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

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 reg...

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Main Authors: Irina Perfilieva, Vladik Kreinovich
Format: Article
Language:English
Published: Wiley 2011-01-01
Series:Advances in Fuzzy Systems
Online Access:http://dx.doi.org/10.1155/2011/985839
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author Irina Perfilieva
Vladik Kreinovich
author_facet Irina Perfilieva
Vladik Kreinovich
author_sort Irina Perfilieva
collection DOAJ
description 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.
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spelling doaj-art-e421d9d796c9490abba8ba334941f0c32025-02-03T05:59:04ZengWileyAdvances in Fuzzy Systems1687-71011687-711X2011-01-01201110.1155/2011/985839985839Why Fuzzy Transform Is Efficient in Large-Scale Prediction Problems: A Theoretical ExplanationIrina Perfilieva0Vladik Kreinovich1Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Ostrava 70100, Czech RepublicDepartment of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USAIn 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.http://dx.doi.org/10.1155/2011/985839
spellingShingle Irina Perfilieva
Vladik Kreinovich
Why Fuzzy Transform Is Efficient in Large-Scale Prediction Problems: A Theoretical Explanation
Advances in Fuzzy Systems
title Why Fuzzy Transform Is Efficient in Large-Scale Prediction Problems: A Theoretical Explanation
title_full Why Fuzzy Transform Is Efficient in Large-Scale Prediction Problems: A Theoretical Explanation
title_fullStr Why Fuzzy Transform Is Efficient in Large-Scale Prediction Problems: A Theoretical Explanation
title_full_unstemmed Why Fuzzy Transform Is Efficient in Large-Scale Prediction Problems: A Theoretical Explanation
title_short Why Fuzzy Transform Is Efficient in Large-Scale Prediction Problems: A Theoretical Explanation
title_sort why fuzzy transform is efficient in large scale prediction problems a theoretical explanation
url http://dx.doi.org/10.1155/2011/985839
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AT vladikkreinovich whyfuzzytransformisefficientinlargescalepredictionproblemsatheoreticalexplanation