DEA中有效值的一种求法与保序的条件

对DEA中决策单元的有效值,本文给出了求它的二个定理,并给出了在导入新的决策单元后其保序的充分条件,最后举例说明这条件不成立时的结果.     

一种新的学习效应的机器排序问题研究

近年来有关学习效应的排序模型越来越受到关注. 由于机器操作的逐渐熟练,对于工件加工位置有关的学习模型具有更现实的意义. 考虑到工人在加工工件的过程中经验的增加, 与已经加工过的工件之和有关的学习模型也具有一定的现实意义. 本文研究工件加工位置和已经加工过的工件加工时间之和有关的学习模型,对于单机, 流水作业排序的情形作了一些分析,并给出了多项式时间算法.     

证券组合的模糊规划模型

通过结构元方法定义了一种模糊数排序准则,利用模糊约束将Markowitz投资组舍模型转化为模糊线性规划模型,并利用模糊数来描述证券的期望收益率和风险损失率,建立模糊数模糊证券投资组合模型.最后,利用定义的模糊数排序准则把模糊数规划问题转化为经典的线性规划问题,然后再对该模型进行求解,并通过算例阐述了该方法的有效性.     

基于一般学习效应下的单机排序问题

近来具有学习效应的机器排序问题收到广泛的关注.对于机器排序中工件的实际加工来说,与工件加工位置有关的学习模型更具有现实性.本文研究了工件加工位置和与已经加工过的工件之和有关的一般学习效应模型.首先证明文献中与位置和已经加工过的工件加工时间之和有关的学习模型是本模型的特殊情形.其次对于单机排序问题我们提出一般解法.     

基于相对熵的多粒度语言判断矩阵的群决策方法

针对多粒度语言判断矩阵的群决策问题提出基于相对熵的最优化模型的排序方法.在多粒度语言偏好信息的导出函数基础上定义了语言判断矩阵对应的导出模糊互补判断矩阵,并给出其排序向量的计算式;同时采用语言判断矩阵的一致性指标来确定专家重要性程度的权向量;在相对熵的意义下构建了群决策排序向量的最优化模型,探讨了模型的求解方法.实例分析表明该模型是可行和有效的.     

基于模糊结构元表述的模糊数排序

讨论了如何利用结构元理论来解决模糊数的排序问题.首先,给出了四种经典的模糊数排序方法,并证明了这四种方法都可以利用结构元理记来表述;进而,提出了一种基于结构元理论的排序方法,给出了该方法的性质,并同传统方法进行了比较.     

基于交叉评价策略的DEA灰色关联排序模型

数据包络分析(DEA)是评价决策单元相对效率的有效方法,其中的交叉效率评价方法可用来对决策单元进行区分排序.针对原有模型中交叉效率值的不唯一问题,结合灰色关联分析思想,构建理想决策单元,定义各决策单元与理想决策单元的灰色关联度,以灰色关联度值最大为目标,建立优化模型来计算输入和输出指标的最佳权重,据此得出决策单元的交叉效率值,实现对决策单元的完全排序.最后通过算例来验证模型的有效性和实用性.     

基于交叉评价策略的DEA灰色关联排序模型北大核心

数据包络分析(DEA)是评价决策单元相对效率的有效方法,其中的交叉效率评价方法可用来对决策单元进行区分排序.针对原有模型中交叉效率值的不唯一问题,结合灰色关联分析思想,构建理想决策单元,定义各决策单元与理想决策单元的灰色关联度,以灰色关联度值最大为目标,建立优化模型来计算输入和输出指标的最佳权重,据此得出决策单元的交叉效率值,实现对决策单元的完全排序.最后通过算例来验证模型的有效性和实用性.     

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.     

一种新的互补判断矩阵排序方法

排序方法问题是决策分析中的重要问题,具有广泛的应用价值.面对某一项选拔,快速而有效的将备选项目进行排序进而择优和决策显得尤为重要.但由于备选项在各个方面的相近或相同,很难将其排序进行决策,将这些方面以数据来衡量并组合起来,形成判断矩阵.针对互补判断矩阵的乘性一致性定义和加性一致性定义,尝试提出一个新的函数,并分别建立最优化模型,得到了相应的两个排序公式,并从理论上研究了它们的一些性质,通过仿真实例说明该方法的可行性,简便性.     

On the chaotic properties of the von Foerster-Lasota equation

In this article we present a different approach to some of the results published in our recent paper (Brze?niak and Dawidowicz in Semigroup Forum, 78(1):118–137, 2009). This new approach is based on a deep result from a paper (Ergod. Theory Dyn. Syst. 17(4):793–819, 1997) by Desch Schappacher and Webb.     

A unique equilibrium efficient frontier with fixed-sum outputs in data envelopment analysis

Based on the equilibrium efficient frontier data envelopment analysis (EEFDEA) approach, Fang (J Oper Res Soc 67:412–420, 2015a) developed an equivalent linear programming model to improve and strengthen the EEFDEA approach. Furthermore, Fang (2015a) indicated that his secondary goal approach can achieve a unique equilibrium efficient frontier. However, through a simple counterexample we demonstrate that Fang’s secondary goal approach cannot always achieve uniqueness of the equilibrium efficient frontier. In this paper, we propose an algorithm based on the secondary goal approach to address the problem. The proposed algorithm is proven mathematically to be an effective approach to guaranteeing the uniqueness of the equilibrium efficient frontier.     

Economic inefficiency measurement of input spending when decision-making units face different input prices

In a recent paper, Kaoru Tone (J Opl Res Soc (2002) 2: 429–444) showed that when the Farrell measure of cost efficiency is estimated for two firms that have different input prices, a firm with higher costs can be deemed more efficient than a firm with lower costs. As an alternative approach, Tone proposed a radial cost efficiency measure that is estimated using levels of spending on each input, rather than input quantities. Thus, firms with higher costs are less efficient than firms with lower costs. In this paper, we extend Tone's approach by allowing for non-radial changes in spending. Our approach builds on earlier work by Luenberger (J Math Econ (1992) 21: 461–481) and Chambers et al (J Econ Theo (1996) 70: 407–419) who use directional distance functions to measure inefficiency. We provide an example and illustration of our approach using Japanese bank data.     

On approximate solutions for robust convex semidefinite optimization problems

In this paper, we consider approximate solutions (\(\epsilon \)-solutions) for a convex semidefinite programming problem in the face of data uncertainty. Using robust optimization approach (worst-case approach), we prove an approximate optimality theorem and approximate duality theorems for \(\epsilon \)-solutions in robust convex semidefinite programming problem under the robust characteristic cone constraint qualification. Moreover, an example is given to illustrate the obtained results.     

On quasi $$\epsilon $$-solution for robust convex optimization problems

This paper devotes to the quasi \(\epsilon \)-solution (one sort of approximate solutions) for a robust convex optimization problem in the face of data uncertainty. Using robust optimization approach (worst-case approach), we establish approximate optimality theorem and approximate duality theorems in term of Wolfe type on quasi \(\epsilon \)-solution for the robust convex optimization problem. Moreover, some examples are given to illustrate the obtained results.     

二元样条空间维数的若干进展

近年来,计算机辅助几何设计（ＣＡＧＤ）中兴起了一种叫做ｂｌｏｓｓｏｍ的方法,本文综述了方法用之于三角盼上样条空间维数的研究所取得的一些进展。     

Fuzzy BCC Model for Data Envelopment Analysis

Fuzzy Data Envelopment Analysis (FDEA) is a tool for comparing the performance of a set of activities or organizations under uncertainty environment. Imprecise data in FDEA models is represented by fuzzy sets and FDEA models take the form of fuzzy linear programming models. Previous research focused on solving the FDEA model of the CCR (named after Charnes, Cooper, and Rhodes) type (FCCR). In this paper, the FDEA model of the BCC (named after Banker, Charnes, and Cooper) type (FBCC) is studied. Possibility and Credibility approaches are provided and compared with an -level based approach for solving the FDEA models. Using the possibility approach, the relationship between the primal and dual models of FBCC models is revealed and fuzzy efficiency can be constructed. Using the credibility approach, an efficiency value for each DMU (Decision Making Unit) is obtained as a representative of its possible range. A numerical example is given to illustrate the proposed approaches and results are compared with those obtained with the -level based approach.     

Monotonic optimization for sensor cover energy problem

We study the sensor cover energy problem (SCEP) in wireless communication—a difficult nonconvex problem with nonconvex constraints. A local approach based on DC programming called DCA was proposed by Astorino and Miglionico (Optim Lett 10(2):355–368, 2016) for solving this problem. In the present paper, we propose a global approach to (SCEP) based on the theory of monotonic optimization. By using an appropriate reformulation of (SCEP) we propose an algorithm for finding quickly a local optimal solution along with an efficient algorithm for computing a global optimal solution. Computational experiments are reported which demonstrate the practicability of the approach.     

Proximal Hypertopologies Revisited

It is the aim of this paper to prove that for an arbitrary metric space (X,d) and a set of nonempty closed subsets of X which contains all singletons and which is closed under enlargements, we can construct a canonical approach distance on the hyperspace CL(X), having the -proximal topology (resp. the Hausdorff metric) as its topological (resp. p-metric) coreflection. We investigate some properties like, e.g., compactness and completeness of the introduced approach structures. In this way we obtain results which generalize their classical counterparts for proximal hit-and-miss hypertopologies. We also give a characterization of the completion of the introduced approach spaces.     

Model Design Based on the Systems Approach

It is shown how the (extended) systems approach can be successfully used to design mathematical models in a highly systematic way. The systems approach supports interdisciplinarity in that it encourages participation of non-mathematicians in the model design process. The systems approach also leads to a clear documentation of a model.The basic principle explained in this paper is that indices of a model represent elements of an element set of a system, and that variables and constants of a model represent attributes of the elements. Multi-indexed variables and constants refer to attributes of ‘complex entities’ (from extended systems terminology) which cover the information between the elements.