Analysis and prediction of hazard risks caused by tropical cyclones in southern China with fuzzy mathematical and grey models. (English) Zbl 1236.86014
Summary: A hazard-risk assessment model and a grey hazard-year prediction model (GHYPM) are constructed by integrating recent advances in the fuzzy mathematics, grey theory and information spread technique, and then applied to 17-year tropical cyclones (TCs) hazards in Southern China. In constructing the models, a genetic fuzzy mathematical algorithm is first developed to calculate the categorical and ranking weights of TC hazard impact and cause indicators, from which their combined weights are obtained after optimization. The hazard impact and cause index series are then found by coupling the combined weights with their corresponding down-scaled indicators. A two-dimensional normal-spread technique is employed to create a primitive information matrix and a fuzzy relation matrix in order to make fuzzy rough inference of hazard risks with the factorial space theory. An exceeded probability model is developed to assess the possibility of exceeding any given hazard-year category. Results from the GHYPM show that the simulated hazard risk values are more or less consistent with the hazard-impact index series, with more than 60% probability of exceeding a moderate hazard year in Southern China. Results also show small relative errors of the GHYPM, indicating its applicability to the prediction of TC hazard-years up to 20 years.
MSC:
| 86A32 | Geostatistics |
| 86A10 | Meteorology and atmospheric physics |
| 62M86 | Inference from stochastic processes and fuzziness |
| 62P12 | Applications of statistics to environmental and related topics |
Keywords:
combined weights; fuzzy mathematical models; hazard risk analysis; exceeded probability; tropical cyclones; grey prediction modelReferences:
| [1] | Zadeh, L. A., Fuzzy sets, Inform. Control, 8, 338-353 (1965) · Zbl 0139.24606 |
| [2] | Sun, B.-S.; Ma, W.-M., Fuzzy rough set model on two different universes and its application, Appl. Math. Model., 35, 1798-1809 (2011) · Zbl 1217.03041 |
| [3] | Hundecha, Y.; Bardossy, A.; Theisen, H.-W., Development of a fuzzy logic based rainfall-runoff model, Hydrol. Sci. J., 46, 363-377 (2001) |
| [4] | Iliadis, L. S.; Spartalis, S. I., Fundamental fuzzy relation concepts of a D.S.S. for the estimation of natural disasters’ risk (the case of a trapezoidal membership function), Math. Comput. Model., 42, 747-758 (2005) · Zbl 1090.91052 |
| [5] | Yui, P.-S.; Chen, S.-T.; Yang, T.-C., The potential of fuzzy multi-objective model for rainfall forecasting from typhoons, Nat. Hazards, 34, 131-150 (2005) |
| [6] | Cheng, S.-P.; Wang, R.-Y., Analyzing hazard potential of typhoon damage by applying grey analytic hierarchy process, Nat. Hazards, 33, 77-103 (2004) |
| [7] | Zhang, Y. L.; Liu, M., Application of grey prediction model GM (1,1) in fire accident, Acac Scientiarum Naturalium Universitais Nankaiensis (Natural Science Edition), 42, 11-15 (2009) |
| [8] | Huang, C.-F., Information matrix method for risk analysis of natural disaster, J. Natural Dis., 15, 1-10 (2006) |
| [9] | Zhang, J.-X.; Huang, C.-F.; Liu, X.-L., Geographical distribution and risk assessment of typhoon storm surge disasters in coastal regions of Guangdong Province in 1949-2005, J. Basic Sci. Eng., 16, 393-401 (2008) |
| [10] | Feng, L.-H.; Hong, W.-H., On the principle of maximum entropy and the risk analysis of disaster loss, Appl. Math. Model., 33, 2934-2938 (2009) · Zbl 1205.94057 |
| [11] | Andrade, G. M.; Fragoso, M. D.; Carneiro, A. A.F. M., A stochastic approach to the flood control problem, Appl. Math. Model., 25, 499-511 (2001) · Zbl 1031.86009 |
| [12] | Lu, W.-F., The Shanghai area tropical cyclone disaster situation’s appraisal and the famine year forecast, J. Natural Dis., 4, 40-45 (1995) |
| [13] | Chen, P.-Y.; Yang, Y.-H.; Lei, X.-T.; Qian, Y.-Z., Cause analysis and preliminary hazard estimate of typhoon disaster in China, J. Natural Dis., 18, 64-73 (2009) |
| [14] | Jin, J.-L.; Wei, Y.-M.; Ding, J., System evaluation model based on combined weights, Math. Pract. Theory, 33, 51-58 (2003) |
| [15] | Liu, S.-F.; Dang, Y.-G.; Fang, Z.-G., Grey System Theory and its Application (2005), Science Press: Science Press Beijing, pp. 172-175 |
| [16] | Liu, F.-Q.; Zhi, C.-J., Improvement of grey prediction model GM (1,1), Math. Pract. Theory, 35, 11-15 (2005) |
| [17] | Wen, K.-G., China Meteorological Disasters Dictionary (2007), Meteorological Press: Meteorological Press Beijing, pp. 199-250 |
| [18] | China Meteorological Administration (1991-2008). Tropical Cyclone Yearbook (1990-2007).; China Meteorological Administration (1991-2008). Tropical Cyclone Yearbook (1990-2007). |
| [19] | Friedman, J. H.; Turkey, J. W., A projection pursuit algorithm for exploratory data analysis, IEEE Trans. Comput., 23, 881-890 (1974) · Zbl 0284.68079 |
| [20] | Saaty, T. L., The Analytic Hierarchy Process (1980), McGraw-Hill: McGraw-Hill New York · Zbl 1176.90315 |
| [21] | Peng, X.-T.; Wang, P.-Z.; Kandel, A., Knowledge acquisition by random sets, Int. J. Intell. Syst., 11, 113-147 (1996) · Zbl 0843.68100 |
| [22] | Wang, P.-Z., A factor space approach to knowledge representation, Fuzzy Sets Syst., 36, 113-124 (1990) · Zbl 0698.68088 |
| [23] | Wang, L.-X.; Mendel, J. M., Generating fuzzy rules by learning through examples, IEEE Trans. Syst. Man Cybernet., SMC-22, 1414-1427 (1992) |
| [24] | Zhang, Q.; Wu, L.-G.; Liu, Q.-F., Tropical cyclone damages in China (1983-2006), Bull. Am. Meteor. Soc., 90, 489-495 (2009) |
| [25] | Huang, C.-F.; Shi, Y., Towards Efficient Fuzzy Information Processing Using the Principle of Information Diffusion (2002), Physica-Verlag, Springer: Physica-Verlag, Springer Heidelberg, pp. 45-110 · Zbl 1023.68122 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
