Method for multiple attribute decision making based on incomplete linguistic judgment matrix

With respect to the multiple attribute decision making problems with linguistic preference relations on alternatives in the form of incomplete linguistic judgment matrix, a method is proposed to analyze the decision problem. The incomplete linguistic judgment matrix is transformed into incomplete fuzzy judgment matrix and an optimization model is developed on the basis of incomplete fuzzy judgment matrix provided by the decision maker and the decision matrix to determine attribute weights by Lagrange multiplier method. Then the overall values of all alternatives are calculated to rank them. A numerical example is given to illustrate the feasibility and practicality of the proposed method.     

战争复杂系统仿真可信性控制方法研究

针对战争复杂系统仿真可信性这一难题,依据相似的叠加性性质,提出了在层次性原则指导下,分步骤、逐阶段控制仿真各环节,使其与真实作战保持较强的相似性,从而提高仿真可信性的原理。进而,建立并详细阐述了面向＂数据、模型、仿真试验过程、仿真应用＂的战争复杂系统仿真可信性的控制方法——DMPA。这种方法借鉴工业生产质量控制的思路,从减少不可信因素影响的角度出发,提高战争复杂系统仿真的可信性。根据仿真实践,这种方法具有较好的可操作性和实用性。

Abstract：

Aimed at improving the simulation credibility of war complex system, the step-by-step control flow of war complex system simulation credibility was put up under the guidance of hierarchy principle, which improved the simulation credibility of war complex system by increasing similarity with the real war. Then, the war complex system simulation credibility control method oriented ＂data, model, simulation experiment process, and simulation application＂—DMPA were built and expatiated. This method references the thought of industry production quality control to improve war complex system simulation credibility by reducing the influence of unauthentic factors. According to simulation practice, this method has preferable maneuverability and practicability.     

Group decision-making method based on entropy and experts cluster analysis

According to the aggregation method of experts’ evaluation information in group decision-making,the existing methods of determining experts’ weights based on cluster analysis take into account the expert’s preferences and the consistency of expert’s collating vectors,but they lack of the measure of information similarity.So it may occur that although the collating vector is similar to the group consensus,information uncertainty is great of a certain expert.However,it is clustered to a larger group and given a high weight.For this,a new aggregation method based on entropy and cluster analysis in group decision-making process is provided,in which the collating vectors are classified with information similarity coefficient,and the experts’ weights are determined according to the result of classification,the entropy of collating vectors and the judgment matrix consistency.Finally,a numerical example shows that the method is feasible and effective.     

New Method for Constructing Comparison Matrix Based on the Proportion Scales in the AHP

The main faults existing in current scale methods are that the scales do not represent the real importance of alternatives and their relations. This paper presents a proportion judgment scale and introduces a new method based on the proportion scale for construction comparison matrix in the analytic hierarchy process (AHP). The proportion judgment scales do not have the faults existing in current scale methods and the comparison matrix constructed by the new scale     

RESEARCH 0N CONSTBUCTING SYNTHETIC MATRIX IN AHP

This paper presents a new method for constructing synthetic matrix which is obtained by extending the given judgement matrices in the Analytic Hierarchy Process(AHP).The consistency relationship among the given matrices and therir synthetic matrix is studied.The method can be used to deal with situations where the number of the given alternatives is larger than nine,and needs less pairwise comparisons thanany others.Thus it will aid in the design of the AHP,which will reduce the information overload of decision maker,a major drawback of the original AHP algorithm.Finally,a numerical example is given to show the feasibility and effectiveness of the method.     

RESEARCH ON CONSTRUCTING SYNTHETIC MATRIX IN AHP

This paper presents a new method for constructing synthetic matrix which is obtained by extending the given judgement matrices in the Analytic Hierarchy Process (AHP). The consistency relationship among the given matrices and their synthetic matrix is studied. The method can be used to deal with situations where the number of the given alternatives is larger than nine, and needs less pairwise comparisons than any others. Thus it will aid in the design of the AHP, which will reduce the information overload of decision maker, a major drawback of the original AHP algorithm. Finally, a numerical example is given to show the feasibility and effectiveness of the method.     

A New Method of Structuring the Hierarchy of a System

Structuring the hierarchy of a system is an important link of solving problems with the analytic hierarchy process. This paper gives and proves the two theorems about the relationship between the hierarchy and the reachability matrix of the system. On the basis of it, we propose a method of structuring hierarchy by directly using the reachability matrix of the system. This method is simpler and clearer than that of interpretive structural modeling and is suitable for both manual calculating and computer proceeding. It fully shows the simplicity of the AHP.     

CONVERGENCE PROPERTIES OF DFP METHOD WITH MODIFIED QUASI-NEWTON EQUATIONS

1 IntroductionWe know that in order to obtain a superlinearly convergent method it is necessary to approximate the Newton step asymptotically (see [ll). How can we do this without actually evaluatingthe Hessian matrix by ally approximate to the Hessian matrix at every iteration? The answerwas discovered by Davidonl2] and was subsequently developed and popularized by Fletcher andPowell[3l. It consists of starting with any approximation to the Hessian matrir, and at eachiteration, updating th…     

Receding horizon H∞ control for discrete-time Markovian jump linear systems

Receding horizon H∞ control scheme which can deal with both the H∞ disturbance attenuation and mean square stability is proposed for a class of discrete-time Markovian jump linear systems when minimizing a given quadratic performance criteria. First, a control law is established for jump systems based on pontryagin’s minimum principle and it can be constructed through numerical solution of iterative equations. The aim of this control strategy is to obtain an optimal control which can minimize the cost function under the worst disturbance at every sampling time. Due to the difficulty of the assurance of stability, then the above mentioned approach is improved by determining terminal weighting matrix which satisfies cost monotonicity condition. The control move which is calculated by using this type of terminal weighting matrix as boundary condition naturally guarantees the mean square stability of the closed-loop system. A sufficient condition for the existence of the terminal weighting matrix is presented in linear matrix inequality (LMI) form which can be solved efficiently by available software toolbox. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.     

Method for uncertain multi-attribute decisionmaking with preference information in the form of interval numbers complementary judgment matrix

The uncertain multi-attribute decision-making problems because of the information about attribute weights being known partly, and the decision maker's preference information on alternatives taking the form of interval numbers complementary to the judgment matrix, are investigated. First, the decision-making information, based on the subjective uncertain complementary preference matrix on alternatives is made uniform by using a translation function, and then an objective programming model is established. The attribute weights are obtained by solving the model, thus the overall values of the alternatives are gained by using the additive weighting method. Second, the alternatives are ranked, by using the continuous ordered weighted averaging (C-OWA) operator. A new approach to the uncertain multi-attribute decision-making problems, with uncertain preference information on alternatives is proposed. It is characterized by simple operations and can be easily implemented on a computer. Finally, a practical example is illustrated to show the feasibility and availability of the developed method.     

基于专家可信度的不确定型AHP方法及其应用

在一个基于不确定型AHP方法的群决策过程中,现有文献对专家决策可信度的研究,亦即专家可信度的衡量,都是采取简单的算术平均法或加权平均法,是一种静态的权重赋权法,没有体现出专家间的动态盖异性.本文在综合运用可信度理论和不确定型AHP有关理论的基础上,提出了基于不确定型判断矩阵相似性和差异性的专家可信度的不确定型AHP方法.本文研究中,结合权重的主客观理论,得出不确定型AHP的最终权重,并将其应用到地基工程质量风险评价中,取得了比较理想的评判结果.     

关于互补判断矩阵的群决策的专家评判水平

在群决策分析中，如何从一致性分析的角度来分析专家评判水平或对专家评判水平进行分类是一个重要的研究课题。本文针对群决策中基于互补判断矩阵偏好信息的专家评判水平的排序与分类问题，提出了一种分析方法。首先，分析了互补判断矩阵及其一致性的有关性质；然后，通过构造每个专家给出互补判断矩阵的导出矩阵及其向量表示，计算每个专家给出互补判断矩阵与一致性互补判断矩阵之间的偏差，并得到每个专家评判水平的排序结果和专家们评判水平的分类。最后，通过一个算例说明了本文给出的分析方法。     

群组决策中求最优决策向量的迭代算法

AHP是群组决策中非常有效的工具,而判断矩阵是AHP方法的基础.在群组决策中一般要由多名专家给出多个判断矩阵.能否合理综合专家意见是影响决策质量     

关于AHP中逆判问题的研究

针对 AHP中逆判问题 ,给出一种解决方法 .该方法利用统计学理论 ,对于评判专家在各自的判断矩阵中所提供的信息进行反判 ,从而可对评判专家的评判水平进行排序 ,并通过算例验证该方法的实用性和有效性.     

基于特征选择验证的故障注入仿真可信度评估

针对故障注入仿真的数据复杂、细节特征多,导致单一指标可信度评估和专家目测评估方法难以得到准确的评估结果和评估专家按照AHP方法给出的是区间互补判断矩阵,导致可信度指标的权重难以确定的问题。提出了一种基于特征选择验证FSV(Feature Selection Validation)的多指标综合可信度评估模型,通过FSV方法计算可信度指标的定量或定性的可信度值;定义了区间数的模糊度和相离度,构建了多目标优化模型计算可信度指标的权重。实例证明了方法的可行性和有效性。     

基于群组AHP的复杂仿真系统可信度评估方法

针对复杂仿真系统的学科面广、仿真规模大、技术领域宽等特点,提出了基于群组层次分析法（analytic hierarchy process, AHP)的复杂仿真系统可信度评估方法。首先,根据判断矩阵对专家水平进行评判,并结合专家的主观权重,给出了一种确定专家综合权重的方法。然后,利用Hadamard凸组合对不同专家所建立的判断矩阵进行集结,并证明了判断矩阵Hadamard凸组合的一个性质,进而获得复杂仿真系统可信度的群体评估值。最后给出一个实例验证了方法的有效性。     

基于判断矩阵的专家聚类赋权研究

群组AHP评价方法研究中,现有赋权方法虽考虑了专家评判的具体内容的一致性,但缺乏对专家本身逻辑性的度量,以致可能出现虽然最后评判结果与群体共识相近,而评判结果并非完全为某位专家本意,却给予了与其他专家相同权重的问题。对此,提出了一种将判断矩阵赋权和专家聚类赋权相结合的方法,该方法采用聚类分析原理,将专家个体排序向量进行分类,根据分类结果和判断矩阵一致性确定专家权重系数。算例表明,该方法可行有效。     

确定模糊判断矩阵排序向量的两类方法

在给出模糊判断矩阵的加性一致性和乘性一致性概念的基础上,提出了确定模糊判断矩阵排序向量的两类方法,第1类方法是先将一致性或具有满意一致性的模糊判断矩阵转化为AHP判断矩阵,然后将后者的排序向量作为前者的排序向量;第2类方法是直接由一致性或具有满意一致性的模糊判断矩阵计算排序向量。最后进行了算例分析。     

AHP方法中判断矩阵的标度扩展构造法

AHP在实际使用中常常因判断矩阵出现一致性检验错误而导致决策难产，且这个问题至今没有得到根本性解决，本文通过实例分析说明，导致一致性检验错误的根本原因是判断短阵的传统构造方法存在严重缺陷，它固化了选定的标度，使原先有差别的候选方案在比较过程中失去差别，因此，本文提出一种新的判断矩阵构造方法－标度扩展法，并证明该方法无论使用什么标度，所构造的判断矩阵都是完全一致的。故不需进行一致性检验且排序向量也容易获得，从而提高AHP方法决策的可靠性，并使AHP方法变得简便易行。     

基于语言判断矩阵的群决策逆判问题研究

针对基于语言判断矩阵的群决策逆判问题，通过对语言判断矩阵进行“量化”，将其转化成为互反判断矩阵，进而提出了一种依据数理统计理论的分析方法．该方法通过引进随机误差的概念，得出了一致性判断矩阵中元素的相对误差服从均值为零的正态分布的结论，进一步依据这一结论，根据各评判专家所提供的判断矩阵对专家们进行反判，即通过计算各专家的偏离度，对专家们进行排序，并且根据假设检验理论对排序进行检验、对专家们进行分类、最后用一个算例说明了该方法的有效性和实用性．