Abstract:

A novel 3-step solution concept based on fuzzy cooperative games was developed aimed at optimizing the water resources reallocation in water-stressed regions. In the first step, the characteristic function of the crisp water-sharing coalitions among water using sectors was constituted based on the “priority rule”, which dedicated to the reasonable illustration of the water resource sharing mode in each crisp coalition. In the second step, based on the fuzzy cooperative games in the form of Choquet integrals, and the characteristic function of crisp coalition constituted in Step 1, the characteristic function of fuzzy water resource sharing coalitions among water using sectors was established. In the third step, based on the results above, the optimal water resource reallocation model was proposed, and optimum fuzzy coalitions were obtained by solving this model. Furthermore, in this step, each optimum coalition was considered as a grand coalition, and the benefit of each grand coalition was distributed to water using sectors in a rational way by using the nucleolus method. This methodology was examined by applying it to a case study of water resource reallocation in the “Beijing-Tianjin-Hebei Region”. The results show that the proposed 3-step optimal water resource allocation model can ensure the maximum effect of water utilization, and can realize optimal water resource allocation. Moreover, the proposed model does not need to have the constrain of fuzzy Shapley value equation, if the model was constructed based on the fuzzy cooperative games in the form of Choquet integrals, that is, the optimal allocation model without affecting the validity of the distribution results obtained by using different distribution methods. Furthermore, the nucleolus solution of each optimum coalition uniquely exists, which can guarantee the stability of each optimum coalition by satisfying both individual rationality and group rationality criterions, which means that the proposed method based on nucleolus is more effective than the exiting method (Shapley value, fuzzy least core, and fuzzy weak least core) in the issue discussed in this paper.

Key words: optimal allocation of water resources, fuzzy cooperative games, coalition profit distribution, group rationality

摘要：

为提高水资源短缺区域的水资源利用效率，实现区域水资源初始配置后的有效再配置，提出三阶段水资源短缺区域水资源优化配置方法：阶段1，利用高效的“优先规则”构建部门间水资源合作清晰联盟的用水收益支付函数，对联盟成员水资源共用、获益方式进行了合理刻画；阶段2，基于Choquet积分形式的模糊合作博弈、阶段1中的清晰联盟支付函数，构建部门间水资源模糊联盟支付函数；阶段3，基于上述成果，构建水资源短缺区域水资源优化配置模型，求解得到用水部门最优水资源合作联盟，并将求得的最优模糊联盟视为大联盟，通过求解其核仁解获得最优模糊联盟的收益分配。以京津冀区域水资源优化配置问题为例，算例结果表明：①基于Choquet积分形式模糊合作博弈的三阶段水资源优化配置模型能够最大化区域整体用水收益水平，实现水资源短缺区域中的水资源优化配置，并使区域中用水部门有机会分得更多的获益；②本文模型无需引入模糊Shapley值等分配方法作为约束条件即可求得最优联盟，模型不影响不同收益分配方法分配结果的有效性；③采用将最优模糊水资源合作联盟视为大联盟，并求联盟收益的核仁解的方法分配最优联盟收益，无论最优联盟的核心是否为空，都能保证联盟收益分配结果满足个体理性和集体理性要求，即能保证最优联盟中各成员不会“叛逃”最优联盟、联盟稳定存在，且保证获得的分配方案为确定分配值而非分配区间。即本问题中该分配方法优于Shapley值、模糊最小核、弱最小核方法。所构建的水资源短缺区域水资源优化配置模型及最优水资源合作联盟收益分配方法对水资源短缺区域的水资源优化配置问题有较好的适用性，能够为我国京津冀区域等水资源短缺区域的水资源优化配置工作提供参考。

关键词: 水资源优化配置, 模糊合作博弈, 联盟收益分配, 集体理性