随机线性不等式组的确定性等价式

在大量的决策问题中，经常会出现含有随机变量的不等式或不等式组。把这类含有随机变理的模型转化成确定性的模型是解决问题的重要途径。它们在随机控制和不完全信息群体决策随机决策问题中起着重要的作用。因此，如何将随机不等林或随机不等式组转化为相应的确定性等价式的问题受到人们的关注。本文对含有确定分布的随机变量的线性不等式组，就其相应的概率表达式作出分类，并根据其左端系数矩阵和右端向量含有随机因素的情形分别进行讨论，系统地导出了它们相应的确定性等价式。     

模糊二阶矩过程及均方收敛性

基于可信性测度,定义了新的模糊二阶矩过程,证明了该二阶矩过程存在方差函数和协方差函数.对于在可信性空间(Θ,()(Θ),Cr)上具有二阶矩的模糊变量集合H,证明了其对通常的线性运算封闭,并在H中研究了模糊均方收敛的必要条件和充分条件.最后讨论了模糊均方收敛的若干性质.     

不同风险态度下的三层供应链集成优化

研究了在决策者不同风险态度下的由供应商、分销商和零售商组成三层供应链集成优化问题。考虑供应链中价格、质量、交货、需求和供应的不确定风险因素为模糊变量,应用可信性理论建立了模糊机会约束规划模型,可信性测度的置信水平代表了决策者的风险偏好程度。使用模糊变量的乐观值和悲观值将机会约束转化为清晰的等价形式。最后,通过数值算例分析了决策者的风险态度的变化对集成供应链的影响。     

基于LMI方法的一类非线性模糊脉冲系统的鲁棒模糊控制

通过推广一般T-S模糊模型定义了一类非线性模糊脉冲系统.基于线性矩阵不等式(LMI)方法提出了一种鲁棒模糊控制新方案.采用并行分布补偿(PDC)的基本思想设计状态反馈控制器,并利用Lyapunov方法理论证明闭环系统全局指数稳定.最后基于LMI方法,将鲁棒模糊控制器的设计问题转化为线性矩阵不等式问题(LMIP).仿真表明本方法的有效性.     

带有模糊约束的房地产投资随机期望值模型

基于可信性理论,提出一类新的带有模糊约束的房地产投资随机期望值模型来处理房地产经济中的不确定性信息.另一方面,通过目标函数和可信性函数的一些性质将提出的房地产投资问题转化为一个等价的线性形式,从而可以利用经典的线性规划算法进行求解.最后,给出一个房地产投资问题的实例并通过Lindo软件进行求解.     

一类不确定模糊脉冲切换系统的H∞控制

研究了一类参数不确定的模糊脉冲切换系统在任意切换下的H_∞控制问题.利用Lyapunov稳定性理论与线性矩阵不等式方法,给出了连续的脉冲切换系统满足H_∞性能的充分条件,并把这个条件转化为一个线性矩阵不等式,便于实现.     

一种基于交互熵的模糊信息测度

通过借用Shannon信息理论中的相关概念,对已有文献中基于模糊熵测度的模糊对称交互熵(FSCE)进行了改进,提出了对称改进模糊交互熵(SIFCE)这一距离测度.接下来证明了它是度量空间中的度量,满足非负性、对称性、三角不等式三个条件,并且满足有界性,还讨论了它与模糊熵之间的关系.最后提出基于该测度的模糊贴近度σ_(SIF),利用数值例子说明了在模糊模式识别中,σ_(SIF)与常见的模糊贴近度可以得到一致的识别结果,从而为模糊模式识别提供了新的研究方法.     

基于可信性安全准则的模糊动态投资组合模型

研究了模糊环境下的动态投资组合模型,将证券的收益率描述为模糊变量,提出了基于可信性测度的安全准则,可信性安全准则反映了投资者对灾难事件的容忍水平.建立了基于可信性安全准则的模糊动态投资组合模型,对建立的模型设计了基于模糊模拟的混合智能算法进行求解,并在Visual C++环境下,用C语言实现了对实例的求解,证明了混合智能算法的有效性和合理性.     

基于2可加模糊测度的多线性效用函数建模和求解

构建合适的多属性效用函数是多属性效用分析的关键。针对不同偏好假设,文献从可加独立、效用独立、效用依赖等分别进行了多属性效用函数构建的研究。然而,由于求解的复杂性,多属性效用理论的应用绝大部分限于可加效用函数和多乘效用函数。提出一种基于2可加模糊测度的多线性效用函数建模和求解方法。首先,证明多线性效用函数和基于模糊测度的多线性模型之间的等价性,提出利用基于模糊测度的多线性模型对多线性效用函数进行表示。其次,针对多线性模型的特点和模糊测度识别的复杂性,利用Banzhaf交互指数和2可加模糊测度对多线性模型进行表示,并利用最小方法差进行模糊测度和Banzhaf交互指数识别,进而实现多线性效用函数的求解。最后,将方法用于某可穿戴医疗设备基于顾客需求的多属性效用函数构建,确认了可行性。方法为多线性效用函数的求解提供了一种新思路。     

基于模糊积分的金融数据建模方法

以非可加模糊测度代替经典可加测度,基于模糊积分建立非线性回归模型是新近出现的数据建模方法.该方法充分考虑自变量因素之间的信息熔合(含协同或冲突)作用.本文完整地给出了适用于实数范围内的基于模糊积分(含Choquet积分和(S)ipo(s)积分)的多元非线性回归模型转化为普通线性回归模型的非线性转换方法及其简化算法.并将该方法应用于金融市场数据分析,结果表明效果较之普通多元线性回归有大的提高,且方法简便容易应用.     

模糊多属性决策的三种结构元方法

将结构元理论引入到模糊多属性决策中,按照经典多属性决策的乐观型准则、悲观型准则和乐观-悲观结合型准则,对应地建立了基于模糊结构元理论的模糊乐观型、模糊悲观型、模糊乐观-悲观结合型决策方法。借助一个实例,本文运用这三种算法进行了决策,得出了和传统决策算法一致的结论。本文提出的算法不仅易于理解,而且计算的速度也远比传统算法要快,对于进一步研究模糊多属性决策问题有很好的参考作用。     

Stackelberg solutions for fuzzy random two-level linear programming through probability maximization with possibility

This paper considers Stackelberg solutions for decision making problems in hierarchical organizations under fuzzy random environments. Taking into account vagueness of judgments of decision makers, fuzzy goals are introduced into the formulated fuzzy random two-level linear programming problems. On the basis of the possibility and necessity measures that each objective function fulfills the corresponding fuzzy goal, together with the introduction of probability maximization criterion in stochastic programming, we propose new two-level fuzzy random decision making models which maximize the probabilities that the degrees of possibility and necessity are greater than or equal to certain values. Through the proposed models, it is shown that the original two-level linear programming problems with fuzzy random variables can be transformed into deterministic two-level linear fractional programming problems. For the transformed problems, extended concepts of Stackelberg solutions are defined and computational methods are also presented. A numerical example is provided to illustrate the proposed methods.     

区间直觉模糊集的模糊熵群决策方法

针对专家权重未知、专家判断信息以区间直觉模糊集给出的多属性群决策问题,提出了一种新的模糊熵决策方法。通过定义区间直觉模糊集的模糊熵判断专家信息的模糊程度,进而确定每位专家的权重;然后计算备选方案距理想方案和负理想方案的模糊交叉熵距离,得到每个专家对方案的排序;再分别利用加权算术算子和加权几何算子集结专家的排序结果,得到专家群体对方案的排序。实例分析验证了方法的有效性。     

Study on divergence measures for intuitionistic fuzzy sets and its application in medical diagnosis

As far as medical diagnosis problem is concerned, predicting the actual disease in complex situations has been a concerning matter for the doctors/experts. The divergence measure for intuitionistic fuzzy sets is an effective and potent tool in addressing the medical decision making problems. We define a new divergence measure for intuitionistic fuzzy sets (IFS) and its interesting properties are studied. The existing divergence measures under intuitionistic fuzzy environment are reviewed and their counter-intuitive cases has been explored. The parameter $\alpha $ is incorporated in the proposed divergence measure and it is defined as parametric intuitionistic fuzzy divergence measure (PIFDM). The different choices of the parameter $\alpha$ provide different decisions about the disease. As we increase the value of $\alpha $, the information about the disease increases and move towards the optimal solution with the reduced in the uncertainty. Finally, we compare our results with the already existing results, which illustrate the role of the parameter $\alpha $ in obtaining the optimal solution in the medical decision making application. The results demonstrate that the parametric intuitionistic fuzzy divergence measure (PIFDM) is more comprehensive and effective than the proposed intuitionistic fuzzy divergence measure and the existing intuitionistic fuzzy divergence measures for decision making in medical investigations.     

Contribution to application of energy measure of fuzzy sets

The works of De Luca & Termini continued by, for example, Knopfmacher, Loo and Gottwald, are the most important on the topic of determination of measures of fuzzy sets. The matter is to evaluate how fuzzy a fuzzy set is. There are two general concepts of measures of fuzzy set, i.e. entropy and energy measures.We show that the special kind of energy measure is better suited than the entropy kind of measure in many practical situations.Applications of the use of energy measure discussed in detail include decision making, fuzzy process control and prediction in fuzzy systems.     

一种基于Choquet积分的多属性直觉模糊决策方法

研究了决策者对方案的主观偏好值以及属性值均为直觉模糊数的且属性间存在关联的多属性决策问题.利用Choquet模糊积分作为集结算子,构建了基于属性关联的M OD和SOD模型.通过求解模型获得属性的权重,进而给出了一种新的直觉模糊多属性决策方法.最后通过一个算例说明了该决策方法的有效性和可行性.     

Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group

Szmidt and Kacprzyk (Lecture Notes in Artificial Intelligence 3070:388–393, 2004a) introduced a similarity measure, which takes into account not only a pure distance between intuitionistic fuzzy sets but also examines if the compared values are more similar or more dissimilar to each other. By analyzing this similarity measure, we find it somewhat inconvenient in some cases, and thus we develop a new similarity measure between intuitionistic fuzzy sets. Then we apply the developed similarity measure for consensus analysis in group decision making based on intuitionistic fuzzy preference relations, and finally further extend it to the interval-valued intuitionistic fuzzy set theory.     

Multicriteria decision-making method using the Dice similarity measure based on the reduct intuitionistic fuzzy sets of interval-valued intuitionistic fuzzy sets

This paper proposes the concept of the reduct intuitionistic fuzzy sets of interval-valued intuitionistic fuzzy sets (IVIFSs) with respect to adjustable weight vectors and the Dice similarity measure based on the reduct intuitionistic fuzzy sets to explore the effects of optimism, neutralism, and pessimism in decision making. Then a decision-making method with the pessimistic, optimistic, and neutral schemes desired by the decision maker is established by combining adjustable weight vectors and the Dice similarity measure for IVIFSs. The proposed decision-making method is more flexible and adjustable in practical problems and can determine the ranking order of alternatives and the optimal one(s), so that it can overcome the difficulty of the ranking order and decision making when there exist the same measure values of some alternatives in some cases. This adjustable feature can provide the decision maker with more selecting schemes and actionable results for the decision-making analysis. Finally, two illustrative examples are employed to show the feasibility of the proposed method in practical applications.     

一种区间Pythagorean模糊VIKOR多属性群决策方法

针对属性信息为区间Pythagorean模糊集且属性权重和专家权重均未知的一类群决策问题, 结合信息熵理论, 提出了一种区间Pythagorean模糊VIKOR多属性群决策方法。首先定义一种新的区间Pythagorean模糊距离测度, 并讨论其性质。其次基于该距离测度定义了区间Pythagorean模糊相对距离指数, 并基于相对距离指数构建了一种熵权模型确定专家权重和属性权重。然后提出一种区间Pythagorean模糊VIKOR多属性群决策方法。最后通过企业生产方案选择案例说明了提出新方法的可行性与有效性。