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石家庄铁道大学

数学建模竞赛论文

题目B：北京市水资源短缺风险综合评价

队号 19

领队教师：马祥旺

2014年5月18

日

数学竞赛论文

一． 摘要 ··································································································· 2

关键词： ··································································································· 2 二． 问题重述 ····························································································· 3 B题：水资源短缺风险综合评价 ··········································································· 3 三． 问题提出 ····························································································· 4 四． 建模过程 ····························································································· 4

基本假设 ··································································································· 4

符号说明 ····························································································· 5 问题一： ··································································································· 6

1.构建模糊物元 ···················································································· 7 2.权重系数的熵值法确定 ········································································ 7 3. 权重求解及主要风险因子的确定 ··························································· 9 结论 ·································································································· 12 问题二 ····································································································· 13 问题三 ····································································································· 15 问题四 ····································································································· 17

分析思路 ···························································································· 17 给北京市水行政主管部门的建议报告 ······················································· 18 水资源短缺原因 ·················································································· 18 缓解北京水资源短缺的有效措施与建议 ···················································· 18

五、模型评价与改进························································································· 21 六、参考文献 ·································································································· 22

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数学竞赛论文

一． 摘要

“水资源短缺风险综合评价”模型是通过模糊物元分析法确定危险因子，通过危险因子所占的权重提出建议，保障水资源的供应。基于熵权法所建立的模型，通过各个危险因子所占的权重进行风险等级评测。确立风险等级的划分。通过对历年统计数据进行分析，做出其合理的线性方程，合理大胆预测北京市未来水资源发展趋势，由预测发展趋势可以得到有效预警并采取措施。通过合理分配水资源走向，调整产业结构，合理外迁工业等严重耗水资源企业能有效降低水资源短缺风险发生的可能性。

关键词：

水资源；北京用水；模糊物元法；风险等级划分；发展预测；熵权分析法；多元线性拟合；隶属函数

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