Fuzzy Data. Psychometrika 71, 733–761 (2006). https://doi.org/10.1007/s11336-003-1105-1
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DOI: https://doi.org/10.1007/s11336-003-1105-1