一种基于组合不确定型OWA算子的区间数群决策方法

在群决策中,由于决策环境的不确定性,决策者给出区间效信息.基于区间数可能度矩阵公式和互补判断矩阵的排序公式,提出了一种组合不确定型OWA算子,它是不确定型OWA算子的推广.该算子能集结群决策中区间数信息,文中给出了其在应用的具体步骤,最后实例分析说明了该方法的有效性和可行性.     

基于改进区间数密度集结算子指标群赋权方法

针对指标数据已知,而权重数据未知的群组赋权问题,给出了一种基于改进的区间数密度集结算子来进行指标群组赋权的决策方法。首先给出了区间数和区间数密度集结算子(IDM)的定义及性质,改进了以前区间数聚类的方法,应用直接法对一维区间数据组进行聚类,并定义了模糊统计量,以确定最为合理的一种聚类方式。然后基于改进的区间数密度集结算子这种数学模型,来解决指标值数据已知,而权重未知的群组赋权问题。最后举例说明该方法的可行性和实用性。     

考虑可信度和属性优先级的犹豫模糊决策方法

研究了考虑可信度的犹豫模糊混合集成因子以及考虑属性优先级的犹豫模糊多属性决策方法。首先给出了用于衡量数据差异程度的加权变异率公式,并证明了其具有类似于基尼系数的优良度量性质,之后在此基础上提出了可信度诱导犹豫模糊混合平均(CIHFHA)算子。针对属性权重信息未知的犹豫模糊决策问题,构建了一种新的考虑属性优先级的熵值修正G1的组合赋权方法,该方法可有效地利用属性客观评价数据以及通过考虑属性优先级体现专家意见,解决了主客观权重分配问题,得出的属性权重更加客观、合理。之后给出了一种基于CIHFHA算子和组合赋权方法的多属性决策方法,算例说明该方法的有效性和实用性。     

基于二型直觉三角前景T2ITFNHA算子的多准则群决策方法

在二型直觉模糊集与直觉三角模糊数的基础上,定义了二型直觉三角模糊数及其运算法则,给出基于二型直觉三角模糊数的加权算术平均(WAA)算子,有序加权平均(OWA)算子和混合集结(HA)算子.考虑决策者有限理性决策行为下的异化风险态度与敏感性,定义二型直觉三角模糊前景效应与前景价值函数,构造前景T2ITFNHA算子.针对多方参与决策且决策者权重确定,准则权重未知的多准则群决策问题,采用正态分布赋权法计算前景T2ITFNHA算子指标置换下的位置权重,提出基于二型直觉三角前景T2ITFNHA算子的决策方法.该方法利用前景T2ITFNHA算子集结群体准则的二型直觉三角前景价值函数,运用灰色系统理论确定准则权重,并通过计算前景集对记分函数对方案进行对比和排序.最后,案例分析说明了二型直觉三角模糊数的实际应用背景及所提高的决策方法的有效性和可行性.     

梯形模糊有序加权几何算子及其在决策中的应用

针对梯形模糊数据信息的集成问题,给出了梯形模糊数两两比较的可能度公式和梯形模糊有序加权几何(TFOWG)算子.基于可能度公式和TFOWG算子,提出了一种准则权重信息完全未知且准则值以梯形模糊数形式给出的不确定多准则决策方法.最后,实例分析表明了该方法的可行性和有效性.     

综合主、客观权重信息的最优组合赋权方法

首先构造了一种多属性决策主观权重确定的偏好比率法,介绍了属性客观权重确定的熵值法,提出了一种基于离差平方和的最优组合赋权方法,并给出了具体算例.通过提出的方法可以将多属性决策问题中主、客观权重的信息进行有效地综合.     

不确定语言环境下基于ULHGA算子的群决策方法

研究属性权重和专家权重为确定的实数,属性值为不确定语言变量的多属性群决策问题.提出了一种新的数据信息集成算子不确定语言混合几何集结(ULHGA)算子,并给出不确定语言环境下基于ULWGM算子和ULHGA算子的一种群决策方法.最后进行实例分析,说明该方法的实用性和有效性.     

权重为直觉模糊数的直觉模糊多属性群决策方法

针对属性权重以直觉模糊数形式给出的直觉模糊多属性群决策问题,提出了一种新的集成算子,首先证明了该算子具有诸如单调性等良好的性质,然后将该算子应用到权重为直觉模糊数的直觉模糊多属性群决策方法中,给出了决策方法的一般步骤,最后用实例说明了该方法的有效性和实用性.     

导出的纯语言OWGA算子及其在的群决策中的应用

研究属性权重、专家权重和属性值均为纯语言变量的多属性群决策问题,利用纯语言变量的运算规律,提出一种新的数据信息集成算子:导出的纯语言有序加权几何平均(IPLOWGA)算子。并且给出纯语言环境下基于IPLOWGA算子和PLOWGA算子的一种群决策方法。最后,进行实例分析,说明该方法的实用性和有效性。     

一种模糊有序加权(FOWA)算子及其应用

针对多个三角模糊数的集结问题，提出一种新的模糊有序加权(FOWA)算子。该算子是对传统OWA算子的扩展，它使三角模糊数可根据其所在排序位置进行集结。分析FOWA算子所具有的性质，给出在群决策中模糊信息集结的一个应用算例。     

Linear feature-weighted support vector machine

The existing support vector machines (SVMs) are all assumed that all the features of training samples have equal contributions to construct the optimal separating hyperplane. However, for a certain real-world data set, some features of it may possess more relevances to the classification information, while others may have less relevances. In this paper, the linear feature-weighted support vector machine (LFWSVM) is proposed to deal with the problem. Two phases are employed to construct the proposed model. First, the mutual information (MI) based approach is used to assign appropriate weights for each feature of the whole given data set. Second, the proposed model is trained by the samples with their features weighted by the obtained feature weight vector. Meanwhile, the feature weights are embedded in the quadratic programming through detailed theoretical deduction to obtain the dual solution to the original optimization problem. Although the calculation of feature weights may add an extra computational cost, the proposed model generally exhibits better generalization performance over the traditional support vector machine (SVM) with linear kernel function. Experimental results upon one synthetic data set and several benchmark data sets confirm the benefits in using the proposed method. Moreover, it is also shown in experiments that the proposed MI based approach to determining feature weights is superior to the other two mostly used methods.     

基于理想点-矢量投影法的创新需求权重确定方法

现有的创新需求权重计算方法大多只考虑顾客、技术人员和决策者三者中的一方或者两方对创新需求权重的影响,鲜有方法将三方同时纳入需求权重计算过程,这很容易造成因信息考虑不全面,造成需求权重的精确度不高或失准等问题。鉴于此,本文提出一种基于理想点-矢量投影法的创新需求权重确定方法,它将顾客、技术人员和决策者三方的诉求在三维矢量空间中进行集成。分别计算创新需求的需求类别因子、需求技术成熟度和需求偏好度,采用理想点-矢量投影法得到理想需求矢量,并在此基础上计算每项创新需求权重值。文章最后通过汽车方向盘的研发的案例,验证了所提方法的有效性和可行性。     

Pareto set approximation by the method of adjustable weights and successive lexicographic goal programming

A nonlinear multiobjective optimization problem is considered. Two methods are proposed to generate solutions with an approximately uniform distribution in a Pareto set. The first method is supposed to find the solutions as minimizers of weighted sums of objective functions where the weights are properly selected using a branch and bound type algorithm. The second method is based on lexicographic goal programming. The proposed methods are compared with several metaheuristic methods using two and three-criteria tests and applied problems.     

Determining attribute weights to improve solution reliability and its application to selecting leading industries

In multiple attribute decision analysis, many methods have been proposed to determine attribute weights. However, solution reliability is rarely considered in those methods. This paper develops an objective method in the context of the evidential reasoning approach to determine attribute weights which achieve high solution reliability. Firstly, the minimal satisfaction indicator of each alternative on each attribute is constructed using the performance data of each alternative. Secondly, the concept of superior intensity of an alternative is introduced and constructed using the minimal satisfaction of each alternative. Thirdly, the concept of solution reliability on each attribute is defined as the ordered weighted averaging (OWA) of the superior intensity of each alternative. Fourthly, to calculate the solution reliability on each attribute, the methods for determining the weights of the OWA operator are developed based on the minimax disparity method. Then, each attribute weight is calculated by letting it be proportional to the solution reliability on that attribute. A problem of selecting leading industries is investigated to demonstrate the applicability and validity of the proposed method. Finally, the proposed method is compared with other four methods using the problem, which demonstrates the high solution reliability of the proposed method.     

区间型符号数据的特征选择方法

对区间型符号数据进行特征选择,可以降低数据的维数,提取数据的关键特征。针对区间型符号数据的特征选择问题,本文提出了一种新的特征选择方法。首先,该方法使用区间数Hausdorff距离和区间数欧氏距离度量区间数的相似性,通过建立使得样本点与样本类中心相似性最大的优化模型来估计区间型符号数据的特征权重。其次,基于特征权重构建相应的分类器来评价所估计特征权重的优劣。最后,为了验证本文方法的有效性,分别在人工生成数据集和真实数据集上进行了数值实验,数值实验结果表明,本文方法可以有效地去除无关特征,识别出与类标号有关的特征。     

An improved method for ranking alternatives in multiple criteria decision analysis

Scoring rules are an important disputable subject in data envelopment analysis (DEA). Various organizations use voting systems whose main object is to rank alternatives. In these methods, the ranks of alternatives are obtained by their associated weights. The method for determining the ranks of alternatives by their weights is an important issue. This problem has been the subject at hand of some authors. We suggest a three-stage method for the ranking of alternatives. In the first stage, the rank position of each alternative is computed based on the best and worst weights in the optimistic and pessimistic cases, respectively. The vector of weights obtained in the first stage is not a singleton. Hence, to deal with this problem, a secondary goal is used in the second stage. In the third stage of our method, the ranks of the alternatives approach the optimistic or pessimistic case. It is mentionable that the model proposed in the third stage is a multi-criteria decision making (MCDM) model and there are several methods for solving it; we use the weighted sum method in this paper. The model is solved by mixed integer programming. Also, we obtain an interval for the rank of each alternative. We present two models on the basis of the average of ranks in the optimistic and pessimistic cases. The aim of these models is to compute the rank by common weights.     

Outlier detection and robust covariance estimation using mathematical programming

The outlier detection problem and the robust covariance estimation problem are often interchangeable. Without outliers, the classical method of maximum likelihood estimation (MLE) can be used to estimate parameters of a known distribution from observational data. When outliers are present, they dominate the log likelihood function causing the MLE estimators to be pulled toward them. Many robust statistical methods have been developed to detect outliers and to produce estimators that are robust against deviation from model assumptions. However, the existing methods suffer either from computational complexity when problem size increases or from giving up desirable properties, such as affine equivariance. An alternative approach is to design a special mathematical programming model to find the optimal weights for all the observations, such that at the optimal solution, outliers are given smaller weights and can be detected. This method produces a covariance estimator that has the following properties: First, it is affine equivariant. Second, it is computationally efficient even for large problem sizes. Third, it easy to incorporate prior beliefs into the estimator by using semi-definite programming. The accuracy of this method is tested for different contamination models, including recently proposed ones. The method is not only faster than the Fast-MCD method for high dimensional data but also has reasonable accuracy for the tested cases.     

基于方案贴近度和满意度的交互式不确定多属性决策方法

针对属性权重信息部分确知且对方案有偏好的不确定多属性决策问题,提出一种基于方案贴近度和满意度的交互式决策方法.方法首先利用已知的客观信息和决策者的主观要求建立单目标规划模型,其次通过对方案满意度和综合度的给定与修正来实现人机交互决策.最后,通过实例说明模型及方法的可行性和有效性.     

A portfolio model for performance assessment: the <Emphasis Type="Italic">Financial Times</Emphasis> MBA ranking

The ranking of MBA programmes by newspapers and magazines is common and usually controversial. This paper discusses the use of the most popular method of making these rankings via a multicriteria model which uses the weighted sum of a number of performance measures to give an overall score on which selection or ranking may be based. The weights are a quantitative model of the preferences of those making the evaluation. Many methods are available to obtain weights from preference statements so that for any set of preferences a number of different weight sets can be found depending on the method used. Cognitive limits lead to inconsistency in preference judgements so that weights may be subject both to uncertainty and to bias. It is proposed that choosing weights to minimize discrimination between alternatives (not weights) guards against unjustified discrimination between alternatives. Applying the method to data collected by the Financial Times shows the effect of varying the level of discrimination between weights and also the effect of using a reduced data set made necessary by the partial publication of information.     

语言多属性决策的一种组合方法

研究了属性权重完全未知,方案属性值和偏好值均为语言变量的多属性决策问题.首先,通过分析相关文献中利用方案属性值与偏好值之间的偏差得到属性权重的不合理性,在最小化方案综合属性值与偏好值的偏差的基础上,建立了一个求解属性权重的规划模型.其次,在各方案的属性值与属性正理想点的偏差最小的基础上,又建立一个求解属性权重的规划模型.第三,在综合考虑各属性下所有决策方案总的组合偏差之和最小的基础上,将上述两个规划模型相结合,得到了一个反映出决策者对两种不同信息的偏好程度的求解属性权重的规划模型,得到了语言多属性决策的一种组合方法.最后,通过实例说明方法的可行性与有效性.