模糊环境下水资源系统优化决策理论与方法研究
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摘要
水资源的开发、利用、治理、保护、管理是人类作用于自然水系统的理性活动。人类通过采取上述各种活动从自然水系统中或获取资源，或实施减灾把损失减小，而人类的这些活动必然涉及决策。影响水资源系统优化决策的因素有很多，涉及到自然、社会、经济、技术等多个相互联系但又相互制约的因素。这些因素可以划分为两类：复杂性模式和不确定性模式。模糊集理论对处理这两种模式表现出强大的能力，为此本文在模糊水文水资源学有关优化决策理论、模型与方法的基础上，研究了模糊环境下的水资源系统优化决策问题，其主要研究内容和成果如下：
(1)在分析目标相对隶属度计算公式类型的基础上，提出了一组相对隶属度计算公式。并通过水库洪水优化调度方案优选的实例分析了非线性程度和不同类型的相对隶属度计算公式对决策结果的影响。本文提出的相对隶属度计算公式综合考虑了目标特征值变化范围和权重的影响，因而能得到较好的计算结果。进一步分析了相对隶属度的变化对决策结果影响的敏感性，给出了保持模糊优选模型最优决策序列不变的相对隶属度变化范围的一个充分条件。
(2)模糊优选、模糊模式识别和模糊聚类是水资源系统优化模糊集分析理论的数学基础，在水资源系统优化决策中获得广泛的应用。然而这些模型在模糊环境下如何应用，尚缺乏研究。本文在分析三角模糊数之间距离和梯形模糊数之间距离的计算公式的基础上，把模糊数的概念分别引入陈守煜教授建立的模糊优选、模糊识别和模糊聚类模型中，从而把这些模型拓展应用到模糊环境下优化决策问题的求解。可以有效地处理模糊环境下的决策，方便地获取决策者的经验、知识和偏好，对求解模糊环境下的复杂水资源系统优化决策问题提供了一种新的方法。实例验证了这些方法的可行性和有效性。
(3)把模糊环境下的模糊识别理论具体应用到地下水脆弱性评价中。参照DRASTIC方法的经验性数据，给出了10个级别7项指标以三角模糊数表示的标准特征值，给出了三角模糊数表示的指标权重。并由此提出了模糊环境下地下水污染性难易程度评价的模糊识别方法。大连市地下水脆弱性评价表明此方法具有实用性和操作性的特点。
(4)水资源系统决策常常具有多目标多阶段特性，本文将模糊模式识别模型，模糊交叉迭代模型以及模糊环境下的模糊识别模型作为一类模糊集合算子。这类算子不仅可以集成定量目标和定性目标的影响，还可以在动态决策过程中通过非结构性决策分析方法实时地获取决策者的经验、知识和偏好。然后把这类模糊集合算子结合到模糊识别动态规划中，把模糊识别动态规划模型拓展应用于求解模糊环境条件下的水资源系统多
目标多阶段决策问题。上述算子通过水资源优化配置和梯级水库防洪优化调度两个实例
予以验证。
（5）把模糊模式识别模型与遗传算法有机地结合起来，提出了一种多目标遗传算
法。并应用此遗传算法对丰满水电站防洪发电多目标优化调度问题进行了研究，提出了
防洪与发电多目标优化调度模型。在模型求解过程中，将模糊模式识别模型作为遗传算
法的适应度函数，丰满水电站防洪与发电多目标优化调度研究表明了这种方法的实用性
和有效性。
最后对全文作了总结，并对有待进一步研究的问题作了展望。
The exploitation, utilization, restoration, protection and management of water resources are all the activities to natural water systems, by which human beings can obtain the resources or reduce the loss from disasters. The above activities must involve decision makings. The factors effecting optimization of water resources systems arise from nature, society, economy, techniques, which are classified into two types: complex paradigm and uncertainty paradigm. Fuzzy sets theory is a powerful tool to deal with the two paradigms. Based on theories, models and approaches of optimization and decision makings in the context of fuzzy hydrology and water resources, this paper concentrates on the theories of optimization and decision making for water resources systems under fuzzy environment. The conclusions are as follows.
By analyzing the types of the formulas of relative membership degrees, a pair of formulas of relative membership degree is proposed. The effects on the optimization results from non-linearization and different types are analyzed through the case study of optimum operation of flood control. The formulas proposed in this paper are with good results because of the integration of the influence from the scope of objective values and objective weights. Furthermore, the sensitivity of relative membership degrees is analyzed and a sufficient condition is derived for keeping the optimal decision ranking unchanged.
Fuzzy optimization, fuzzy pattern recognition and fuzzy clustering are the mathematical basis for optimization and decision of water resources systems, and they have received a variety of applications. However there is a little study on how to apply the models to fuzzy environment. This paper first introduces the distance measure between triangular fuzzy numbers and between trapezoid fuzzy numbers. Then it applies the fuzzy numbers to the models proposed by Prof. Chen Shouyu, including fuzzy optimization, fuzzy pattern recognition and fuzzy clustering. In this way, the models are extended to optimization and decision makings under fuzzy environment. The proposed models can efficiently deal with uncertainty and capture the judgment, knowledge and preference, so they provide a new approach to complex optimization and decision making for water resources under fuzzy environment. The case study demonstrates the efficiency and feasibility of the proposed models.
The proposed fuzzy pattern recognition model under fuzzy environment is applied to the
IV
evaluation of groundwater vulnerability. According to the experiential data of the DRASTIC index, the standard values of 10 classes for 7 indexes are proposed in the form of triangular fuzzy numbers, and similarly the weights of indexes are expressed in the form of triangular fuzzy numbers. A fuzzy recognition approach thereby is applied to evaluate the groundwater vulnerability under fuzzy environment. The case study of Dalian shows that the approach is robust and practical.
Decision makings of water resources systems are of the characteristics of multi-objective and multistage. The fuzzy pattern recognition model, fuzzy cross iteration model and fuzzy pattern recognition model under fuzzy environment are regarded as a class of aggregation operators. The operators can not only integrate the influence of quantitative and qualitative objectives but also obtain the judgment, knowledge and preference of decision makers through nonstructural decision analysis method in the dynamic decision making process. Further, the operators are incorporated into fuzzy optimization dynamic programming, which are in this way extended to multiobjective and multistage decision making problems of water resources systems under fuzzy environment.
Genetic algorithms are combined with fuzzy pattern recognition model to establish a multiobjective genetic algorithm. Then it is applied to solve the problem of flood control, where a multiobjective flood control model is established and the fuzzy pattern recognition is used to evaluate the individual fitness. Flood control of Feng
(1)在分析目标相对隶属度计算公式类型的基础上，提出了一组相对隶属度计算公式。并通过水库洪水优化调度方案优选的实例分析了非线性程度和不同类型的相对隶属度计算公式对决策结果的影响。本文提出的相对隶属度计算公式综合考虑了目标特征值变化范围和权重的影响，因而能得到较好的计算结果。进一步分析了相对隶属度的变化对决策结果影响的敏感性，给出了保持模糊优选模型最优决策序列不变的相对隶属度变化范围的一个充分条件。
(2)模糊优选、模糊模式识别和模糊聚类是水资源系统优化模糊集分析理论的数学基础，在水资源系统优化决策中获得广泛的应用。然而这些模型在模糊环境下如何应用，尚缺乏研究。本文在分析三角模糊数之间距离和梯形模糊数之间距离的计算公式的基础上，把模糊数的概念分别引入陈守煜教授建立的模糊优选、模糊识别和模糊聚类模型中，从而把这些模型拓展应用到模糊环境下优化决策问题的求解。可以有效地处理模糊环境下的决策，方便地获取决策者的经验、知识和偏好，对求解模糊环境下的复杂水资源系统优化决策问题提供了一种新的方法。实例验证了这些方法的可行性和有效性。
(3)把模糊环境下的模糊识别理论具体应用到地下水脆弱性评价中。参照DRASTIC方法的经验性数据，给出了10个级别7项指标以三角模糊数表示的标准特征值，给出了三角模糊数表示的指标权重。并由此提出了模糊环境下地下水污染性难易程度评价的模糊识别方法。大连市地下水脆弱性评价表明此方法具有实用性和操作性的特点。
(4)水资源系统决策常常具有多目标多阶段特性，本文将模糊模式识别模型，模糊交叉迭代模型以及模糊环境下的模糊识别模型作为一类模糊集合算子。这类算子不仅可以集成定量目标和定性目标的影响，还可以在动态决策过程中通过非结构性决策分析方法实时地获取决策者的经验、知识和偏好。然后把这类模糊集合算子结合到模糊识别动态规划中，把模糊识别动态规划模型拓展应用于求解模糊环境条件下的水资源系统多
目标多阶段决策问题。上述算子通过水资源优化配置和梯级水库防洪优化调度两个实例
予以验证。
（5）把模糊模式识别模型与遗传算法有机地结合起来，提出了一种多目标遗传算
法。并应用此遗传算法对丰满水电站防洪发电多目标优化调度问题进行了研究，提出了
防洪与发电多目标优化调度模型。在模型求解过程中，将模糊模式识别模型作为遗传算
法的适应度函数，丰满水电站防洪与发电多目标优化调度研究表明了这种方法的实用性
和有效性。
最后对全文作了总结，并对有待进一步研究的问题作了展望。
The exploitation, utilization, restoration, protection and management of water resources are all the activities to natural water systems, by which human beings can obtain the resources or reduce the loss from disasters. The above activities must involve decision makings. The factors effecting optimization of water resources systems arise from nature, society, economy, techniques, which are classified into two types: complex paradigm and uncertainty paradigm. Fuzzy sets theory is a powerful tool to deal with the two paradigms. Based on theories, models and approaches of optimization and decision makings in the context of fuzzy hydrology and water resources, this paper concentrates on the theories of optimization and decision making for water resources systems under fuzzy environment. The conclusions are as follows.
By analyzing the types of the formulas of relative membership degrees, a pair of formulas of relative membership degree is proposed. The effects on the optimization results from non-linearization and different types are analyzed through the case study of optimum operation of flood control. The formulas proposed in this paper are with good results because of the integration of the influence from the scope of objective values and objective weights. Furthermore, the sensitivity of relative membership degrees is analyzed and a sufficient condition is derived for keeping the optimal decision ranking unchanged.
Fuzzy optimization, fuzzy pattern recognition and fuzzy clustering are the mathematical basis for optimization and decision of water resources systems, and they have received a variety of applications. However there is a little study on how to apply the models to fuzzy environment. This paper first introduces the distance measure between triangular fuzzy numbers and between trapezoid fuzzy numbers. Then it applies the fuzzy numbers to the models proposed by Prof. Chen Shouyu, including fuzzy optimization, fuzzy pattern recognition and fuzzy clustering. In this way, the models are extended to optimization and decision makings under fuzzy environment. The proposed models can efficiently deal with uncertainty and capture the judgment, knowledge and preference, so they provide a new approach to complex optimization and decision making for water resources under fuzzy environment. The case study demonstrates the efficiency and feasibility of the proposed models.
The proposed fuzzy pattern recognition model under fuzzy environment is applied to the
IV
evaluation of groundwater vulnerability. According to the experiential data of the DRASTIC index, the standard values of 10 classes for 7 indexes are proposed in the form of triangular fuzzy numbers, and similarly the weights of indexes are expressed in the form of triangular fuzzy numbers. A fuzzy recognition approach thereby is applied to evaluate the groundwater vulnerability under fuzzy environment. The case study of Dalian shows that the approach is robust and practical.
Decision makings of water resources systems are of the characteristics of multi-objective and multistage. The fuzzy pattern recognition model, fuzzy cross iteration model and fuzzy pattern recognition model under fuzzy environment are regarded as a class of aggregation operators. The operators can not only integrate the influence of quantitative and qualitative objectives but also obtain the judgment, knowledge and preference of decision makers through nonstructural decision analysis method in the dynamic decision making process. Further, the operators are incorporated into fuzzy optimization dynamic programming, which are in this way extended to multiobjective and multistage decision making problems of water resources systems under fuzzy environment.
Genetic algorithms are combined with fuzzy pattern recognition model to establish a multiobjective genetic algorithm. Then it is applied to solve the problem of flood control, where a multiobjective flood control model is established and the fuzzy pattern recognition is used to evaluate the individual fitness. Flood control of Feng
引文
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