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1.
在平面几何中,合理添加辅助线,构造恰当模型,往往成为顺利解题的关键,而在证明有关线段成比例的定理中,常用的有两个,下面用模型表示:图11° 若DE∥BC,则DAAC=EAAB,△DAE∽△CAB.2° 若DE∥BC,则ADAB=AEAC,ADDB=AEEC,△ADE∽△ABC.我们不妨把1°的模型叫X型,2°的模型叫A型,这两种模型在证明有关线段成比例的问题上,能帮助我们快速、有效地作出辅助线.下面结合一道命题对此作出阐述.命题 过△ABC的顶点C任意作一条直线,与边AB及中线AD分别交于F、E…  相似文献   

2.
没有附加随机有界条件的B值随机元列的有界重对数律   总被引:2,自引:0,他引:2  
没有附加随机有界条件的B值随机元列的有界重对数律刘立新,杨小云(保定师范专科学校,保定071051)(吉林大学数学系,长春130023)BOUNDEDLAWOFTHEITERATEDLOGARITHMFORASEQUENCEOFB-VALUEDRAN...  相似文献   

3.
一种预测的新方法──DEA方法应用的新领域   总被引:3,自引:0,他引:3  
数据包络分析(简称DEA)是用数学规划来评价有多投入多产出的一个(或同一类)部门管理水平的一种新型的效率评价方法。本文则尝试将DEA方法的应用推广到预测领域,特别是回归预测法难以计算的多投入多产出的预测问题,并给出了具体的算法。  相似文献   

4.
二阶可加混料模型参数估计的I_λ──最优设计关颖男,张崇岐(东北大学数学系,沈阳110006)I_λ-OPTIMALDESIGNSOFPARAMETERESTIMATIONFORTHEADDITIVEMIXTUREMODELOF2-DEGREE¥GUA...  相似文献   

5.
双下标L~p-混合随机变量和及其在线性模型中的应用胡舒合(安徽大学数学系,合肥230039)SUMSOFDOUBLEARRAYSOFL~p-MIXINGALESEQUENCEANDITSAPPLICATIONINLINEARMODELS¥HUSHUHE...  相似文献   

6.
哮喘模型的谱方法与逆谱方法   总被引:4,自引:0,他引:4  
鲁百年 《计算数学》1995,17(3):229-237
哮喘模型的谱方法与逆谱方法鲁百年(陕西师范大学数学系)SPECTRALANDPSEUDOSPECTRALAPPROXIMATIONSFORTHEMODELOFWHEEZES¥LuBai-mian(DepartmentofMathematics,Sha...  相似文献   

7.
李元香  黄樟灿 《计算数学》1996,18(3):313-320
一阶线性和拟线性双曲型方程的格点模型李元香(武汉大学软件工程国家重点实验室)黄樟灿(武汉工学院)LATTICEMODELSFORFIRSTORDERLINEARANDQUASI-LINEARHYPEBOLICEQUATIONS¥LiYuan-xian...  相似文献   

8.
用Maxwell方程组反演层状地球模型中的ε,μ   总被引:1,自引:0,他引:1  
用Maxwell方程组反演层状地球模型中的ε,μ郑家茂,王元明(东南大学数学系,南京210018)SOLVINGε,μINLAYEREDEARTHMODELBYMAXWELLSYSTEM¥ZHENGJIAMAO;WANGYUANMING(Depart...  相似文献   

9.
已知圆内接四边形ABCD的边分别为AB=2 ,BC =6,CD =DA =4,求四边形ABCD的面积 .解 如图 ,连接AC、BD .在CB上截取CE =CD =4并且连接AE ,DE .AE交DB于F .∵CD =DA =4,∴ ∠ 1=∠ 2 .∵ ABCD四点共圆 ,∴ ∠ 1=∠ 3 , ∠ 2 =∠ 4.∴ ∠ 3 =∠ 4.∴ BF为∠ABE的平分线 .∵ BE =CB -CE =6-4 =2 ,∴ AB =BE =2 .∴ △BAE为等腰△ .∵ BF为∠ABE的平分线 ,∴ BF垂直平分AE .  又∵ BFD在一条直线上 ,∴ DA =DE =4.∴ DE =DC =CE =4.∴ △C…  相似文献   

10.
最优设计是基于回归模型的一种试验设计方法,A-最优,D-最优,E-最优等是常用的最优准则。本讲第一部份对最优设计作一简介,第二部份介绍正交设计的D-最优性。利用正交表的D-最优性,可以显着地增加高水平(4水平以上)正交表的使用效率  相似文献   

11.
Data envelopment analysis (DEA) is the leading technique for measuring the relative efficiency of decision-making units (DMUs) on the basis of multiple inputs and multiple outputs. In this technique, the weights for inputs and outputs are estimated in the best advantage for each unit so as to maximize its relative efficiency. But, this flexibility in selecting the weights deters the comparison among DMUs on a common base. For dealing with this difficulty, Kao and Hung (2005) proposed a compromise solution approach for generating common weights under the DEA framework. The proposed multiple criteria decision-making (MCDM) model was derived from the original non-linear DEA model. This paper presents an improvement to Kao and Hung's approach by means of introducing an MCDM model which is derived from a new linear DEA model.  相似文献   

12.
Lack of discrimination power and poor weight dispersion remain major issues in Data Envelopment Analysis (DEA). Since the initial multiple criteria DEA (MCDEA) model developed in the late 1990s, only goal programming approaches; that is, the GPDEA-CCR and GPDEA-BCC were introduced for solving the said problems in a multi-objective framework. We found GPDEA models to be invalid and demonstrate that our proposed bi-objective multiple criteria DEA (BiO-MCDEA) outperforms the GPDEA models in the aspects of discrimination power and weight dispersion, as well as requiring less computational codes. An application of energy dependency among 25 European Union member countries is further used to describe the efficacy of our approach.  相似文献   

13.
Data envelopment analysis (DEA) and stochastic multicriteria acceptability analysis (SMAA-2) are methods for evaluating alternatives based on multiple criteria. While DEA is mainly an ex-post tool used for classifying alternatives into efficient and inefficient ones, SMAA-2 is an ex-ante tool for supporting multiple criteria decision-making. Both methods use a kind of value function where the importance of criteria is modeled using weights. Unlike many other methods, neither DEA nor SMAA-2 requires decision-makers’ weights as input. Instead, these so-called non-parametric methods explore the weight space in order to identify weights favorable for each alternative. This paper introduces the SMAA-D method, which is a combination of DEA and SMAA-2. SMAA-D can be characterized as an extension of DEA to handle uncertain or imprecise data to provide stochastic efficiency measures. Alternatively, the combined method can be seen as a variant of SMAA-2 with a DEA-type value function.  相似文献   

14.
This study discusses nine desirable properties that a measure of technical efficiency (TE) needs to satisfy from the perspective of production economics and optimization. Seven data envelopment analysis (DEA) models are theoretically compared from a viewpoint of nine TE criteria. All the seven DEA models suffer from a problem of multiple projections even though a unique projection for efficiency comparison is one of the nine desirable properties. Furthermore, all the DEA models violate the property on aggregation of inputs and outputs. Thus, the seven DEA models do not satisfy all desirable TE properties. In addition, the comparison provides us with the following guidelines: (a) The additive model violates all desirable TE properties. (b) Russell measure and SBM (=ERGM) perform as well as RAM as a non-radial measure. If we are interested in strict monotonicity, the two models outperform the other DEA models including RAM. In contrast, if we are interested in translation invariance, RAM is better than Russell measure and SBM (=ERGM). (c) The radial measures (CCR and BCC) have the property of linear homogeneity. (d) The CCR model is useful for measuring a frontier shift among different periods. (e) If a data set contains a negative value, RAM becomes a DEA model to handle the negative value because it has the property of translation invariance. After examining the desirable TE properties, this study proposes a new approach to deal with an occurrence of multiple projections. The proposed approach includes a test to examine an occurrence of multiple projections, a mathematical expression of a projection set, and a selection process of a unique reference set as the largest one covering all the possible reference sets.  相似文献   

15.
针对单准则广义DEA模型在评价决策单元有效性时的局限性,从输入和输出两个角度同时考虑,建立了双准则广义DEA模型,并应用模糊数学理论给出其求解方法.  相似文献   

16.
Operational research (OR) offers efficient tools to support managers in strategic decision-making processes. Data envelopment analysis (DEA) and multiple criteria decision aid (MCDA) are two important research areas in OR. These two domains are both based on the evaluation of “objects” according to multiple “points of views”. Within the MCDA framework, choosing appropriate weights for the different criteria often arises as a problem itself for decision makers. As a consequence, researchers have developed original methodologies to help them during this elicitation phase. In this work, we aim to investigate how DEA can be used to propose weights in the context of the PROMETHEE II method. More precisely, we suggest an extension of the so-called “decision maker brain” used in the GAIA plane (also known as PROMETHEE VI) based on DEA. The underlying idea is based on the computation of weights in PROMETHEE (GAIA brain) which are compatible with the DEA analysis. We end this paper with a numerical example.  相似文献   

17.
Data envelopment analysis (DEA) is a method to estimate the relative efficiency of decision-making units (DMUs) performing similar tasks in a production system that consumes multiple inputs to produce multiple outputs. So far, a number of DEA models with interval data have been developed. The CCR model with interval data, the BCC model with interval data and the FDH model with interval data are well known as basic DEA models with interval data. In this study, we suggest a model with interval data called interval generalized DEA (IGDEA) model, which can treat the stated basic DEA models with interval data in a unified way. In addition, by establishing the theoretical properties of the relationships among the IGDEA model and those DEA models with interval data, we prove that the IGDEA model makes it possible to calculate the efficiency of DMUs incorporating various preference structures of decision makers.  相似文献   

18.
Data envelopment analysis methods classify the decision making units into two groups: efficient and inefficient ones. Therefore, the fully ranking all DMUs is demanded by most of the decision makers. However, data envelopment analysis and multiple criteria decision making units are developed independently and designed for different purposes. However, there are some applications in problem solving such as ranking, where these two methods are combined. Combination of multiple criteria decision making methods with data envelopment analysis is a new idea for elimination of disadvantages when applied independently. In this paper, first the new combined method is proposed named TOPSIS-DEA for ranking efficient units which not only includes the benefits of both data envelopment analysis and multiple criteria decision making methods, but also solves the issues that appear in former methods. Then properties and advantages of the suggested method are discussed and compared with super efficiency method, MAJ method, statistical-based model (CCA), statistical-based model (DR/DEA), cross-efficiency—aggressive, cross-efficiency—benevolent, Liang et al.’s model, through several illustrative examples. Finally, the proposed methods are validated.  相似文献   

19.
The application of Data Envelopment Analysis (DEA) as an alternative multiple criteria decision making (MCDM) tool has been gaining more attentions in the literatures. Doyle (Organ. Behav. Hum. Decis. Process. 62(1):87?C100, 1995) presents a method of multi-attribute choice based on an application of DEA. In the first part of his method, the straightforward DEA is considered as an idealized process of self-evaluation in which each alternative weighs the attributes in order to maximize its own score (or desirability) relative to the other alternatives. Then, in the second step, each alternative applies its own DEA-derived best weights to each of the other alternatives (i.e., cross-evaluation), then the average of the cross-evaluations that get placed on an alternative is taken as an index of its overall score. In some cases of multiple criteria decision making, direct or indirect competitions exist among the alternatives, while the factor of competition is usually ignored in most of MCDM settings. This paper proposes an approach to evaluate and rank alternatives in MCDM via an extension of DEA method, namely DEA game cross-efficiency model in Liang, Wu, Cook and Zhu (Oper. Res. 56(5):1278?C1288, 2008b), in which each alternative is viewed as a player who seeks to maximize its own score (or desirability), under the condition that the cross-evaluation scores of each of other alternatives does not deteriorate. The game cross-evaluation score is obtained when the alternative??s own maximized scores are averaged. The obtained game cross-evaluation scores are unique and constitute a Nash equilibrium point. Therefore, the results and rankings based upon game cross-evaluation score analysis are more reliable and will benefit the decision makers.  相似文献   

20.
The advent of data envelopment analysis (DEA) enabled the measurement of efficiency to be extended to the case of multiple outputs. Prior to DEA we had the parametric approach based on multiple regression. We highlight some difficulties associated with these two approaches and present a hybrid which overcomes them whilst maintaining the respective advantages of each. This hybrid models the efficient frontier using an algebraic expression; the resulting smooth representation allows all units to be naturally enveloped and hence slacks to be avoided. (Slacks are potential improvements for inefficient units which are not accounted for in the DEA (radial) score, and so have been problematic for DEA.) The approach identifies the DEA-efficient units and fits a smooth model to them using maximum correlation modelling. This new technique extends the method of multiple regression to the case where there are multiple variables on each side of the model equation (eg outputs and inputs). The resulting expression for the frontier permits managers to estimate the effect on their efficiency score of adjustments in one or more input or output levels.  相似文献   

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