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Subtractive set paire potential trapezoidal fuzzy number random simulation method for drought risk assessment
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摘要:
定量评估旱灾风险对经济社会的防控管理具有重要意义。针对差异度系数取值具有峰值较宽的分布特征及其随评价样本值变化的动态特性问题，在半偏减法集对势联系分量微观层次迁移的基础上，采用梯形模糊数动态取值表征差异度系数的不确定性和连续变化过程，通过随机模拟方法模拟梯形模糊数，实现以置信区间形式定量描述评价结果，由此构建基于减法集对势梯形模糊数随机模拟的旱灾风险评估模型，并在宿州市进行旱灾风险动态评估的实证研究，与现有方法作对比分析。结果表明：宿州市2007—2010年间旱灾风险负向发展趋势强度增大，2011—2017年间旱灾风险负向发展趋势强度减小，风险等级长期高于2级，处于偏旱状态，2010年为最危险年份；整体波动幅度较小，有向好发展的趋势，判别出危险性子系统和抗旱能力子系统是导致宿州市旱灾风险的主要因素。该方法原理解释性强、结果合理准确，评价结果以置信区间形式表示，为旱灾风险的动态分析和定量评估提供了新途径。
Abstract:Quantitative assessment of drought risk is of great significance for economic and social prevention and control management. In response to the problem of the wide peak distribution characteristics of the difference coefficient value and its dynamic characteristics as it changes with the evaluation sample value, based on the micro level migration of the connection components in the semi partial subtraction set pair potential, the trapezoidal fuzzy number dynamic value is used to characterize the uncertainty and continuous change process of the difference coefficient. The trapezoidal fuzzy number is simulated using random simulation method to quantitatively describe the evaluation results in the form of confidence intervals, a drought risk assessment model based on subtractive set pairwise potential trapezoidal fuzzy number random simulation is constructed, and an empirical study on dynamic drought risk assessment is conducted in Suzhou City, comparing and analyzing with existing methods. The results show that the negative development trend of drought risk in Suzhou City increased in intensity from 2007 to 2010, and decreased in intensity from 2011 to 2017. The risk level remained above level 2 for a long time and was in a state of partial drought. 2010 was the most dangerous year; the overall fluctuation range is relatively small and there is a trend towards positive development. It is identified that the risk subsystem and drought resistance subsystem are the main factors leading to the drought risk in Suzhou City. This method has strong explanatory principles, reasonable and accurate results, and the evaluation results are expressed in the form of confidence intervals, providing a new and effective approach for dynamic analysis and quantitative assessment of drought risk.
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图 1 差异度系数与等级标准阈值的对应关系
Figure 1. Correspondence between difference coefficient and grade standard thresholds
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图 2 “I”最可能值及左右两端点的转化
Figure 2. The most probable value of “I” and the transformation of left and right end points
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图 3 梯形模糊数及两种临界状态下隶属度函数图
Figure 3. Trapezoidal fuzzy number and membership function diagram under two critical states
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图 4 随机模拟100组联系分量的联系数值和评价等级值
Figure 4. Connection values and evaluation level values of 100 sets of connection components in random simulation
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图 5 宿州市2007—2017年旱灾风险联系数值及评价等级值
Figure 5. Connection number and evaluation grade value of drought risk in Suzhou City from 2007 to 2017
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图 6 宿州市2007—2017年旱灾风险各子系统联系数值
Figure 6. Connection number of each subsystem in the drought risk of Suzhou City from 2007 to 2017
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图 7 宿州市2007—2017年旱灾风险各子系统评价等级值
Figure 7. Evaluation grade values of each subsystem of drought risk in Suzhou City from 2007 to 2017
表 1 基于梯形模糊数静态取值随机模拟的宿州市旱灾风险联系数值及评价等级值
Table 1 Connection number and evaluation grade value of drought risk in Suzhou City based on random simulation of static value of trapezoidal fuzzy number
年份 样本联系数 差异度系数值区间 联系数值区间 评价等级值区间 2007 0.288+0.363I+0.349J [−0.803, 0.806] [−0.352, 0.232] [1.768, 2.352] 2008 0.236+0.385I+0.379J [−0.803, 0.806] [−0.452, 0.167] [1.833, 2.452] 2009 0.216+0.399I+0.385J [−0.803, 0.806] [−0.489, 0.153] [1.847, 2.489] 2010 0.190+0.388I+0.422J [−0.803, 0.806] [−0.544, 0.081] [1.919, 2.544] 2011 0.225+0.392I+0.383J [−0.803, 0.806] [−0.473, 0.158] [1.842, 2.473] 2012 0.232+0.393I+0.375J [−0.803, 0.806] [−0.459, 0.174] [1.826, 2.459] 2013 0.258+0.395I+0.347J [−0.803, 0.806] [−0.406, 0.229] [1.771, 2.406] 2014 0.239+0.408I+0.353J [−0.803, 0.806] [−0.442, 0.215] [1.785, 2.442] 2015 0.241+0.407I+0.352J [−0.803, 0.806] [−0.438, 0.217] [1.783, 2.438] 2016 0.289+0.401I+0.310J [−0.803, 0.806] [−0.343, 0.302] [1.698, 2.343] 2017 0.287+0.404I+0.309J [−0.803, 0.806] [−0.346, 0.304] [1.696, 2.346] 
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表 2 基于梯形模糊数动态取值随机模拟的宿州市旱灾风险联系数值、态势及评价等级值
Table 2 Connection number, situation, and evaluation grade value of drought risk in Suzhou City based on random simulation of dynamic value of trapezoidal fuzzy number
年份 差异度系数值区间 联系数值区间 联系数值期望及态势 半偏减法集对势值及态势 评价等级值区间 评价等级值期望 级别特征值 2007 [−0.404, 0.345] [−0.208, 0.064] −0.072（均势） −0.078（均势） [1.936, 2.208] 2.072 2.061 2008 [−0.420, 0.281] [−0.305, −0.035] −0.170（均势） −0.188（均势） [2.035, 2.305] 2.170 2.143 2009 [−0.419, 0.253] [−0.336, −0.068] −0.202（偏反势） −0.225（偏反势） [2.068, 2.336] 2.202 2.169 2010 [−0.454, 0.226] [−0.408, −0.144] −0.276（偏反势） −0.307（偏反势） [2.144, 2.408] 2.276 2.232 2011 [−0.420, 0.266] [−0.323, −0.054] −0.188（均势） −0.209（偏反势） [2.054, 2.323] 2.188 2.158 2012 [−0.413, 0.273] [−0.305, −0.036] −0.171（均势） −0.189（均势） [2.036, 2.305] 2.171 2.143 2013 [−0.388, 0.301] [−0.242, 0.030] −0.106（均势） −0.118（均势） [1.970, 2.242] 2.106 2.089 2014 [−0.389, 0.276] [−0.273, −0.001] −0.137（均势） −0.153（均势） [2.001, 2.273] 2.137 2.114 2015 [−0.388, 0.278] [−0.269, 0.002] −0.133（均势） −0.148（均势） [1.998, 2.269] 2.133 2.111 2016 [−0.352, 0.330] [−0.162, 0.111] −0.025（均势） −0.028（均势） [1.889, 2.162] 2.025 2.021 2017 [−0.350, 0.327] [−0.163, 0.110] −0.027（均势） −0.029（均势） [1.890, 2.163] 2.027 2.022
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