区间合作博弈的区间核心的研究

研究了区间合作博弈的区间核心,得出满足超可加性的2人区间合作博弈区间核心是存在的,并通过引入左、右博弈的概念,讨论了通过左、右博弈的核心来构造区间合作博弈区间核心的问题,举例说明了左、右博弈的核心可以非空而区间博弈核心可以为空。通过引入合于的概念,给出了通过左、右博弈的核心可构造区间核心的充要条件。讨论了区间核心为空时左、右博弈的核心的分离性,以及对具有非空区间核心的区间博弈进行压缩的问题,最后讨论了区间合作博弈区间核心计算问题,并用实例予以说明。     

严格对角占优指派博弈解的研究

合作博弈在经济学研究中具有广泛的应用。通过数学证明的方法,研究严格对角占优指派博弈的解:研究了严格对角占优指派博弈的PS性;讨论了满足PS性的严格对角占优指派博弈的Shapley值、核仁与τ-值之间的关系;证明了严格对角占优指派博弈满足PS性的充分必要条件;得到了满足PS性的严格对角占优指派博弈的Shapley值在核心中,以及其Shapley值与核仁、τ-值一致的结论。     

基于妥协算法的区间数多属性决策新方法

妥协(VIKOR)算法往往用于精确数的评估中,但由于决策者的经验等原因,往往在决策时给出的评估值为区间数.文章针对这一情况.将VIKOR引入到区间数的评价中,利用区间数的特性分别计算出理想解和非理想解,以及方案综合评价值和利益比率;并应用区间数的可能度排序方法进行排序.实例证明,该方法是有效的.     

基于效用最大化的区间值投资组合模型及其应用

采用区间数测度投资收益,利用半绝对偏差作为投资风险的测度,并在考虑投资者效用的条件下提出一种新的基于效用最大化的区间值投资组合模型。为得到该模型的解,引入一个反映市场经济环境因素的系数,从而将区间值规划问题转化成为一个一般的线性规划问题,并结合实例说明该模型的应用。     

基于集值统计的区间综合评判及其应用

综合评判是根据评判对象的评判因素,采用综合评判模型对评判对象作出一个综合判断。为了克服传统综合评判的不足,研究了基本集值统计的区间综合评判,探讨了集值统计区间分析处理方法。运用了集值统计判断矩阵计算因素权重区间;集值统计和属性测度构建评判矩阵;综合评判区间构建可能度矩阵计算相对权重;得到了综合评判区间排序。该综合评判的优点在于充分体现了评价者的真实意图,充分融合了集值统计区间分析处理多种方法的优点。通过案例分析,基于集值统计的区间综合评判是可行的,具有较强的操作性。     

基于区间数观察值的灰色白化权函数聚类模型重构

针对区间数观察值的白化权函数取值范围是一个区间数的思路,文章结合单一实数值不同测度白化权在不同区段内白化权取值的增减特性,给出一种基于区间数观察值的典型、上限、三角、下限测度白化权函数的新算法,并结合区间数可能度排序方法,提出了新的对于区间数观察值的灰色白化权函数聚类决策步骤.并验证了本文算法的有效性.     

动态联盟供应链生产任务分配的优化方法研究

本文针对网状供应链结构,建立了动态联盟供应链生产任务分配的整数规划模型.同时,结合指派博弈理论证实了基于上述模型的联盟博弈核心的存在性,这说明通过上述模型得到的分配方案能够最大化动态联盟的整体收益,从而可以促进动态联盟供应链的正常生产.另外,为便于供应链的统筹规划,提出了当量产品概念.     

基于前景理论的区间数多准则决策方法

针对准则偏好值为区间数的不确定性决策问题,提出了一种基于前景理论的多准则决策方法。该方法将准则值看作给定区间内N个等差随机数,利用正态分布的分布函数来表示区间内准则值的分布规律,在给定各准则参考点的基础上,通过价值函数和决策权重函数计算方案在各准则下的前景值,并通过加权平均得到各方案的总前景值;根据前景值的大小对所有方案排序并得到最优方案。该方案的可行性通过一个简单实例得到了论证。     

基于正态分布点值化的区间主成分评价法及应用

针对区间数据点值化过程中所存在的“代表性不足”的缺陷,提出了基于正态分布的点值化方法并将之应用于区间主成分评价法。通过与基于中心点值化的区间主成分法的比较,得到三个主要结论：第一,基于正态分布的点值化方法能将各样品的点值化结果导向指标均值,而非区间值的中心点;第二,基于正态分布的点值化结果增加了数据信息量;第三,基于正态分布点值化的区间主成分评价法提高了数据降维效果,具有更好的因子命名能力。应用结果表明,在考虑正态分布情况下,对区间数据的点值化处理方法具有较好的效果,基于正态分布点值化的方法可推广至基于区间数的评价和决策问题。     

一种区间信度的扩展分配及合成方法

区间数是表示不精确信息的常用表达方式.在无法获得精确信息的情况下,信度结构需要扩展为区间值信度结构,相应的基本信度分配由区间数表示.文章提出利用证据理论合成区间信度的新方法,通过对区间值信度结构的分析,将区间信度分为"确知信度"和"未知信度"两部分,从而将区间值信度结构转换为识别框架下的扩展信度分配;然后利用Dempscer合成规则合成扩展的信度分配,并且证明得到的综合区间值信度结构仍是有效的;最后给出一个对比实例验证了该方法的有效性.     

Confidence intervals for the mean of a normal distribution with restricted parameter space

For a normal distribution with known variance, the standard confidence interval of the location parameter is derived from the classical Neyman procedure. When the parameter space is known to be restricted, the standard confidence interval is arguably unsatisfactory. Recent articles have addressed this problem and proposed confidence intervals for the mean of a normal distribution where the parameter space is not less than zero. In this article, we propose a new confidence interval, rp interval, and derive the Bayesian credible interval and likelihood ratio interval for general restricted parameter space. We compare these intervals with the standard interval and the minimax interval. Simulation studies are undertaken to assess the performances of these confidence intervals.     

Validation of tolerance interval

The tolerance interval receives very much attention in literature and is widely applied in industry. However, it is generally constructed through the criterion of minimum width by Eisenhart et al. (1947). Although effort for clarification of several prediction related intervals has been made recently by Huang et al. (2010), the appropriateness of the tolerance interval for its role in industry applications is insufficiently discussed. According to manufacturers' requests, a concept of admissibility of tolerance intervals is defined in this paper and we show that these types of tolerance intervals are not admissible due to short of confidence. We further prove that a 100(1−α)% confidence interval of a γ-coverage interval is admissible and is appropriate for use.     

A NEW SHORT EXACT GEOMETRIC CONFIDENCE INTERVAL

For discrete distributions, the standard method of producing a two‐sided confidence interval generates an interval that is exact but conservative. This paper proposes a new algorithm to produce a short exact geometric confidence interval with proven properties, and compares the new interval with the standard interval.     

Interval estimation for the generalized inverted exponential distribution under progressive first failure censoring

In this paper, we consider the inferential procedures for the generalized inverted exponential distribution under progressive first failure censoring. The exact confidence interval for the scale parameter is derived. The generalized confidence intervals (GCIs) for the shape parameter and some commonly used reliability metrics such as the quantile and the reliability function are explored. Then the proposed procedure is extended to the prediction interval for the future measurement. The GCIs for the reliability of the stress-strength model are discussed under both equal scale and unequal scale scenarios. Extensive simulations are used to demonstrate the performance of the proposed GCIs and prediction interval. Finally, an example is used to illustrate the proposed methods.     

Inference for a binomial proportion in the presence of ties

We suppose a case is to be compared with controls on the basis of a test that gives a single discrete score. The score of the case may tie with the scores of one or more controls. However, scores relate to an underlying quantity of interest that is continuous and so an observed score can be treated as the rounded value of an underlying continuous score. This makes it reasonable to break ties. This paper addresses the problem of forming a confidence interval for the proportion of controls that have a lower underlying score than the case. In the absence of ties, this is the standard task of making inferences about a binomial proportion and many methods for forming confidence intervals have been proposed. We give a general procedure to extend these methods to handle ties, under the assumption that ties may be broken at random. Properties of the procedure are given and an example examines its performance when it is used to extend several methods. A real example shows that an estimated confidence interval can be much too small if the uncertainty associated with ties is not taken into account. Software implementing the procedure is freely available.     

Some Small-Sample Properties of the Student t Confidence Intervals

For the two-sided Student t confidence interval for the mean of a normal distribution there is, for any sample size, a sufficiently large confidence level that ensures that the interval covers all the observations; there are also sufficiently small confidence levels guaranteeing, respectively, that (a) the interval does not cover all the observations and (b) the interval lies within the extreme observations. Necessary and sufficient conditions are also obtained for the width of the confidence interval to always exceed the sample range, as well as for the reverse inequality. Some implications of the results are discussed.     

Confidence intervals for the difference in paired Youden indices

Comparison of accuracy between two diagnostic tests can be implemented by investigating the difference in paired Youden indices. However, few literature articles have discussed the inferences for the difference in paired Youden indices. In this paper, we propose an exact confidence interval for the difference in paired Youden indices based on the generalized pivotal quantities. For comparison, the maximum likelihood estimate‐based interval and a bootstrap‐based interval are also included in the study for the difference in paired Youden indices. Abundant simulation studies are conducted to compare the relative performance of these intervals by evaluating the coverage probability and average interval length. Our simulation results demonstrate that the exact confidence interval outperforms the other two intervals even with small sample size when the underlying distributions are normal. A real application is also used to illustrate the proposed intervals. Copyright © 2012 John Wiley & Sons, Ltd.     

An improved score interval with a modified midpoint for a binomial proportion

One of the most basic and important problems in statistical inference is the construction of the confidence interval (CI). In this paper, we propose a novel CI for a binomial proportion by modifying the midpoint of the score interval. The proposed modified interval can solve the ‘downward spikes’ problem of the score interval without enlarging the interval length. Simulation studies are carried out to illustrate the performance of the modified interval. With regard to the criterions of coverage probability, mean absolute error and expected length, our method is competitive among the several commonly used methods for constructing a CI. A real data example is also presented to show the application of our method.     

Confidence intervals for a bounded mean in exponential families

Setting confidence bounds or intervals for a parameter in a restricted parameter space is an important issue in applications and is widely discussed in the recent literature. In this article, we focus on the distributions in the exponential families, and propose general forms of the truncated Pratt interval and rp interval for the means. We take the Poisson distribution as an example to illustrate the method and compare it with the other existing intervals. Besides possessing the merits from the theoretical inferences, the proposed intervals are also shown to be competitive approaches from simulation and real-data application studies.