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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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Advances in Fuzzy Systems |
| Online Access: | http://dx.doi.org/10.1155/2011/985839 |
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| _version_ | 1832552332172197888 |
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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. |
| format | Article |
| id | doaj-art-e421d9d796c9490abba8ba334941f0c3 |
| institution | Kabale University |
| issn | 1687-7101 1687-711X |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Fuzzy Systems |
| 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 |
| work_keys_str_mv | AT irinaperfilieva whyfuzzytransformisefficientinlargescalepredictionproblemsatheoreticalexplanation AT vladikkreinovich whyfuzzytransformisefficientinlargescalepredictionproblemsatheoreticalexplanation |