查询字段 中文标题 英文标题 作者中文名 作者英文名 单位中文名 单位英文名 中文关键词 英文关键词 中文摘要 英文摘要 基金项目中文名 DOI 栏目名称 文章编号 检索词 从 1975 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 到 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991 1990 1989 1988 1987 1986 1985 1984 1983 1982 1981 1980 1979 1975
 水利水运工程学报   2019 Issue (6): 38-49.  DOI: 10.16198/j.cnki.1009-640X.2019.06.005 0

### 引用本文 [复制中英文]

[复制中文]
JIN Juliang, SHEN Shixing, ZHANG Haoyu, et al. Dynamic evaluation of regional water resources carrying capacity based on full partial certainty degree[J]. Hydro-science and Engineering, 2019(6): 38-49. (in Chinese) DOI: 10.16198/j.cnki.1009-640X.2019.06.005.
[复制英文]

### 文章历史

1. 合肥工业大学 土木与水利工程学院, 安徽 合肥 230009;
2. 合肥工业大学 水资源与环境系统工程研究所, 安徽 合肥 230009

1 评价方法的构建

 ${a_1}\left( {i,k,j} \right) = \left\{ \begin{array}{l} 1,\;正向指标\;x\left( {i,k,j} \right) \le s\left( {1,j} \right)或反向指标\;x\left( {i,k,j} \right) \ge s\left( {1,j} \right)\\ 1 - 2\frac{{x\left( {i,k,j} \right) - s\left( {1,j} \right)}}{{s\left( {2,j} \right) - s\left( {1,j} \right)}},正向指标\;s\left( {1,j} \right) < {x_{ij}} \le s\left( {2,j} \right)\;或反向指标\\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;s\left( {i,1,j} \right) > x\left( {i,k,j} \right) \ge s\left( {2,j} \right)\\ - 1,正向指标\;x\left( {i,k,j} \right) > s\left( {2,j} \right)\;或反向指标\;x\left( {i,k,j} \right) \ge s\left( {2,j} \right) \end{array} \right.$ (1)
 ${b_1}\left( {i,k,j} \right) = \left\{ \begin{array}{l} 1 - 2\frac{{s\left( {1,j} \right) - x\left( {i,k,j} \right)}}{{s\left( {1,j} \right) - s\left( {0,j} \right)}},正向指标\;x\left( {i,k,j} \right) \le s\left( {1,j} \right)\;或反向指标\;x\left( {i,k,j} \right) \ge s\left( {1,j} \right)\\ 1,正向指标\;s\left( {1,j} \right) < x\left( {i,k,j} \right) \le s\left( {2,j} \right)\;或反向指标\;s\left( {1,j} \right) > x\left( {i,k,j} \right) \ge s\left( {2,j} \right)\\ 1 - 2\frac{{x\left( {i,k,j} \right) - s\left( {2,j} \right)}}{{s\left( {3,j} \right) - s\left( {2,j} \right)}},正向指标\;s\left( {2,j} \right) < x\left( {i,k,j} \right) \le s\left( {3,j} \right)\;或反向指标\\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{s_{2j}} > x\left( {i,k,j} \right) \ge {s_{3j}}\\ - 1,正向指标\;x\left( {i,k,j} \right) > s\left( {3,j} \right)或反向指标\;x\left( {i,k,j} \right) < s\left( {3,j} \right) \end{array} \right.$ (2)
 ${c_1}\left( {i,k,j} \right) = \left\{ \begin{array}{l} - 1,正向指标\;x\left( {i,k,j} \right) \le s\left( {1,j} \right)或反向指标\;x\left( {i,k,j} \right) \ge s\left( {1,j} \right)\\ 1 - 2\frac{{s\left( {2,j} \right) - x\left( {i,k,j} \right)}}{{s\left( {2,j} \right) - s\left( {1,j} \right)}},正向指标\;s\left( {1,j} \right) < x\left( {i,k,j} \right) \le s\left( {2,j} \right)或反向指标\\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;s\left( {1,j} \right) > x\left( {i,k,j} \right) \ge s\left( {2,j} \right)\\ 1,正向指标\;s\left( {2,j} \right) < x\left( {i,k,j} \right) \le s\left( {3,j} \right)或反向指标\;s\left( {2,j} \right) > x\left( {i,k,j} \right) \ge s\left( {3,j} \right) \end{array} \right.$ (3)

 $\left\{ \begin{array}{l} a_2^*\left( {i,k,j} \right) = 0.5 + 0.5{a_1}\left( {i,k,j} \right)\\ b_2^*\left( {i,k,j} \right) = 0.5 + 0.5{b_1}\left( {i,k,j} \right)\\ c_2^*\left( {i,k,j} \right) = 0.5 + 0.5{c_1}\left( {i,k,j} \right) \end{array} \right.$ (4)
 $\left\{ \begin{array}{l} {a_2}\left( {i,k,j} \right) = \frac{{a_2^*\left( {i,k,j} \right)}}{{a_2^*\left( {i,k,j} \right) + b_2^*\left( {i,k,j} \right) + c_2^*\left( {i,k,j} \right)}}\\ {b_2}\left( {i,k,j} \right) = \frac{{b_2^*\left( {i,k,j} \right)}}{{a_2^*\left( {i,k,j} \right) + b_2^*\left( {i,k,j} \right) + c_2^*\left( {i,k,j} \right)}}\\ {c_2}\left( {i,k,j} \right) = \frac{{c_2^*\left( {i,k,j} \right)}}{{a_2^*\left( {i,k,j} \right) + b_2^*\left( {i,k,j} \right) + c_2^*\left( {i,k,j} \right)}} \end{array} \right.$ (5)

 ${u_{2,1}}\left( {i,k,j} \right) = {a_{2,1}}\left( {i,k,j} \right) + {b_{2,1}}\left( {i,k,j} \right)I + {c_{2,1}}\left( {i,k,j} \right)J$ (6)
 ${u_{2,1}}\left( {i,k} \right) = {a_{2,1}}\left( {i,k} \right) + {b_{2,1}}\left( {i,k} \right)I + {c_{2,1}}\left( {i,k} \right)J$ (7)
 ${u_{2,1,i}} = {a_{2,1,i}} + {b_{2,1,i}}I + {c_{2,1,i}}J$ (8)

 $\left\{ \begin{array}{l} {a_g}\left( {i,k} \right) = \frac{{{a_{2g}}\left( {i,k} \right)}}{{{a_{2g}}\left( {i,k} \right) + {b_{2g}}\left( {i,k} \right) + {c_{2g}}\left( {i,k} \right)}}\\ {a_{gi}} = \frac{{{a_{2gi}}}}{{{a_{2gi}} + {b_{2gi}} + {c_{2gi}}}}\\ {b_g}\left( {i,k} \right) = \frac{{{b_{2g}}\left( {i,k} \right)}}{{{a_{2g}}\left( {i,k} \right) + {b_{2g}}\left( {i,k} \right) + {c_{2g}}\left( {i,k} \right)}}\\ {b_{gi}} = \frac{{{b_{2gi}}}}{{{a_{2gi}} + {b_{2gi}} + {c_{2gi}}}}\\ {c_g}\left( {i,k} \right) = \frac{{{c_{2g}}\left( {i,k} \right)}}{{{a_{2g}}\left( {i,k} \right) + {b_{2g}}\left( {i,k} \right) + {c_{2g}}\left( {i,k} \right)}}\\ {c_{gi}} = \frac{{{c_{2gi}}}}{{{a_{2gi}} + {b_{2gi}} + {c_{2gi}}}} \end{array} \right.$ (9)
 ${u_g}\left( {i,k} \right) = {a_g}\left( {i,k} \right) + {b_g}\left( {i,k} \right)I + {c_g}\left( {i,k} \right)J$ (10)
 ${u_{gi}} = {a_{gi}} + {b_{gi}}I + {c_{gi}}J$ (11)

 ${\xi _{{b_{gi}}{a_{gi}}}} = {a_{gi}}\left( {1 + {b_{gi}}} \right)$ (12)

 ${r_{{b_{gi}}{a_{gi}}}} = \frac{1}{N}\sum\limits_{i = 1}^N {{\xi _{{b_{gi}}{a_{gi}}}}}$ (13)

 ${u_{gi}} = {a_{gi}} + {b_{gi}}\left( {{{r'}_{{b_{gi}}{a_{gi}}}} - {{r'}_{{b_{gi}}{c_{gi}}}}} \right) + {c_{gi}}J$ (14)

 $v_{gi}^ * = 0.5 + 0.5{u_{gi}}$ (15)

 ${v_{gi}} = v_{gi}^*/\sum\limits_{g = 1}^G {v_{gi}^*}$ (16)

 ${H_i} = \sum\limits_{g = 1}^G {{v_{gi}}} \cdot g$ (17)

 ${g_i} = \left\{ \begin{array}{l} 1,{v_{1i}} > \lambda \\ 2,{v_{1i}} \le \lambda \;且\;{v_{1i}} + {v_{2i}} > \lambda \\ 3,{v_{1i}} + {v_{2i}} \le \lambda \;且\;{v_{1i}} + {v_{2i}} + {v_{3i}} > \lambda \end{array} \right.$ (18)

2 实例分析

 图 1 2011—2015年安徽省16个地市水资源承载力时空分布 Fig.1 Spatial-temporal distribution of water resources carrying capacity in 16 cities of Anhui Province from 2011 to 2015

 图 2 2011—2015年安徽省16个地市水资源承载支撑力时空分布 Fig.2 Spatial and temporal distribution of water resources support capacity in 16 cities of Anhui Province from 2011 to 2015
 图 3 2011—2015年安徽省16个地市水资源承载压力时空分布 Fig.3 Spatial-temporal distribution of water resources carrying pressure in 16 cities of Anhui Province from 2011 to 2015
 图 4 2011—2015年安徽省16个地市水资源承载调控力时空分布 Fig.4 Spatial and temporal distribution of water resources control capacity in 16 cities of Anhui Province from 2011 to 2015

3 结语

(1) 运用同一度、差异度、对立度三者之间的模糊关系信息，求解同一度与差异度、对立度与差异度之间的全偏确定度，从而改进差异度系数的分配方式，实际运用的结果与安徽省水资源承载实际情况基本一致，表明对差异度系数I的取值方式是合理可靠的，充分挖掘出联系数隐含的信息。

(2) 安徽省水资源承载力状况有向好趋势，但是仍然处于临界超载状态，由北往南有着明显的地区差别，其中皖北地区水资源形势处在超载状态，前景不容乐观，皖中地区水资源形势处在临界超载状态，皖南地区水资源形势处在未超载状态。水资源支撑力等级值方面皖北较大，皖南中等，皖北最小；压力方面皖北、皖南较小，皖中较大; 调控力方面皖北较大，皖中、皖南较小。

(3) 安徽省皖北水资源承载力处在超载状态，主要由于该地区水资源支撑力、调控力较小，且压力较大，导致最终的水资源形势不乐观。皖中水资源承载力处在临界超载状态，主要由于3个子系统相对均衡，且3个系统等级值均较高。皖南水资源承载力处在未超载状态，主要是由于水资源调控力、支撑力较大，压力较小，水资源承载力状况全省最好。

 [1] 孙鸿烈. 中国资源科学百科全书[M]. 北京: 中国大百科全书出版社, 2000. ( SUN Honglie. China encyclopedia of resources science[M]. Beijing: China Encyclopedia Publishing House, 2000. (in Chinese)) [2] 冯尚友. 水资源持续利用与管理导论[M]. 北京: 科学出版社, 2000. ( FENG Shangyou. Introduction to sustainable utilization of water resources[M]. Beijing: Science Press, 2000. (in Chinese)) [3] 汤奇成, 张捷斌. 西北干旱地区水资源与生态环境保护[J]. 地理科学进展, 2001, 20(3): 227-233. ( TANG Qicheng, ZHANG Jiebin. Water resources and eco-environment protection in the arid regions in Northwest of China[J]. Progress in Geography, 2001, 20(3): 227-233. (in Chinese)) [4] 金菊良, 沈时兴, 郦建强, 等. 基于联系数的区域水资源承载力评价与诊断分析方法[J]. 华北水利水电大学学报(自然科学版), 2018, 39(1): 1-9. ( JIN Juliang, SHEN Shixing, LI Jianqiang, et al. Assessment and diagnosis analysis method for regional water resources carrying capacity based on connection number[J]. Journal of North China University of Water Resources and Electric Power (Natural Science Edition), 2018, 39(1): 1-9. (in Chinese)) [5] 吴开亚, 金菊良, 魏一鸣, 等. 基于指标体系的流域水安全诊断评价模型[J]. 中山大学学报(自然科学版), 2008, 47(4): 105-113. ( WU Kaiya, JIN Juliang, WEI Yiming, et al. Diagnosis assessment model of watershed water security based on index system[J]. Acta Scientiarum Naturalium Universitatis Sunyatseni, 2008, 47(4): 105-113. (in Chinese)) [6] REN C F, GUO P, LI M, et al. An innovative method for water resources carrying capacity research—Metabolic theory of regional water resources[J]. Journal of Environmental Management, 2016, 167: 139-146. [7] HARRIS J M, KENNEDY S. Carrying capacity in agriculture: global and regional issues[J]. Ecological Economics, 1999, 29(3): 443-461. [8] 张永勇, 夏军, 王中根. 区域水资源承载力理论与方法探讨[J]. 地理科学进展, 2007, 26(2): 126-132. ( ZHANG Yongyong, XIA Jun, WANG Zhonggen. Research on regional water resources carrying capacity theory and method[J]. Progress in Geography, 2007, 26(2): 126-132. (in Chinese)) [9] 金菊良, 董涛, 郦建强, 等. 区域水资源承载力评价的风险矩阵方法[J]. 华北水利水电大学学报(自然科学版), 2018, 39(2): 46-50. ( JIN Juliang, DONG Tao, LI Jianqiang, et al. Risk matrix method for evaluating regional water resources carrying capacity[J]. Journal of North China University of Water Resources and Electric Power (Natural Science Edition), 2018, 39(2): 46-50. (in Chinese)) [10] MENG L H, CHEN Y N, LI W H, et al. Fuzzy comprehensive evaluation model for water resources carrying capacity in Tarim River Basin, Xinjiang, China[J]. Chinese Geographical Science, 2009, 19(1): 89-95. [11] MOSLEY L M, ZAMMIT B, LEYDEN E, et al. The impact of extreme low flows on the water quality of the Lower Murray River and Lakes (South Australia)[J]. Water Resources Management, 2012, 26(13): 3923-3946. [12] 金菊良, 张浩宇, 宁少尉, 等. 效应全偏联系数及其在区域水资源承载力评价中的应用[J]. 华北水利水电大学学报(自然科学版), 2019, 40(1): 1-8. ( JIN Juliang, ZHANG Haoyu, NING Shaowei, et al. Effect full partial connection number and its application in evaluation of regional water resources carrying capacity[J]. Journal of North China University of Water Resources and Electric Power (Natural Science Edition), 2019, 40(1): 1-8. (in Chinese)) [13] 左其亭, 张培娟, 马军霞. 水资源承载能力计算模型及关键问题[J]. 水利水电技术, 2004, 35(2): 5-8, 11. ( ZUO Qiting, ZHANG Peijuan, MA Junxia. Calculating model and key questions about carrying capacity of water resources[J]. Water Resources and Hydropower Engineering, 2004, 35(2): 5-8, 11. (in Chinese)) [14] 刘童, 杨晓华, 宋帆. 水资源承载力评价的Logistic集对分析模型及其应用[J]. 华北水利水电大学学报(自然科学版), 2019, 40(1): 27-33. ( LIU Tong, YANG Xiaohua, SONG Fan. Logistic set pair analysis model for water resources carrying capacity assessment and its application[J]. Journal of North China University of Water Resources and Electric Power (Natural Science Edition), 2019, 40(1): 27-33. (in Chinese)) [15] 李陶, 付强, 丁红. 基于灰色关联度的集对分析差异系数研究[J]. 黑龙江水专学报, 2010, 37(1): 97-99. ( LI Tao, FU Qiang, DING Hong. Research for variation coefficient in set pair analysis based on correlation degree of grey theory[J]. Journal of Heilongjiang Hydraulic Engineering, 2010, 37(1): 97-99. (in Chinese)) [16] 邓聚龙. 灰色系统理论教程[M]. 武汉: 华中理工大学出版社, 1990. ( DENG Julong. Course of grey system theory[M]. Wuhan: Huazhong University of Science and Technology Press, 1990. (in Chinese)) [17] 李辉, 金菊良, 吴成国, 等. 基于联系数的安徽省水资源承载力动态诊断评价研究[J]. 南水北调与水利科技, 2018, 16(1): 42-49. ( LI Hui, JIN Juliang, WU Chengguo, et al. Dynamic evaluation and diagnostic analysis for water resources carrying capacity in Anhui province based on connection number[J]. South-to-North Water Transfers and Water Science & Technology, 2018, 16(1): 42-49. (in Chinese)) [18] 赵克勤. 集对分析及其初步应用[M]. 杭州: 浙江科技出版社, 2000. ( ZHAO Keqin. Set pair analysis and its application[M]. Hangzhou: Zhejiang Science and Technology Press, 2000. (in Chinese)) [19] SONG X M, KONG F Z, ZHAN C S. Assessment of water resources carrying capacity in Tianjin City of China[J]. Water Resources Management, 2011, 25(3): 857-873. [20] 王友贞, 施国庆, 王德胜. 区域水资源承载力评价指标体系的研究[J]. 自然资源学报, 2005, 20(4): 597-604. ( WANG Youzhen, SHI Guoqing, WANG Desheng. Study on evaluation indexes of regional water resources carrying capacity[J]. Journal of Natural Resources, 2005, 20(4): 597-604. (in Chinese)) [21] 金菊良, 洪天求, 王文圣. 基于熵和FAHP的水资源可持续利用模糊综合评价模型[J]. 水力发电学报, 2007, 26(4): 22-28. ( JIN Juliang, HONG Tianqiu, WANG Wensheng. Entropy and FAHP based fuzzy comprehensive evaluation model of water resources sustaining utilization[J]. Journal of Hydroelectric Engineering, 2007, 26(4): 22-28. (in Chinese)) [22] 金菊良, 沈时兴, 陈梦璐, 等. 遗传层次分析法在区域水资源承载力评价指标体系筛选中的应用[J]. 华北水利水电大学学报(自然科学版), 2019, 40(2): 1-6, 15. ( JIN Juliang, SHEN Shixing, CHEN Menglu, et al. Application of genetic analytic hierarchy process in screening the evaluation index system of regional water resources carrying capacity[J]. Journal of North China University of Water Resources and Electric Power (Natural Science Edition), 2019, 40(2): 1-6, 15. (in Chinese)) [23] CUI Y, FENG P, JIN J L, et al. Water resources carrying capacity evaluation and diagnosis based on set pair analysis and improved the entropy weight method[J]. Entropy, 2018, 20(5): 359. [24] 金菊良, 吴开亚, 魏一鸣. 基于联系数的流域水安全评价模型[J]. 水利学报, 2008, 39(4): 401-409. ( JIN Juliang, WU Kaiya, WEI Yiming. Connection number based assessment model for watershed water security[J]. Journal of Hydraulic Engineering, 2008, 39(4): 401-409. (in Chinese)) [25] 王文圣, 金菊良, 丁晶, 等. 水资源系统评价新方法——集对评价法[J]. 中国科学(E辑):技术科学, 2009, 52(9): 3017-3023. ( WANG Wensheng, JIN Juliang, DING Jing, et al. A new approach to water resources system assessment―set pair analysis method[J]. Science in China(SerE): Technological Sciences, 2009, 52(10): 3017-3023. (in Chinese)) [26] 金菊良, 张浩宇, 陈梦璐, 等. 基于灰色关联度和联系数耦合的农业旱灾脆弱性评价和诊断研究[J]. 灾害学, 2019, 34(1): 1-7. ( JIN Juliang, ZHANG Haoyu, CHEN Menglu, et al. Evaluation and diagnosis of agricultural drought vulnerability based on grey correlation and connection number coupling[J]. Journal of Catastrophology, 2019, 34(1): 1-7. (in Chinese)) [27] ZOU Q, ZHOU J Z, ZHOU C, et al. Comprehensive flood risk assessment based on set pair analysis-variable fuzzy sets model and fuzzy AHP[J]. Stochastic Environmental Research and Risk Assessment, 2013, 27(2): 525-546. [28] 程乾生. 属性识别理论模型及其应用[J]. 北京大学学报(自然科学版), 1997, 33(1): 12-20. ( CHENG Qiansheng. Attribute recognition theoretical model with application[J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 1997, 33(1): 12-20. (in Chinese))
Dynamic evaluation of regional water resources carrying capacity based on full partial certainty degree
JIN Juliang 1,2, SHEN Shixing 1,2, ZHANG Haoyu 1,2, CHEN Menglu 1,2, CHEN Yajing 1, ZHANG Huolian 1, XU Xinghan 1
1. School of Civil and Hydraulic Engineering, Hefei University of Technology, Hefei 230009, China;
2. Water Resources and Environmental Systems Engineering Institute, Hefei University of Technology, Hefei 230009, China
Abstract: The value of information should be mined as much as possible when using the connection number, so as to evaluate the spatial and temporal situation of regional water resources carrying capacity more accurately. In this article, by using the fuzzy relation between the identical, discrepancy and contrary degree as the basis of calculation, the partial certainty between them is solved, and the distribution mode of the coefficient of difference degree is improved. The method is applied to the dynamic evaluation of regional water resources carrying capacity. The application results show that: 1) The results obtained by the improved distribution method of difference coefficient are basically consistent with the actual situation of water resources carrying capacity in Anhui Province. 2) The water resources carrying capacity in Anhui Province from 2011 to 2015 has a trend of good development with time, but it is still in the critical condition. According to the spatial distribution, the status in Anhui Province is gradually improved from north to south, in which the north is in a state of overload, the middle is in a critical state of overload, and the south is in a state of being able to carry. In terms of sub-systems, the bearing capacity is larger in south, the pressure in north is greater, and the control power is on the larger side of middle Anhui and southern Anhui. 3) The evaluation results show that the northern Anhui Province is in an overload situation, mainly due to the weak support of water resources; relative balanced development among load-bearing subsystems is the main reason for the critical condition of load-bearing in central Anhui Province; southern Anhui Province has the best water resources carrying capacity, benefiting from strong control and support force. Above all, the results of the dynamic evaluation analysis are reasonable and reliable. Since the fact that the method is very intuitive and simple, it has proved that the method has considerable value in popularizing and applying in the dynamic evaluation and analysis of the carrying capacity of other resources and environment.
Key words: water resources carrying capacity    dynamic evaluation    temporal and spatial situation    connection number    full partial certainty degree    Anhui Province