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针对偏序集方法不能解决含有权重的多准则决策问题,提出一种“隐式”赋权的偏序决策方法。首先将含有m个方案和n个准则的决策问题表示成偏序集,之后按权重由大到小的顺序,对准则进行逐步相加形成n个新的准则,得到一个新的偏序集。根据偏序集间的包含关系,证明了新偏序集不仅蕴含了权重信息,而且比初始偏序集有更强的排序能力。结果表明,该法在应用中仅需获取权重排序信息,无需精确权重,适用于权重难以确定的多准则决策问题。以三峡库区水质评价为例,例子表明新方法明显优于原有的偏序决策方法,能够对13个方案进行聚类和排序,而原有方法在该例中几乎难以应用。 相似文献
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徐克龙 《数学的实践与认识》2009,39(3)
ELECTRE法是一种多目标属性决策方法.将该法中以一定风险程度建立超序关系的思想引入到风险决策中,提出了基于超序关系的风险决策方法并对求得的偏序结构进行了分析.最后给出的实例可表明该法是简单实用的. 相似文献
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在具有模糊观测数据的线性回归问题中,通过定义模糊序指标实现模糊数的排序,借助经典最小二乘法原理,给出了使平方误差和在此排序方法下达到最小的模糊回归系数最小二乘序估计方法。三个例子的结果表明,文中的最小二乘方法能很好的对输入和输出为模糊数,回归系数为精确值的回归模型进行估计,更重要的是,此方法不仅对三角模糊数适用,对其他类型的模糊观测数据也适用。 相似文献
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针对模糊互补矩阵次序一致性检验和调整存在争议和繁杂问题,提出了模糊互补矩阵次序一致性检验与调整的偏序集表示方法。在定义了偏序集、模糊互补矩阵、截集矩阵等相关概念基础上,求出模糊互补矩阵B的0.5水平截集矩阵,证明了模糊互补判断矩阵次序一致性和0.5水平截集矩阵为偏序关系矩阵的等价性;模糊互补判断矩阵完全次序一致性的充要条件是任意截集均满足传递性;任意截集满足传递性和偏序关系矩阵的等价性。结果表明,利用0.5水平截集矩阵转换为矩阵来检验模糊互补矩阵的次序一致性;通过调整每个截集矩阵满足传递性并赋值,能够达到模糊互补矩阵完全次序一致性。最后,通过两个算例验证该检验和调整方法的合理性和可行性。 相似文献
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定义L-模糊偏序集上的L-核系统,给出了任一L-模糊偏序集上的L-核算子与L-核系统之间的一一对应关系,从而推广了有界完备L-模糊偏序集的情形,并使得模糊的情况与分明的情况更加协调。另外,也给出了L-闭包算子与L-闭包系统的相关结论。 相似文献
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焊接工作者的经验总是有限的,凭经验选出的焊接方法不能保证最合适,因此开发出一种多属性决策专家系统是当前焊接工作者所急需的.在分析各种多属性决策方法的优缺点基础上,提出了基于级别优序关系和层次分析法的铝合金焊接方法决策算法.采用对数模糊优先规划方法从模糊判断矩阵中得出精确权重值,采用基于级别优序关系中的偏好顺序结构评估法(PROMETHEE)对可行方案进行排序,通过一个具体实例阐述了决策流程,结果表明方法具有一定的实用价值.最后指出研究中的不足和进一步研究方向. 相似文献
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The Spectral Decomposition of Covariance Matrices for the Variance Components Models 总被引:2,自引:0,他引:2
The aim of this paper is to propose a simple method to determine the number of distinct eigenvalues and the spectral decomposition of covariance matrix for a variance components model. The method introduced in this paper is based on a partial ordering of symmetric matrix and relation matrix. A method is also given for checking straightforwardly whether these distinct eigenvalues are linear dependent as functions of variance components. Some examples and applications to illustrate the results are presented. 相似文献
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拟序是图能量排序中一种有效方法,基于该方法,已经得到了大量图类的极值能量排序的结果.Gutman给出了点数和为n的两条路的并的能量排序,而三条路的并的能量排序没有一个理想的结论.本文利用拟序法给出点数和为n的三条路的并的极值能量及一类图能量的排序. 相似文献
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《Optimization》2012,61(2):283-289
An inventory system with unit demand, varying ordering levels and random lead times is considered in this paper. Ordering level is determined by the number of demands during last lead time. The ordering quantity will be such as to bring back the inventory level to S at the ordering epoch. No backlog is permitted. The time dependent probability distribution of the inventory level is obtained. Correlation between the number of demands during a lead time and the length of the next inventory dry period is obtained and it is illustrated by an example. 相似文献
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Two devices are subjected to shocks arriving according to a general counting process. Let M1 and M2 be the random number of shocks that cause the failure of the first and the second device, respectively. We find conditions on the counting process such that the mean residual life ordering, the increasing convex ordering and the expectation ordering between M1 and M2 are preserved in the random lifetimes of the two devices. 相似文献
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《Journal of computational and graphical statistics》2013,22(4):978-994
Many procedures have been proposed to compute nonparametric maximum likelihood estimators (NPMLEs) of survival functions under stochastic ordering constraints. However, each of them is only applicable to a specific type of stochastic ordering constraint and censoring, and is often hard to implement. In this article, we describe a general and flexible method based on geometric programming for computing the NPMLEs from right- or interval-censored data. To this end, we show that the monotonicity properties of the likelihood function and the stochastic ordering constraints considered in the literature allow us to reformulate the estimation problem as a geometric program (GP), a special type of mathematical optimization problem, which can be transformed to a convex optimization problem, and then solved globally and efficiently. We apply this GP-based method to real data examples to illustrate its generality in handling different types of ordering constraints and censoring. We also conduct simulation studies to examine its numerical performance for various sample sizes. Supplemental materials including technical details, computer code, and data files are available online. 相似文献
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可换BCH-代数 总被引:1,自引:1,他引:0
李金龙 《数学的实践与认识》2014,(23)
引入了可换BCH-代数的概念,给出了可换BCH-代数的两个充要条件.对偏序可换BCH-代数进行了讨论,给出了偏序BCH-代数是可换的两个充要条件.证明了偏序可换BCH-代数的每个分支是一个下半格,局部有界偏序可换BCH-代数的每个分支是一个格. 相似文献
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We describe the basis of a matrix ordering heuristic for improving the incomplete factorization used in preconditioned conjugate gradient techniques applied to anisotropic PDE's. Several new matrix ordering techniques, derived from well-known algorithms in combinatorial graph theory, which attempt to implement this heuristic, are described. These ordering techniques are tested against a number of matrices arising from linear anisotropic PDE's, and compared with other matrix ordering techniques. A variation of RCM is shown to generally improve the quality of incomplete factorization preconditioners.This work was supported by by the Natural Sciences and Engineering Research Council of Canada, and by the Information Technology Research Center, which is funded by the Province of Ontario. 相似文献
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The linear ordering problem is an NP-hard combinatorial problem with a large number of applications. Contrary to another very popular problem from the same category, the traveling salesman problem, relatively little space in the literature has been devoted to the linear ordering problem so far. This is particularly true for the question of developing good heuristic algorithms solving this problem.In the paper we propose a new heuristic algorithm solving the linear ordering problem. In this algorithm we made use of the sorting through insertion pattern as well as of the operation of permutation reversal. The surprisingly positive effect of the reversal operation, justified in part theoretically and confirmed in computational examples, seems to be the result of a unique property of the problem, called in the paper the symmetry of the linear ordering problem. This property consists in the fact that if a given permutation is an optimal solution of the problem with the criterion function being maximized, then the reversed permutation is a solution of the problem with the same criterion function being minimized. 相似文献
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1.BackgroundMom1979,WuWentsunbeganthestudyofautomatedtheoremprovingindifferentialgeometry[1].Inhismethod,thehypotheses,representedbydifferentialpolynomials,aretriangulatedaccordingtoanorderofthevariablesinthepolynomials;theconclusionisprovedbythetriangulatedresultcalledcharacteristicset.Wuusedelement-basedorderingmethodwhichcanbeillustratedbythisexample'LettingxKybetwosmoothfunctionsofthesamevariable,thenxKX'KX"K'Ky'y,Ky"'.ThisorderisthefoundationofWu'seliminationprinciple.However,a… 相似文献