变权决策中变权效果分析与状态变权向量的确定

引入状态变权向量调节度和标准调节度以及调权水平的概念，为分析状态变权向量调节权重的能力提供了可量化的工具．利用标准调节度讨论了选择状态变权向量的一些基本原则和理论依据，并由调权水平给出了一种选择状态变权向量的可操作性方法．     

Soliciting weights or probabilities from experts for rule-based expert systems

Rule-based expert systems attach a weight to each rule in order to represent uncertainty or strength of association. There are a number of schemes that are used to represent uncertainty in expert systems. Some of these methods allow the system designer to solicit either the probabilities, used to compute the weights, or to solicit the weights directly, or both.This paper presents results that indicate that if the weights are gathered directly, rather than using probabilities, then the weights may not meet the underlying conditions of the mathematical model of uncertainty on which the weights are based or the weights may imply highly unusual behavior for the underlying probabilities and implicit utility function.In one system it is found that there were violations of the mathematical properties of the model in over forty percent of the weights on the rules of the system. If the weights do not meet the constraints of the underlying mathematical models then such violations may yield inappropriate parameterization of other weights in order to make the model work. Further, such violations can lead to an inappropriate estimation of the probabilities of events by the system and yield inappropriate inferred weights.In another case it was found that a system was dominated by weights that suggest highly unusual behavior for the underlying probabilities.From an operational perspective these inconsistencies indicate the importance of the method used in gathering the weights, e.g. indirectly through the probabilities or directly through the weights. It also indicates the importance of validating and verifying the weights to ensure that the weights meet the needs of the underlying theory and do not force unusual relationships onto the underlying probabilities.     

Steady-state weights solution to affine projection algorithm

A new expression of the weights update equation for the affine projection algorithm (APA) is proposed that improves the convergence rate of an adaptive filter,particularly for highly colored input sign...     

Global convergence and limit cycle behavior of weights of perceptron.

In this paper, it is found that the weights of a perceptron are bounded for all initial weights if there exists a nonempty set of initial weights that the weights of the perceptron are bounded. Hence, the boundedness condition of the weights of the perceptron is independent of the initial weights. Also, a necessary and sufficient condition for the weights of the perceptron exhibiting a limit cycle behavior is derived. The range of the number of updates for the weights of the perceptron required to reach the limit cycle is estimated. Finally, it is suggested that the perceptron exhibiting the limit cycle behavior can be employed for solving a recognition problem when downsampled sets of bounded training feature vectors are linearly separable. Numerical computer simulation results show that the perceptron exhibiting the limit cycle behavior can achieve a better recognition performance compared to a multilayer perceptron.     

基于自适应权重的粗糙K均值聚类算法

原有Rough K-means算法中类的上、下近似采用固定经验权重,其科学性值得商榷,针对这一问题,设计了一种基于自适应权重的粗糙K均值聚类算法。基于自适应权重的粗糙聚类算法在每一次迭代过程中,根据当前的数据划分状态,动态计算每个样本对于类的权重,降低了原有算法对初始权重的依赖。此外,该算法采用近似集合中的高斯距离比例来表现样本权重,从而可以在多种数据分布上得到更精确的聚类结果。实验结果表明,基于自适应权重的粗糙K均值算法是一种较优的聚类算法。     

Least‐squared ordered weighted averaging operator weights

The ordered weighted averaging (OWA) operator by Yager (IEEE Trans Syst Man Cybern 1988; 18; 183–190) has received much more attention since its appearance. One key point in the OWA operator is to determine its associated weights. Among numerous methods that have appeared in the literature, we notice the maximum entropy OWA (MEOWA) weights that are determined by taking into account two appealing measures characterizing the OWA weights. Instead of maximizing the entropy in the formulation for determining the MEOWA weights, a new method in the paper tries to obtain the OWA weights that are evenly spread out around equal weights as much as possible while strictly satisfying the orness value provided in the program. This consideration leads to the least‐squared OWA (LSOWA) weighting method in which the program is to obtain the weights that minimize the sum of deviations from the equal weights since entropy is maximized when all the weights are equal. Above all, the LSOWA method allocates the positive and negative portions to the equal weights that are identical but opposite in sign from the middle point in the number of criteria. Furthermore, interval LSOWA weights can be constructed when a decision maker specifies his or her orness value in uncertain numerical bounds and we present a method, with those uncertain interval LSOWA weights, for prioritizing alternatives that are evaluated by multiple criteria. © 2008 Wiley Periodicals, Inc.     

基于熵理论的多属性群决策专家权重的调整算法

研究多属性群决策中决策者权重的调整问题.在得到决策者主观权重的基础上,提出一种权重调整算法.通过计算专家个体决策结果与群体决策结果的偏差量并结合熵理论求得专家的客观权重,将其作为权重调整值,进行决策者的权重调整.计算调整后的决策结果,并据此继续对权重进行调整.通过反复调整,直至计算出稳定的权重和决策结果.最后通过算例表明了该方法的可行性与实用性.     

案例推理分类器属性权重的内省学习调整方法

针对案例推理（CBR）分类器中案例属性权重的分配问题,提出一种基于内省学习的属性权重迭代调整方法。该方法可根据CBR分类器对训练案例分类的结果调整属性的权重。基于成功驱动的权重学习策略,若当前训练案例分类成功,则首先根据权重调整公式增加匹配属性的权重并减少不匹配属性的权重;然后对所有权重进行归一化从而得到当次迭代的新权重。实验结果表明,所提方法的CBR分类器在UCI数据集PD、Heart和WDBC的准确率比传统CBR分类器分别提高1.72%、4.44%和1.05%。故成功驱动的内省学习权重调整方法可以提高权重分配的合理性,进而提高CBR分类器的准确率。     

Minimizing deviations of input and output weights from their means in data envelopment analysis

In this paper, we propose a model that minimizes deviations of input and output weights from their means for efficient decision-making units in data envelopment analysis. The mean of an input or output weight is defined as the average of the maximum and the minimum attainable values of the weight when the efficient decision making unit under evaluation remains efficient. Alternate optimal weights usually exist in the linear programming solutions of efficient decision-making units and the optimal weights obtained from most of the linear programming software are somewhat arbitrary. Our proposed model can yield more rational weights without a priori information about the weights. Input and output weights can be used to compute cross-efficiencies of decision-making units in peer evaluations or group decision-making units, which have similar production processes via cluster analysis. If decision makers want to avoid using weights with extreme or zero values to access performance of decision-making units, then choosing weights that are close to their means, may be a rational choice.     

基于输出层权值解析修正的神经网络有效训练

根据神经网络训练误差对权值的梯度特征分析,提出了网络输出层权值与网络隐含层权值轮换修正的思想,并基于网络输出层权值与网络隐含层权值之间的依赖关系,建立了网络输出层权值解析修正和隐含层权值修正的具体方法,所提出的方法通过提高网络权值修正的准确性而提高网络训练的有效性。根据网络输出节点的输出误差与其总输入误差的关系,提出了进一步提高所获得网络推广性的具体方法。实例计算结果表明,所提出的方法可以显著地提高网络的训练效率,并有效地增强网络推广性。     

A criteria weighting approach by combining fuzzy quality function deployment with relative preference relation

In past, fuzzy multi-criteria decision-making (FMCDM) models desired to find an optimal alternative from numerous feasible alternatives under fuzzy environment. However, researches seldom focused on determination of criteria weights, although they were also important components for FMCDM. In fact, criteria weights can be computed through extending quality function deployment (QFD) under fuzzy environment, i.e. fuzzy quality function deployment (FQFD). By FQFD, customer demanded qualities expressing the opinions of customers and service development capabilities presenting the opinions of experts can be integrated into criteria weights for FMCDM. However, deriving criteria weights in FQFD may be complex and different to multiply two fuzzy numbers in real world. To resolve the tie, we will combine FQFD with relative preference relation on FMCDM problems. With the relative preference relation on fuzzy numbers, it is not necessary multiplying two fuzzy numbers to derive criteria weights in FQFD. Alternatively, adjusted criteria weights will substitute for original criteria weights through relative preference relation. Obviously, adjusted criteria weights are clearly determined and then utilized in FMCDM models.     

Optimal weight tuning method for unit selection cost functions in syllable based text-to-speech synthesis

This paper proposes a method for tuning the weights of unit selection cost functions in syllable based text-to-speech (TTS) synthesis system. In this work, unit selection cost functions, namely target cost and concatenation cost, are designed appropriate to syllables. The method tunes the weights in such a way that perceptual preference patterns are appropriately considered while selecting the units. The method uses genetic algorithm to derive the optimal weights. Fitness function is designed to map perceptual preference patterns into weights of unit selection cost functions. The effectiveness of proposed method is evaluated by both subjective and objective measures. From the results, it is observed that the derived optimal weights can synthesize good quality speech compared to manually tuned weights.     

Improving minimax disparity model to determine the OWA operator weights

Determining the Ordered Weighted Averaging (OWA) operator weights is important in decision making applications. Several approaches have been proposed in the literature to obtain the associated weights. This paper provides an alternative disparity model to identify the OWA operator weights. The proposed mathematical model extends the existing disparity approaches by minimizing the sum of the deviation between two distinct OWA weights. The proposed disparity model can be used for a preference ranking aggregation. A numerical example in preference ranking and an application in search engines prove the usefulness of the generated OWA weights.     

基于灰色系统理论的多属性群决策专家权重的调整算法

研究多属性群决策中专家权重的调整问题.在得到专家主观权重的基础上,提出一种权重调整算法.通过计算专家个体决策结果与群体决策结果的灰色关联度并结合初始权重求得专家的综合权重,运用专家的综合权重计算调整后的决策结果,并据此继续对权重进行调整,直至计算出稳定的权重和决策结果.通过对嵌入式计算机的性能评价表明了该方法的可行性与实用性.     

Aligning JN-25 messages in depth using weights when the code groups scan

By the end of 1943, US Navy mathematician/codebreaker Marshall Hall Jr. had developed a system of statistical weights to align JN-25 messages in depth. Although then-current methods of aligning JN-25 messages in depth were working satisfactorily, Hall developed his method “just in case.” On 1 December 1943, the Japanese changed the method of numbering the lines and columns of additives on pages of the JN-25 additive book, and Hall’s weights, which had been developed “just in case,” were needed immediately. This paper discusses both the mathematical idea that was the foundation of Hall’s weights and the construction of the weights. It also explores the navy’s use of the weights as well as their use at Bletchley Park. At the same time, the navy was exploring the use of two other systems of weights to align JN-25 messages in depth, and those systems of weights are also described.     

主客观权重集成及扩展VIKOR的多属性群决策方法

针对评价信息、属性权重均为不同粒度语言短语的多属性群决策问题,提出一种基于主客观权重集成及扩展多准则协调优化解（VIKOR）的多属性群决策方法。由基本语言评价集实现对多粒度语言评价矩阵的一致化,基于同一粒度的语言决策矩阵计算群体对属性的评价偏差,基于群体评价意见的一致性原则得到属性客观权重,通过二元语义加权算术平均（T-WAA）算子得到属性主观权重,从而集成主、客观权重求得属性综合权重。集结转化后的单个评价矩阵得到群体评价矩阵及其导出矩阵,由扩展VIKOR方法,根据群效用值、个体遗憾值及综合评价值分别对方案进行排序,获得折衷方案。算例分析表明该方法的有效性与可行性。     

Negative effects of sufficiently small initial weights on back-propagation neural networks

In the training of feedforward neural networks,it is usually suggested that the initial weights should be small in magnitude in order to prevent premature saturation.The aim of this paper is to point out the other side of the story:In some cases,the gradient of the error functions is zero not only for infinitely large weights but also for zero weights.Slow convergence in the beginning of the training procedure is often the result of sufficiently small initial weights.Therefore,we suggest that,in these cases,the initial values of the weights should be neither too large,nor too small.For instance,a typical range of choices of the initial weights might be something like(0.4,0.1) ∪(0.1,0.4),rather than(0.1,0.1) as suggested by the usual strategy.Our theory that medium size weights should be used has also been extended to a few commonly used transfer functions and error functions.Numerical experiments are carried out to support our theoretical findings.     

基于层次分析法的本体映射

运用层次分析法来解决相似度计算中的权值分配问题。它将影响相似度计算的各个因素划分成相关联的有序层次,通过判断矩阵的建立、权值计算和一致性检验得到结果。该方法将定性分析和定量分析相结合,综合考虑不同属性对于概念含义影响程度的差别,有效地减小了使用等权算法或者是人为确定权值所产生的计算误差,使权值的分配更科学,提高了相似度计算的准确度。     

A constrained non-linear optimization model for fuzzy pairwise comparison matrices using teaching learning based optimization

Non-linear optimization models have been recently proposed to derive crisp weights from fuzzy pairwise comparison matrices. In this paper, a TLBO (Teaching Learning Based Optimization) based solution is presented for solving an optimization model as a system of non-linear equations to derive crisp weights from fuzzy pairwise comparison matrices in AHP (Analytic Hierarchy Process). This fuzzy-AHP method is named as TLBO-1. It has been found that TLBO-1 can lead to inconsistent or less consistent weights. To solve the problem of inconsistent weights, a new constrained non-linear optimization model is proposed in this paper. This model is based on the min-max approach for fuzzy pairwise comparison ratios of weights. TLBO is again used to solve this optimization model, and crisp weights are derived. This fuzzy AHP method is named as TLBO-2. The effectiveness of the proposed model is illustrated by three examples. For each example, the consistency of the derived crisp weights is compared with other optimization models. The results show that the TLBO-2 method can derive more consistent weights for the fuzzy AHP based Multi-Criteria Decision Making (MCDM) systems as compared to the other optimization models.     

自顶向下聚集型代数多重网格预条件的边权选择

针对基于图划分的自顶向下聚集型代数多重网格预条件,考察了利用METIS软件包进行多重网格构建的方法,并就该软件包只能处理整型权重,不能处理实型权重的问题,提出了一种将实型边权转化为整型边权的有效方法。之后将这种转化方法应用到METIS图划分软件中的边权选择,并用其给出了对自顶向下聚集型代数多重网格预条件的一种改进算法。通过对二维与三维模型偏微分方程离散所得稀疏线性方程组的数值实验表明,带边权的改进型算法大大提高了多重网格预条件共轭斜量法的迭代效率,特别是对各向异性问题,改进效果更加显著。