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Advances in Fuzzy Systems
Volume 2011 (2011), Article ID 985839, 5 pages
http://dx.doi.org/10.1155/2011/985839
Research Article

Why Fuzzy Transform Is Efficient in Large-Scale Prediction Problems: A Theoretical Explanation

1Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Ostrava 70100, Czech Republic
2Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA

Received 15 May 2011; Accepted 6 June 2011

Academic Editor: Salvatore Sessa

Copyright © 2011 Irina Perfilieva and Vladik Kreinovich. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In many practical situations like weather prediction, we are interested in large-scale (averaged) value of the predicted quantities. For example, it is impossible to predict the exact future temperature at different spatial locations, but we can reasonably well predict average temperature over a region. Traditionally, to obtain such large-scale predictions, we first perform a detailed integration of the corresponding differential equation and then average the resulting detailed solution. This procedure is often very time-consuming, since we need to process all the details of the original data. In our previous papers, we have shown that similar quality large-scale prediction results can be obtained if, instead, we apply a much faster procedure—first average the inputs (by applying an appropriate fuzzy transform) and then use these averaged inputs to solve the corresponding (discretization of the) differential equation. In this paper, we provide a general theoretical explanation of why our semiheuristic method works, that is, why fuzzy transforms are efficient in large-scale predictions.