Bi-matrix Games with Fuzzy Strategies and Fuzzy Payoffs and Their Mathematical Programming Equivalents

A fuzzy bi-matrix game（FBG）,namely a two-person non-zero-sum game with fuzzy strategies and fuzzy payoffs is proposed.We have defined and analyzed the optimal strategies of this FBG,and shown that it can be transformed into a corresponding fuzzy mathematical programming issue,for which a ranking function approach can be applied.In addition,optimal strategies of FBG for both Player I and Player II can be gotten.

Fuzzy mathematics and game theory based D2D multicast network construction

Device to device(D2 D) multi-hop communication in multicast networks solves the contradiction between high speed requirements and limited bandwidth in regional data sharing communication services. However, most networking models demand a large control overhead in eNodeB. Moreover, the topology should be calculated again due to the mobility of terminals, which causes the long delay. In this work, we model multicast network construction in D2 D communication through a fuzzy mathematics and game theory based algorithm. In resource allocation, we assume that user equipment(UE) can detect the available frequency and the fuzzy mathematics is introduced to describe an uncertain relationship between the resource and UE distributedly, which diminishes the time delay. For forming structure, a distributed myopic best response dynamics formation algorithm derived from a novel concept from the coalitional game theory is proposed, in which every UE can self-organize into stable structure without the control from eNodeB to improve its utilities in terms of rate and bit error rate(BER) while accounting for a link maintenance cost, and adapt this topology to environmental changes such as mobility while converging to a Nash equilibrium fast. Simulation results show that the proposed architecture converges to a tree network quickly and presents significant gains in terms of average rate utility reaching up to 50% compared to the star topology where all of the UE is directly connected to eNodeB.

Profit Allocation Scheme Among Players in Supply-Chain Based on Shapley Value of Fuzzy Bi-cooperative Games

The Shapley value of fuzzy bi-eooperative game is developed based on the conventional Shapley value of bi-cooperative game. From the viewpoint that the players can participate in the coalitions to a certain extent and there are at least two independent cooperative projects for every player to choose, Shapley value which is introduced by Grabisch is extended to the case of fuzzy bi-cooperative game by Choquet integral. Moreover, the explicit fuzzy Shapley value is given. The explicit fuzzy Shapley function can be used to allocate the profits among players in supply-chain under the competitive and uncertain environment.

Fuzzy Nash equilibrium of fuzzy n-person non-cooperative game

The fuzzy non-cooperative game with fuzzy payoff function is studied. Based on fuzzy set theory with game theory, the fuzzy Nash equilibrium of fuzzy non-cooperative games is proposed. Most of researchers rank fuzzy number by its center of gravity or by the real number with its maximal membership. By reducing fuzzy number into a real number, we lose much fuzzy information that should be kept during the operations between fuzzy numbers. The fuzzy quantities or alternatives are ordered directly by Yuan＇s binary fuzzy ordering relation. In doing so, the existence of fuzzy Nash equilibrium for fuzzy non-cooperative games is shown based on the utility function and the crisp Nash theorem. Finally, an illustrative example in traffic flow patterns of equilibrium is given in order to show the detailed calculation process of fuzzy Nash equilibrium.

Shapley Value for Cooperative Games with Fuzzy Coalition

Fuzzy Shapley values are developed based on conventional Shapley value. This kind of fuzzy cooperative games admit the representation of rates of players＇ participation to each coalition. And they can be applicable to both supperadditive and subadditvie cooperative games while other kinds of fuzzy cooperative games can only be superadditive. An explicit form of the Shapley function on fuzzy games with λ-fuzzy measure was also proposed.

Solution of Matrix Game with Triangular Intuitionistic Fuzzy Pay-Off Using Score Function

Using score function in a matrix game is very rare. In the proposed paper we have considered a matrix game with pay-off as triangular intuitionistic fuzzy number and a new ranking order has been proposed using value judgement index, available definitions and operations. A new concept of score function has been developed to defuzzify the pay-off matrix and solution of the matrix game has been obtained. A numerical example has been given in support of the proposed method.

Interactive Fuzzy Approaches for Solving Multiobjective Two-Person Zero-Sum Games

In this paper, we consider multiobjective two-person zero-sum games with vector payoffs and vector fuzzy payoffs. We translate such games into the corresponding multiobjective programming problems and introduce the pessimistic Pareto optimal solution concept by assuming that a player supposes the opponent adopts the most disadvantage strategy for the self. It is shown that any pessimistic Pareto optimal solution can be obtained on the basis of linear programming techniques even if the membership functions for the objective functions are nonlinear. Moreover, we propose interactive algorithms based on the bisection method to obtain a pessimistic compromise solution from among the set of all pessimistic Pareto optimal solutions. In order to show the efficiency of the proposed method, we illustrate interactive processes of an application to a vegetable shipment problem.

Game Theory-Based Dynamic Weighted Ensemble for Retinal Disease Classification

An automated retinal disease detection system has long been in exis-tence and it provides a safe,no-contact and cost-effective solution for detecting this disease.This paper presents a game theory-based dynamic weighted ensem-ble of a feature extraction-based machine learning model and a deep transfer learning model for automatic retinal disease detection.The feature extraction-based machine learning model uses Gaussian kernel-based fuzzy rough sets for reduction of features,and XGBoost classifier for the classification.The transfer learning model uses VGG16 or ResNet50 or Inception-ResNet-v2.A novel ensemble classifier based on the game theory approach is proposed for the fusion of the outputs of the transfer learning model and the XGBoost classifier model.The ensemble approach significantly improves the accuracy of retinal disease pre-diction and results in an excellent performance when compared to the individual deep learning and feature-based models.

复杂地质条件下沥青混凝土心墙坝风险识别方法

针对复杂地质条件下沥青心墙坝风险识别问题,本文从“三高一深”复杂地质条件、沥青混凝土心墙和传统土石坝三个风险维度,系统建立沥青混凝土心墙坝风险指标体系。针对主客观信息融合不充分问题,本文采用三角模糊层次分析法(TFAHP)确定风险指标主观权重,通过指标重要性评价法(CRITIC)确定其客观权重,并利用博弈论法(GT)计算最优组合权重,构建基于TFAHP-CRITIC-GT组合赋权模型的沥青心墙坝风险智能识别方法。实例分析表明,新疆奴尔沥青心墙坝工程复杂地质条件风险指标权重占比0.516,是该工程的重要风险因素。综合考虑复杂地质条件风险对于准确识别沥青心墙坝风险因素具有重要工程意义,本文提出的指标体系及识别方法对于西部地区复杂地质条件大坝风险识别及评价研究具有推广价值。

面向车辆与参数服务器双向选择的联邦学习算法

联邦学习框架正逐渐被广泛应用于车联网领域,针对车辆的移动性特点以及大量车辆联邦学习时同时接入参数服务器交互参数易产生的通信拥塞的问题,提出了一种基于模糊逻辑的车辆选择和基于演化博弈的参数服务器选择算法。通过设计模糊逻辑算法,考虑车辆的移动性、设备条件以及数据量因素来选择通信连接较稳定、计算能力较强和数据量多的车辆参与联邦学习。采用演化博弈进一步刻画选出的车辆自主决策选择参数服务器的过程,平衡联邦学习模型准确度以及产生的通信和计算成本,从而避免通信拥塞并最大化车辆个体利益和整体利益。仿真验证了大量车辆场景下所提出算法的性能,实现模型训练的低成本、高精度。

基于新图模糊距离的EDAS决策方法及其应用

研究决策信息为图模糊集的多属性决策问题。首先,针对现有图模糊距离的不足,定义了含参数的弃权度的分配,同时结合一致性概念提出了反映决策者风险偏好的图模糊距离,通过数值算例将新图模糊距离与现有图模糊距离进行比较分析,验证其优越性。其次,针对属性权重,采用博弈论组合赋权法对熵权法确定的客观权重和决策者给出的主观权重进行组合优化。在此基础上,将新图模糊距离拓展到一种离平均方案距离的决策方法(EDAS),并运用新图模糊距离计算各方案与平均方案的正、负距离加权和,进而得到综合得分。最后,通过算例来验证所提决策方法的适用性和有效性。灵敏度与对比分析结果表明:决策者可以依据自身风险偏好调整参数的取值来满足不同的决策需求;所提方法相较于其他现有决策方法更具一般性与灵活性,所得排序结果更加合理。

基于联盟博弈的多虚拟电厂参与日前电力市场竞标模型

当前多虚拟电厂联盟面临售电垄断防范机制匮乏、个体主观性偏好难以多维评估刻画等问题。提出基于联盟博弈的多虚拟电厂参与日前电力市场竞标模型。引入联盟内部动态过网费机制,量化内部功率交互产生的增量运行成本,以防售电垄断;计及虚拟电厂个体在联盟选择问题上的多指标偏好性,建立基于模糊层次分析法-决策试行与评价实验室法的联盟选择结果评估框架,以充分刻画多指标关联性;采用合并-分裂规则构建分布式联盟方案,通过求解配电网-多虚拟电厂联盟双层博弈模型获取多指标评分,基于综合评估结果进行迭代,获得最优联盟方案。算例结果验证了所提模型的有效性及经济性。

基于用户体验的游戏论坛APP界面设计研究

在当前游戏产业快速发展的背景下,游戏论坛APP界面设计已经不符合大众要求。因此,文章基于用户体验,深入发掘游戏论坛APP界面的用户需求,构建用户游戏论坛APP界面用户体验模型,从本能层、行为层、反思层剖析游戏论坛APP界面设计方法,最终提出游戏论坛APP界面优化设计方案,并且通过案例对比验证了该设计方法的有效性。通过文章的研究,以期为优化游戏论坛APP用户体验提供范例参考。

优化模糊综合评价模型在水质评价中的应用

基于熵权法和层次分析法,并采用博弈论,将主客观权重相结合,确定了综合权重,优化了模糊综合评价模型的赋权过程,最后结合加权平均法,构建了水质评价优化模型。通过对案例中的水样进行评价,结果显示:7个采样点当中,Ⅱ类水和Ⅲ类水的采样点有4个,占比57.14%;Ⅳ类水的采样点有3个,占比42.86%。相较于单一熵权法赋权的模糊综合评价模型,优化后的评价模型综合考虑了主客观权重和评价因素对于整体水质影响,合理反映了水质特征,可为类似地区的水质评价工作提供参考。

武汉市城市低碳交通发展水平评价

为解决低碳交通发展水平评价中主客观权重差异和群决策定性指标量化的不确定性问题,建立基于博弈论和TOPSIS(逼近理想解排序方法)的城市低碳交通发展水平评价模型。首先,采用可拓层次分析法(EAHP)和熵权法确定指标主客观权重。其次,使用博弈论确定指标综合权重,以解决主客观权重带来的差异问题。最后,采用三角模糊数对定性指标进行量化,并结合TOPSIS进行综合评价,客观全面反映不同专家对定性指标的意见。通过上述模型对武汉市2015-2021年低碳交通发展各方面和综合发展水平进行评价。结果表明,2015-2021年武汉市低碳交通发展水平呈稳步增长趋势,评价值从0.4048上升到0.6067,与实际情况相符。该评价方法可以应用于其他城市的低碳交通发展水平评价,进而更好地推进城市低碳交通系统建设。

基于三角模糊数序贯博弈的电网安全研究

智能电网系统面临着复杂性、多样性的网络安全风险。针对电网工艺漏洞攻防双方在博弈分析中无法对信息属性损失作出准确判断的问题,提出了一种三角模糊数序贯博弈模型。以序贯博弈树方法进行智能电网攻防博弈,构建出攻击者和防御者的最优策略,实现对智能电网的工控安全防护。通过对智能电网攻击者和防御者构建序贯博弈模型,得到攻防博弈效用。提出运用三角模糊数和概率分布向量的方法来构建非模糊化损失,得到攻防双方清晰化的系统损失值。对三角模糊数序贯博弈算法和贝叶斯序贯算法进行比较,得到智能电网均衡路径中的攻击者和防御者的最优策略,以保障智能电网网络安全运行和防护。该研究为智能电网以及典型工控系统网络安全博弈提供参考。

基于组合赋权-云模型的毕达哥拉斯模糊语言综合评价方法研究

评价本身具有随机性、模糊性以及不确定性的特点。为了避免评价过程太过主观,提出一种基于组合赋权和云模型的毕达哥拉斯模糊语言综合评价方法。针对专家给出的属性值为毕达哥拉斯模糊语言,根据CRITIC-G1(标准间相关性的重要性-序关系分析)法对评价指标进行主客观赋权,由博弈论算法计算权重最优的组合系数得出组合权重。最后构建毕达哥拉斯模糊云模型决策矩阵进行信息集结。通过案例计算分析表明,该方法优化了复杂情境下的决策,具有其可行性和有效性。

基于博弈论与模糊区间理论的森林康养基地评价方法

为了提高森林康养基地等级划分的精度,对相同等级下不同地区之间的优劣做出比较,提出了一种基于博弈论与模糊区间理论的森林康养基地评价方法,建立了区间型森林康养基地评价指标体系.利用博弈论将模糊熵与变异系数权重进行组合,借助模糊区间理论构建评价模型,并采用格贴近度公式得到待评价地区隶属的等级,引入TOPSIS模型对所选取的待评价地区进行优劣排序.结果表明,该评价方法具有良好的适用性与有效性.