基于残缺互补判断矩阵的一种群决策模型

研究了基于残缺互补判断矩阵的群决策模型.首先,利用积型残缺一致性互补判断矩阵和互补判断矩阵的排序向量之间的偏差,建立并求解一个非线性规划模型,得到各专家残缺互补判断矩阵的排序向量.然后,通过最小化专家残缺互补判断矩阵的排序向量与专家群组排序向量的偏差,再次建立并求解一个非线性规划模型,得到反映出专家群组偏好的排序向量,从而得到了残缺互补判决矩阵的群决策模型.最后,通过算例说明了方法的可行性.     

基于相对熵的多粒度语言判断矩阵的群决策方法

针对多粒度语言判断矩阵的群决策问题提出基于相对熵的最优化模型的排序方法.在多粒度语言偏好信息的导出函数基础上定义了语言判断矩阵对应的导出模糊互补判断矩阵,并给出其排序向量的计算式;同时采用语言判断矩阵的一致性指标来确定专家重要性程度的权向量;在相对熵的意义下构建了群决策排序向量的最优化模型,探讨了模型的求解方法.实例分析表明该模型是可行和有效的.     

基于投影模型的区间不同形式偏好信息的群体决策方法

研究了决策者的偏好信息以区间互反判断矩阵和区间互补判断矩阵形式给出的群决策问题.首先将区间互反判断矩阵转换为区间互补判断矩阵;然后利用可能度计算公式得到相应的模糊判断矩阵,并得到各个专家的排序向量;然后基于投影模型将各个专家的排序向量规范化为群体最优排序向量.最后通过算例说明该方法的可行性和有效性.     

一种基于不同粒度语言判断矩阵的群决策模型

研究了方案判断矩阵为不同粒度语言判断矩阵和专家权重为语言标度的群决策问题.通过拓展相关文献中建立的转换函数的使用范围,将专家给出的不同粒度语言判断矩阵转化为互补判断矩阵,并证明了转化的合理性,同时,将专家语言权重向量转化为数值单位权重向量.然后,利用积型一致性互补性判断矩阵和互补判断矩阵的排序向量之间的偏差,建立一个非线性规划模型,求出互补判断矩阵的排序向量,根据合成矩阵的排序向量实现方案的排序择优.最后,通过一个实例来说明方法的可行性与有效性.     

关于AHP群体判断矩阵权向量优化计算方法

本文提出的ＡＨＰ群体判断矩阵权向量优化计算方法,是运用非线性规划方法求解与各判断矩阵列向量偏角相差综合最小的向量．实例证明,该方法是简便有效的     

一种群决策专家客观权重确定的改进方法

针对传统的群决策专家客观权重确定的两类主要方法(即基于判断矩阵一致性程度和基于专家排序向量或判断矩阵元素的聚类分析)的缺陷,提出了一种综合考虑两方面因素的改进方法.首先利用聚类分析方法根据各专家的排序向量得到专家类别间的权重,然后根据单个专家的判断矩阵一致性以及排序向量到类核心的距离确定最终权重.文末给出的算例表明该方法是可行、有效的.     

关于AHP群体判断矩阵权向量优化计算方法

本提出的AHP科体判断矩阵权向量优化计算方法．是运用非线性规划方法求解与各判断矩阵列向量偏角相差综合最小的向量,实例证明．该方法是简便有效的。     

区间数互反矩阵几何加权集成多属性群决策方法

研究了属性值以区间数表示的群决策问题,提出了区间数决策向量转化为互反判断矩阵的公式,定义了区间数互反判断矩阵几何加权集成算子.在此基础上,提出了区间数多属性群决策的新方法.方法首先针对每一个属性,将各决策者、各方案对应此属性的区间数向量转换为互反判断矩阵,由新定义的集成算子进行集成.由集成区间数矩阵的上界、下界矩阵计算各方案关于此属性的排序向量.由属性权重、可能度和排序公式对方案进行排序.最后给出一个实例进行分析,结果表明了此方法的实用性和可行性.     

层次分析法中基于SVDD群体信息提取方法

针对层次分析法中群决策问题提出一种基于支持向量域描述(SVDD)的集结方法.首先利用生成树的方法把判断矩阵进行一致性剖分;然后利用支持向量域描述的方法排除干扰信息,找出群体公共信息,引入群体相容性,最优解等概念,提出并证明了关于群体信息球的特性;根据最大特征值法把群体信息球中的向量合成为群决策最优解,即关于方案的排序向量.并通过一个具体示例给出该方法的算法步骤同时显示了该方法的可行性和有效性.     

一种基于互补判断矩阵逆判问题的新方法

针对群决策中互补判断矩阵的逆判问题,给出一种新的分析方法.方法通过对互补判断矩阵的导出矩阵向量化后进行偏差比较来对评判专家的评判水平进行排序,给出了对评判专家分类的模糊数学方法,并通过算例验证该方法的实用性和有效性.     

Utilizing feed-back neural network approach for solving linear Fredholm integral equations system

This paper intended to offer an architecture of artificial neural networks (NNs) for finding approximate solution of a second kind linear Fredholm integral equations system. For this purpose, first we substitute the N-th truncation of the Taylor expansion for unknown functions in the origin system. By applying the suggested neural network for adjusting the real coefficients of given expansions in resulting system. The proposed NN is a two-layer feed-back neural network such that it can get a initial vector and then calculates it’s corresponding output vector. In continuance, a cost function is defined by using output vector and the target outputs. Consequently, the reported NN using a learning algorithm that based on the gradient descent method, will adjust the coefficients in given Taylor series. Eventually, we have showed this method in comparison with existing numerical methods such as trapezoidal quadrature rule provides solutions with good generalization and high accuracy. The proposed method is illustrated by several examples with computer simulations.     

Multiperson decision-making based on multiplicative preference relations

A multiperson decision-making problem, where the information about the alternatives provided by the experts can be presented by means of different preference representation structures (preference orderings, utility functions and multiplicative preference relations) is studied. Assuming the multiplicative preference relation as the uniform element of the preference representation, a multiplicative decision model based on fuzzy majority is presented to choose the best alternatives. In this decision model, several transformation functions are obtained to relate preference orderings and utility functions with multiplicative preference relations. The decision model uses the ordered weighted geometric operator to aggregate information and two choice degrees to rank the alternatives, quantifier guided dominance degree and quantifier guided non-dominance degree. The consistency of the model is analysed to prove that it acts coherently.     

Monotonicity of the mapping associated with a noncooperative multiperson game

A noncooperative multiperson game can be associated with a mapping that generates a variational inequality. The problem of searching for Nash points in the game is equivalent to solving this inequality. Numerical methods for solving the variational inequality rely heavily on the monotonicity of the mapping generating the inequality. At the same time, the mapping associated with the noncooperative multiperson game may not be monotone. Necessary and sufficient conditions are established under which the mapping associated with a finite noncooperative mixed-strategy game of three or more persons is monotone.     

Parameter range reduction for ODE models using cumulative backward differentiation formulas

We consider fitting an ODE model to time series data of the system variables. We assume that the parameters of the model have some initial range of possible values and the goal is to reduce these ranges to produce a smaller parameter region from which to start a global nonlinear optimization algorithm. We introduce the class of cumulative backward differentiation formulas (CBDFs) and show that they inherit the accuracy and stability properties of their generating backward differentiation formulas (BDFs). Discretizing the system with these CBDFs and applying consistency conditions results in reductions of the parameter ranges. We show that these reductions are better than can be obtained simply using BDFs. In addition CBDFs inherit any monotonicity properties with respect to the parameters that the vector field possesses, and we exploit these properties to make the consistency checking more efficient. We illustrate with several examples, analyze some of the behavior of our range reduction method, and discuss how the method could be extended and improved.     

互反判断阵比对值对满意一致性的影响

满意一致性是互反判断阵可否作为决策依据的指标.对CR>1的互反判断阵,一般是通过比对值的修正,使之达到满意一致性要求.利用多元隐函数偏导数及行列式基本性质,可以得出各比对值变化对满意一致性的影响比例.在已知影响比例情况下,比对值如何修正、修正多少就有了理论上的依据.     

On a Multiperson Pursuit Problem with Integral Constraints on the Controls of the Players

We consider a linear multiperson differential game with integral constraints on the control of the players. The pursuit is assumed terminated if the solution of at least one of the equations describing the game reaches the origin at some instant of time.In the case of one pursuer, we obtain a necessary and sufficient condition for terminating pursuit from all points of space. In the case of many pursuers, we obtain a sufficient condition for terminating pursuit from all points of space.     

基于马氏决策向量过程模型的有限阶段期望总报酬准则及其最优方程

在马氏决策向量过程模型的理论基础上,结合决策向量和相合度等新定义,进一步提出有限阶段期望总报酬准则和最优方程,并证明最优方程的解的存在性.     

基于群体一致性的犹豫模糊多属性决策方法

犹豫模糊集允许一个元素属于一个集合的隶属度可以是多个不同的值,是表达决策者之间偏好不一致性的有力工具。针对决策者评价偏差不宜过大的问题,提出了一种基于群体一致性的犹豫模糊多属性决策方法。首先, 我们定义了犹豫模糊元的犹豫度函数,进而定义了犹豫模糊元的一致性指数;在此基础上,构建了基于群体一致性指数最大化的权重优化模型,通过求解优化模型可以得到属性的权重向量。然后,运用灰色关联分析法实现对方案的排序和择优。最后,通过实例分析说明了该方法的可行性和有效性。     

基于最大长度区间的区间权重向量标准化方法

区间权重向量在不确定多准则决策分析和AHP中都发挥重要作用,鉴于区间权重向量的不确定性,区间权重向量的标准化问题成为研究的一个热点.在相关研究的基础上,提出基于最大长度区间的区间权重向量标准化方法.首先为了更好理解标准化权重向量,给出标准化区间权重向量的一个等价命题;其次,提出简便的标准化区间权重向量的判定方法,并提出不同情形下,通过调整最大长度区间的区间权重向量的标准化方法;最后,通过算例及与其他方法的对比,说明该方法是简便有效的.     

On an inverse linear programming problem

A method for solving the following inverse linear programming (LP) problem is proposed. For a given LP problem and one of its feasible vectors, it is required to adjust the objective function vector as little as possible so that the given vector becomes optimal. The closeness of vectors is estimated by means of the Euclidean vector norm. The inverse LP problem is reduced to a problem of unconstrained minimization for a convex piecewise quadratic function. This minimization problem is solved by means of the generalized Newton method.