基于证据理论和Vague集的多属性群决策方法研究

为了解决人们在复杂环境中决策困难的问题,论文基于Vague集描述不确定事物的优势,通过证据理论对Vague集进行合成,得到一种信息集结的多属性群决策方法。该算法首先考虑专家评分的可信度,在分析Vague集与证据理论的数学关系后,使用证据理论将各方案在各属性下的专家集证据集结。然后通过Vague集记分函数进行属性权重的计算,将方案集在属性集下的Vague评价值进行加权修正,再通过证据理论将属性集证据集结得到各方案最终的Vague评价值。之后使用记分函数计算每一方案的得分来确定最优方案。最后通过算例进一步说明所提方法的可行性与有效性。文章给出的算法使决策者在不确定环境下可以进行理性决策,从而选出最优方案。     

直觉模糊模型检测在工程决策上的应用

将直觉模糊Kripke结构扩展到加权直觉模糊Kripke结构,将直觉模糊计算树逻辑诱导到加权直觉模糊计算树逻辑;研究在此之上的直觉模糊期望测度和多属性工程决策问题。用加权直觉模糊Kripke结构的权值自然地刻画了工程问题中的成本和收益,直觉模糊测度量化工程进展的不确定性,用加权直觉模糊计算树逻辑描述不确定性工程属性约束。给出了基于直觉模糊模型检测的多属性工程寻优算法,并讨论了算法的复杂度。     

基于双向改进余弦相似度的话题发现算法

话题发现是网络社交平台上进行热点话题预测的一个重要研究问题。针对已有话题发现算法大多基于传统余弦相似度衡量文本数据间的相似性,无法识别各维度取值成比例变化时数据对象间的差异,文本数据相似度计算结果不准确,影响话题发现正确率的问题,提出基于双向改进余弦相似度的话题发现算法(TABOC),首先从方向和取值两个角度改进余弦相似度,提出双向改进余弦相似度,能够区分各维度取值成比例变化的数据对象,保留传统余弦相似度在方向判别上的优势,提高衡量文本相似度的准确性;进一步定义集合的双向改进余弦特征向量和双向改进余弦特征向量的加法等相关定义定理,舍弃无关信息,直接计算新合并集合的特征向量,减小话题发现过程中的时间和空间消耗;还结合增量聚类框架,高效处理新增数据。采用百度贴吧数据进行实验表明,TABOC算法进行话题发现是有效可行的,算法正确率和时间效率总体上优于其他对比算法。     

分类属性数据的泛化中心聚类算法

针对采用经典划分思想的聚类算法以一个点来代表类的局限,提出一种基于泛化中心的分类属性数据聚类算法。该算法通过定义包含多个点的泛化中心来代表类,能够体现出类的数据分布特征,并进一步提出泛化中心距离及类间距离度量的新方法,给出泛化中心的确定方法及基于泛化中心进行对象到类分配的聚类策略,一般只需一次划分迭代就能得到最终聚类结果。将泛化中心算法应用到四个基准数据集,并与著名的划分聚类算法K-modes及其两种改进算法进行比较,结果表明泛化中心算法聚类正确率更高,迭代次数更少,是有效可行的。     

基于广义回归估计的校准加权设计效应模型研究

校准是最常用的加权调整方法,然而传统加权调整设计效应模型只考虑有差异权数导致的精度损失,忽略使用辅助信息后的精度改进,因此应用于设计效应计算时存在一定的缺陷。本文在Spencer模型的基础上进行拓展,引入反映辅助变量和调查变量相关关系的广义回归估计量,构建了校准加权设计效应的一般模型。数值分析结果显示,校准加权设计效应模型的效果优于传统加权调整设计效应模型;尤其在调查变量与辅助变量高度相关的情形下,校准加权设计效应模型能够准确地估计出不等概率抽样设计和校准调整的综合效率。     

一种适用于混合属性数据的K近邻方法

对于传统K近邻算法只适用于数值属性数据类型的问题,提出了一种基于对混合属性数据中的不同属性列赋予不同权值的K近邻算法(K Nearest Neighbor for Mixed-attribute Data,KNNM),使新的K近邻算法能够适用于混合属性数据.由于混合数据间数值属性部分与分类属性部分对整体相似性度量的贡献率不同,又各分量对其所属的属性部分的相似性度量的贡献率不同的特点.提出了考虑数值属性部分与分类属性部分作为整体对混合属性数据间的相似性度量的贡献率,并考虑不同属性数据的各分量对其所属的数据间的相似性度量的贡献率的向量参数计算方法,以此提出了一种适用于混合属性数据的K近邻方法.在5个UCI数据集上的实验结果表明KNNM算法在准确率,宏平均召回率,宏平均精度、宏平均值和ROC均优于传统K近邻算法,以此说明KNNM方法在混合属性数据上的适用性与有效性.     

基于Hausdorff距离的区间数多属性公路网综合评价

公路网评价对于了解区域公路网状态和交通需求间的关系非常重要.讨论了公路网属性表示为区间数的问题,通过计算属性值相对于属性等级的距离矩阵得到相应的加权可变相似度,再对可变相似度进行归一化处理,作为各属性等级的权重向量,同时应用级别特征公式求得综合属性值进行综合评价.实例表明,该方法和其他方法的评价结果一致,且能给出不同标准下的评价结果,计算过程简明且有效,而且能向属性值为其他类型的不确定量进行拓广.     

基于迭代加权回归的推荐算法

评分预测问题是推荐系统研究的核心.本文利用用户评分数据集发掘商品之间的自相关性:将商品看作数据网络中的节点,用商品间的差异度定义节点间的距离,进而将评分预测问题转化为网络回归问题.然后使用迭代加权回归算法进行评分预测.通过对电影评分数据集Movie Lens的分析,验证了算法的有效性,结果表明迭代加权回归算法优于基于项目邻域的协同过滤算法.     

基于相对熵的多属性决策组合赋权方法

综合各种赋权方法给出的主观和客观属性权重信息,建立了求解多属性决策问题属性权重的优化模型,并改进了文献[11]中模型的求解方法.根据各种主客观赋权法给出的赋权结果的贴近度确定其在权重集成中的加权系数,贴近度通过计算权重向量的相对熵来得到,最后通过应用实例对此方法予以说明.     

基于粒关系包含度矩阵的属性约简算法研究

针对信息系统属性约简问题,通过借助粒关系包含度矩阵这一中间工具,给出一种决策表属性启发式约简算法.首先,计算决策表中条件属性与决策属性之间的粒关系包含度矩阵;然后,将粒关系包含度矩阵中隐含的信息L_B作为启发式算子对决策表进行属性约简;最后,删除冗余属性并设置终止条件,实现决策表的属性约简.通过实例验证了该算法的有效性.     

Using the Hamming distance to extend TOPSIS in a fuzzy environment

Considering the fact that, in some cases, determining precisely the exact value of attributes is difficult and that their values can be considered as fuzzy data, this paper extends the TOPSIS method for dealing with fuzzy data, and an algorithm for determining the best choice among all possible choices when the data are fuzzy is also presented. In this approach, to identify the fuzzy ideal solution and fuzzy negative ideal solution, one of the Yager indices which is used for ordering fuzzy quantities in [0, 1] is applied. Using Yager’s index leads to a procedure for choosing fuzzy ideal and negative ideal solutions directly from the data for observed alternatives. Then, the Hamming distance is proposed for calculating the distance between two triangular fuzzy numbers. Finally, an application is given, to clarify the main results developed in the paper.     

Uncertainty index based interval assignment by Interval AHP

In a multi-attribute decision making problem, indigenous values are assigned to attributes based on a decision maker’s subjective judgments. The given judgments are often uncertain, because of the uncertainty of situations and intuitiveness of human judgments. In order to reflect the uncertainty in the assigned values, they are denoted as intervals whose widths represent the possibilities of attributes. Since it is difficult for a decision maker to assign values directly to attributes in case of more than two attributes, he/she gives a pairwise comparison matrix by comparing two attributes at one occasion. The given matrix contains two kinds of uncertainty, one is inconsistency among comparisons and the other is incompleteness of comparisons. This paper proposes the models to obtain intervals of attributes from the given uncertain pairwise comparison matrix. At first, the uncertainty indexes of a set of intervals are defined from the viewpoints of entropy in probability, sum or maximum of widths, or ignorance. Then, considering that too uncertain information is not useful, the intervals of attributes are obtained by minimizing their uncertainty indexes.     

Value reducts and bireducts: A comparative study

In Rough Set Theory, the notion of bireduct allows to simultaneously reduce the sets of objects and attributes contained in a dataset. In addition, value reducts are used to remove some unnecessary values of certain attributes for a specific object. Therefore, the combination of both notions provides a higher reduction of unnecessary data. This paper is focused on the study of bireducts and value reducts of information and decision tables. We present theoretical results capturing different aspects about the relationship between bireducts and reducts, offering new insights at a conceptual level. We also analyze the relationship between bireducts and value reducts. The studied connections among these notions provide important profits for the efficient information analysis, as well as for the detection of unnecessary or redundant information.     

A new learning strategy for stereo matching derived from a fuzzy clustering method

This paper presents an approach to the local stereo correspondence problem. The primitives or features used are groups of collinear connected edge points called segments. Each segment has several associated attributes or properties. We have verified that the differences of the attributes for the true matches cluster in a cloud around a center. Then for each current pair of primitives we compute a distance between the difference of its attributes and the cluster center. The correspondence is established in the basis of the minimum distance criterion (similarity constraint). We have designed an image understanding system to learn the best representative cluster center. For such purpose a new learning method is derived from the Fuzzy c-Means (FcM) algorithm where the dispersion of the true samples in the cluster is taken into account through the Mahalanobis distance. This is the main contribution of this paper. A better performance of the proposed local stereo-matching learning method is illustrated with a comparative analysis between classical local methods without learning.     

一种考虑决策者风险偏好的区间数多属性决策方法

针对属性值以区间数形式给出的多属性决策问题,提出了一种决策分析方法。在本文中,首先描述了属性值为区间数形式的多属性决策问题;然后通过引入决策者的风险偏好因子将区间数决策信息映射为实数值决策信息,并依据属性值与属性均值绝对偏差的大小确定了属性的权重,在此基础上依据所得权重给出了基于加权和法的方案排序方法,通过对风险偏好因子的不同取值还可进行方案排序的灵敏度分析。最后,通过一个算例说明了本文给出方法的可行性和有效性。     

Use of the equivalent attribute technique in multi-criteria planning of local energy systems

This paper discusses how the equivalent attribute technique (EAT) can be used to improve the comprehensibility of a multi-attribute utility theory study. When using EAT, ‘vague’ expected total utility values are converted into equivalent values for one of the attributes being considered, often an economic attribute. Two models are considered: a simplified linear model, and a more advanced non-linear model that includes the DM’s strength-of-preference and risk attitude. EAT is particularly useful in distinguishing between alternatives with similar utility values. When the difference between utility values is larger, the choice among the alternatives should be clear, and EAT therefore becomes less useful. The technique can still be used, although extra care is needed when choosing the equivalent attribute. A local energy-planning problem is used as a case study to illustrate and exemplify the EAT approach.     

Aggregation of utility-based individual preferences for group decision-making

Multi-attribute utility theory (MAUT) elicits an individual decision maker’s preferences for single attributes and develops a utility function by mathematics formulation to add up the preferences of the entire set of attributes when assessing alternatives. A common aggregation method of MAUT for group decisions is the simple additive weighting (SAW) method, which does not consider the different preferential levels and preferential ranks for individual decision makers’ assessments of alternatives in a decision group, and thus seems too intuitive in achieving the consensus and commitment for group decision aggregation. In this paper, the preferential differences denoting the preference degrees among different alternatives and preferential priorities denoting the favorite ranking of the alternatives for each decision maker are both considered and aggregated to construct the utility discriminative values for assessing alternatives in a decision group. A comparative analysis is performed to compare the proposed approach to the SAW model, and a satisfaction index is used to investigate the satisfaction levels of the final two resulting group decisions. In addition, a feedback interview is conducted to understand the subjective perceptions of decision makers while examining the results obtained from these two approaches for the second practical case. Both investigation results show that the proposed approach is able to achieve a more satisfying and agreeable group decision than that of the SAW method.     

基于粗糙集的突发事件属性约简方法

针对突发事件不完备信息系统中的原始数据存在大量属性冗余的问题,提出一种基于粗糙集的不完备信息系统属性约简方法,以剔除冗余属性,提高知识清晰度。首先对缺失、冗余、噪声以及连续型数据进行预处理;然后进行属性分类,将属性分为条件属性与决策属性,进而建立决策表;最后根据决策表的特征,结合有序加权平均算子的思想,提出一种基于属性重要度的启发式属性约简算法。文末,通过实例验证了方法的正确性与有效性,并利用该方法实现了火灾数据的属性约简。     

Research on two different mathematical theories on control

With a brand-new theory, this paper not only provides the differences of attributes in concept, formula expression and function type between fuzzy rough sets and probability statistics, but also introduces their differences in algorithms on target control for better solving the control problem. Some new definitions and theorems concerning fuzzy rough sets and probability statistics are given, but this paper mainly makes a comparison of two control algorithms for the target tracking. The simulation results show that the comprehensive performance of the fuzzy rough sets algorithm is better than that of the probability statistics algorithm, but its control effect is not as good as that of the latter on multisensor target control. Finally, some problems concerning the combination of fuzzy rough sets and the probability statistics phenomenon to be solved and development trends are discussed. By these investigations, we can choose the optimal control algorithms for accomplishing better target control.     

Finite volume schemes on triangles coupled with multiresolution analysis

A multiresolution procedure is used to reduce the costs of flux evaluations in a finite volume scheme. A two-dimensional hyperbolic conservation law is solved on the finest grid among a hierarchy of nested grids. The mean values of the solution on triangles of a given grid are estimated from the coarser level using an original reconstruction algorithm. The size of the differences between the mean values and their reconstruction is a local regularity criterium and dictates the choice of the flux computation method. Numerical experiments with computing time comparisons are presented.