The fuzzy transform (F-transform), introduced by I. Perfilieva, is a powerful tool for the construction of fuzzy approximation models; it is based on generalized fuzzy partitions and it is obtained by minimizing a quadratic (L2-norm) error function. In this paper, within the discrete setting, we describe an analogous construction by minimizing an L1-norm error function, so obtaining the L1-norm F-transform, which is again a general approximation tool. The L1-norm and L2-norm settings are then used to construct two types of fuzzy- valued F-transforms, by defining expectile (L2-norm) and quantile (L1-norm) extensions of the transforms. This allows to model an observed time series in terms of fuzzy-valued functions, whose level-cuts can be interpreted in the setting of expectile and quantile regression. The proposed methodology is illustrated on some financial daily time series.

Quantile and expectile smoothing based on L1-norm and L2-norm fuzzy transforms / Guerra, Maria Letizia; Sorini, Laerte; Stefanini, Luciano. - In: INTERNATIONAL JOURNAL OF APPROXIMATE REASONING. - ISSN 0888-613X. - STAMPA. - 107:(2019), pp. 17-43. [10.1016/j.ijar.2019.01.011]

Quantile and expectile smoothing based on L1-norm and L2-norm fuzzy transforms

Guerra, Maria Letizia
;
2019

Abstract

The fuzzy transform (F-transform), introduced by I. Perfilieva, is a powerful tool for the construction of fuzzy approximation models; it is based on generalized fuzzy partitions and it is obtained by minimizing a quadratic (L2-norm) error function. In this paper, within the discrete setting, we describe an analogous construction by minimizing an L1-norm error function, so obtaining the L1-norm F-transform, which is again a general approximation tool. The L1-norm and L2-norm settings are then used to construct two types of fuzzy- valued F-transforms, by defining expectile (L2-norm) and quantile (L1-norm) extensions of the transforms. This allows to model an observed time series in terms of fuzzy-valued functions, whose level-cuts can be interpreted in the setting of expectile and quantile regression. The proposed methodology is illustrated on some financial daily time series.
2019
Quantile and expectile smoothing based on L1-norm and L2-norm fuzzy transforms / Guerra, Maria Letizia; Sorini, Laerte; Stefanini, Luciano. - In: INTERNATIONAL JOURNAL OF APPROXIMATE REASONING. - ISSN 0888-613X. - STAMPA. - 107:(2019), pp. 17-43. [10.1016/j.ijar.2019.01.011]
Guerra, Maria Letizia; Sorini, Laerte; Stefanini, Luciano
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/663247
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