帕累托最优框架下的水电电价模型

将Shapley值分配方法与帕累托最优理论引入到水电电价模型的研究中.通过Shapley值确定水电电价在不同时段的惩罚因子与奖励因子,在帕累托最优的框架下建立能够提供有效的经济信号的有差别水电电价模型,目标为小水电方经济效益减少量与电网线损减少量比值的最小化,在保证对电网运营方与水电方经济效益弱影响的同时,实现电网的低...     

京津冀大气污染治理省际合作博弈模型

首先，结合目前京津冀区域大气污染的实际情况，提出了通过省际合作达到大气污染治理的 3 个基本假设. 其次，通过构建区域优化模型和 Shapley 值合作收益分配方案，建立了京津冀大气污染治理省际合作博弈模型. 通过求解区域优化模型得到各省份最优去除量和去除成本，进而利用 Shapley 值法获得相对公平的合作收益分配方案. 最后，以 2009 年京津冀各省份 SO₂ 去除为例进行了实证分析，结果显示了京津冀省际合作博弈模型的有效性和实用性，而且模型最优化模拟结果可作为区域决策的重要参考，促使各省份合作共赢.     

基于一致性原理的商业银行经济资本配置方法

论文以一致性原理和博弈论中的夏普利值为基础, 对Denault方法进行了质的改进, 提出了适用于商业银行的经济资本配置方法.通过引入Yasumitsu条件得到了夏普利值满足一致性的充要条件, 找到了判断夏普利值是否满足一致性的更完备的理论依据.这一方法符合银行整体最优的要求, 可以使商业银行从整体最优的角度确定各分支机构的风险贡献, 评估经营绩效, 最终确定各分支机构年度经济资本限额.     

Data fusion based on fuzzy measures

Choquet integral based on fuzzy measure is a very popular data fusion approach. A major problem in applying the Choquet integral is how to determine a large number of fuzzy measures as the number of attributes increases. The λ-fuzzy measure proposed by Sugeno is a powerful method to resolve this problem. However, the modeling ability of the λ-fuzzy measure is too limited to satisfy actual requirements. In this paper, an extended λ-fuzzy measure is proposed using Shapley value index, and the limitation of the λ-fuzzy measure is significantly overcome under little additional computational loads. The extended fuzzy measure has stronger modeling power than the λ-fuzzy measure, straightforwardly representing interaction among attributes. We apply the extended fuzzy measure to an artificial data set and a real dataset in an iron-steel plant. The results verify the usefulness of the extended fuzzy measure compared with other main existing methods.     

Data fusion based on fuzzy measures

Choquet integral based on fuzzy measure is a very popular data fusion approach.A major problem in applying the Cho- quet integral is how to determine a large number of fuzzy measures as the number of attributes increases.Theλ-fuzzy measure proposed by Sngeno is a powerful method to resolve this problem.However,the modeling ability of theλ-fuzzy measure is too limited to satisfy actual requirements.In this paper,an extendedλ-fuzzy measure is proposed using Shapley value index,and the limitation of theλ-fuzzy measure is significantly overcome under little additional computational loads.The extended fuzzy measure has stronger modeling power than theλ- fuzzy measure,straightforwardly representing interaction among attributes.We apply the extended fuzzy measure to an artificial data set and a real dataset in an iron-steel plant.The results verify the usefulness of the extended fuzzy measure compared with other main existing methods.     

系统重心迁移的贡献度分解方法

社会经济系统的重心迁移轨迹可以刻画系统空间演化的发展方向和平衡问题。为分析重心迁移的主导因素,发现并指出了简单分解、方差分解和微分分解等常用的贡献度分解方法在重心法研究中的不适用性及其原因,提出了一种基于夏普里值的、适用于重心法的分解方法。并用中国经济重心迁移对该方法做了验证。     

Some interval-valued intuitionistic uncertain linguistic hybrid Shapley operators

Two interval-valued intuitionistic uncertain linguistic hybrid operators cal ed the induced interval-valued intuitionistic uncertain linguistic hybrid Shapley averaging （I-IIULHSA） operator and the induced interval-valued intuitionistic uncertain linguistic hybrid Shapley geometric （I-IIULHSG） operator are defined. These operators not only reflect the importance of elements and their ordered positions, but also consider the correlations among elements and their ordered positions. Since the fuzzy measures are defined on the power set, it makes the problem exponentially complex. In order to simplify the complexity of solving a fuzzy measure, we further define the induced interval-valued intuitionistic uncertain linguistic hybrid λ-Shapley averaging （I-IIULHλSA） operator and the induced interval-valued intuitionistic uncertain linguistic hybrid λ-Shapley geometric （I-IIULHλSG） operator. Moreover, an approach for multi-attribute group decision making under the interval-valued intuitionistic uncertain linguistic environment is developed. Finally, a numerical example is provided to verify the developed procedure and demonstrate its practicality and feasibility.     

带层次结构效用可转移合作对策的多步Shapley值

作为一种局中人结盟形式,层次结构比联盟结构更具一般性.本文致力于给出带层次结构效用可转移合作对策的多步Shapley值,具体给出了其分配过程及公理化刻画.另外,作为一个等价分配过程,本文还证明了它等价于一个特殊效用可转移合作对策的加权Shapley值.研究结果扩展了带联盟结构效用可转移合作对策的两步Shapley值,可为研究其它带结盟限制合作对策的解提供借鉴.     

T-模糊联盟间相互影响的度量

针对局中人以三角模糊数的形式参与合作对策的问题,给出了T-模糊联盟间相互影响的基本概念.探讨了T-模糊联盟间相互独立时模糊特征函数的表达式及模糊特征函数具有k-严格单调性时T-模糊联盟间相互影响的变化规律,通过对Shapley值和Banzhaf-Coleman势指标度量概念的推广,得到相应的Shapley值和Banzhaf-Coleman势指标,用于表示T-模糊联盟间相互影响的期望度量指标和方差度量指标,并通过算例分析来说明其有效性和实用性.     

一类重复模糊n人合作对策的Shapley值

以模糊结盟为工具,建立了重复模糊合作对策理论,把带加权函数的模糊n人合作对策的Shapley值推广到重复模糊n人合作对策中,并提出了模糊支柱序列的定义以及Shapley值在重复模糊合作对策下应满足的三条公理的概念,进而给出重复模糊n人合作对策下的Shapley值的计算公式及证明,最后给出一个例子予以应用。