This paper is devoted to exploring suitable methods for modelling, estimating and forecasting fuzzy time series, when facing the problem of non-invertibility of the standard Minkovsky addition and multiplication in a fuzzy framework. Some generalized versions of Hukuhara difference, which allow the fuzzy estimation problem to be handled in some L2-type metric space, are first examined from a critical viewpoint. This leads us to propose a new estimation procedure, where the monolithic fuzzy model is broken in several more tractable crisp estimation subproblems, based upon a partial decoupling principle. Our aim is to produce fuzzy estimations with non-negative spreads, capable not only to help decomposing, but also to make the process invertible, by recomposing a nonstationary fuzzy time series from its components, such as trend, cycle, seasonality and the simulated residuals, all of them properly defined as LR-fuzzy sets. Computational Intelligence techniques such as wavelet decomposition and de-noising or nonlinear model fitting with wavelet networks are also addressed. Finally, the proposed methods are exemplified for a fuzzy time series with fuzzy daily temperatures (minimum, average and maximum values).
Fuzzy time series estimation and prediction, Generalized Hukuhara difference, Projection cones vs. projection subspaces, Wavelet decomposition and de-noising, Nonlinear fitting with wavelet networks.
Vasile Georgescu, "Fuzzy Time Series Estimation and Prediction: Criticism, Suitable New Methods and Experimental Evidence", Studies in Informatics and Control, ISSN 1220-1766, vol. 19(3), pp. 229-242, 2010. https://doi.org/10.24846/v19i3y201003
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