A method of multi-attribute decision making
多属性决策分析范文
多属性决策分析范文多属性决策分析（Multi-Attribute Decision Analysis，简称MADA）是一种决策支持方法，用于解决决策问题中存在多个评估指标的情况。
该方法通过对不同属性进行权重分配，并对备选方案进行评估和比较，以找到最佳的决策方案。
首先，确定决策目标并明确评估指标。
在决策问题中，需要明确要达到的目标，并确定用于评估备选方案的指标。
例如，如果我们需要选择一种新的投资项目，决策目标可能是最大化投资回报率，评估指标可能包括投资风险、市场潜力、竞争情况等。
然后，构建层次结构。
层次结构是多属性决策分析的基础，它通过将决策目标、评估指标和备选方案按照层次关系组织起来，形成一个树状结构。
例如，在选择投资项目的决策问题中，可以将决策目标放在最顶层，评估指标放在中间层，备选方案放在底层。
接下来，建立判断矩阵。
判断矩阵用于描述层次结构中各个层次之间元素之间的相对重要性。
对于每一对元素，通过专家判断或问卷调查的方式，使用比较刻度（如1-9）对其重要性进行评估，并填写到判断矩阵中。
例如，在评估指标层次，可以比较每个评估指标相对于决策目标的重要性。
然后，计算权重向量。
利用判断矩阵，可以通过特征向量法计算出各级指标的权重。
计算过程中，需要对判断矩阵进行一致性检验，以确保判断矩阵的一致性。
一般来说，判断矩阵的一致性指标CI应满足CI<0.1，若CI>0.1，则需进行修正。
之后，进行一致性检验。
通过计算一致性比例CR来检验判断矩阵的一致性。
一致性比例CR的计算公式为CR=CI/RI，其中RI为随机一致性指标，根据判断矩阵的阶数n可以在AHP准则表格中找到。
最后，进行评估和排序。
将备选方案的各个属性值与权重值相乘得出加权得分，然后将加权得分进行加总，将各个备选方案按照加权得分的高低进行排序，得出最佳决策方案。
综上所述，多属性决策分析是一种常用的决策支持方法，可以有效地帮助决策者在多个评估指标的情况下做出合理的决策。
基于I-TOPSIS的可比较语言多属性决策方法
基于I-TOPSIS的可比较语言多属性决策方法韩冰;李东【摘要】针对属性值是可比较语言的多属性决策问题，提出了一种新的多属性决策方法———I-TOPSIS法；传统的TOPSIS方法的综合评价值只能反映各评价对象内部的相对接近度，为了体现各方案与理想的最优方案的接近程度，引进I-TOPSIS法，通过定义正负理想点找到最优的参照方案，根据备选方案与最优参照方案之间的距离对备选方案进行排序和择优；最后，通过实例分析说明了方法的有效性和合理性。
%For the multiple-attribute decision making problem with attribute value expressed as comparative linguistic expression, a new multiple-attribute decision making method named improved TOPSIS method is advanced.The evaluation value of the traditional TOPSIS method only reflects the relative proximity of each evaluation object inside.In order to embody the degree of closeness to the ideal solution,I-TOPSIS method is developed by introducing the ranking index based on the concept that the chosen alternative should be as close as possible to the ideal solution.Finally,an example is given to illustrate the proposed method,in which the effectiveness and feasibility are guaranteed.【期刊名称】《重庆工商大学学报（自然科学版）》【年(卷),期】2017(034)001【总页数】4页(P94-97)【关键词】多属性决策;可比较语言;I-TOPSIS方法;最优参照方案【作者】韩冰;李东【作者单位】安徽大学数学科学学院，合肥230601;安徽大学数学科学学院，合肥230601【正文语种】中文【中图分类】O142ZADEH L A在1965年首次提出了模糊集的理论[1]，与传统精确数的理论相比，模糊集的理论能更好地处理不确定性的决策问题。
基于前景理论和三角模糊MULTIMOORA的多阶段决策方法
基于前景理论和三角模糊MULTIMOORA的多阶段决策方法代文锋;仲秋雁;齐春泽【摘要】For the triangular fuzzy multi-attribute decision making problem,in which period weights and attribute weights are completely unknown,a new decisiong making method based on the prospect theory and MULTIMOO-RA was presented.Firstly,the triangular fuzzy prospect decision matrices in different periods are built and the period weight optimization model was established on the basis of the time degree and differences of prospect values of alternatives in different periods.According to the maximise deviation, attribute weights were deter-mined.Then, a novel extension form of MULTIMOORA was proposed based on the triangular fuzzy number. Alternatives are ranked and selected by the triangular fuzzy MULTIMOORA and the dominance theory.Finally, the feasibility and validity of the proposed method are verified with an example.%针对时间权重与属性权重完全未知的三角模糊多属性决策问题,基于前景理论和MULTIMOORA提出一种新的决策方法.首先,建立备选方案在不同时段的三角模糊前景决策矩阵,根据时间度及不同时段内备选方案前景值的差异构建时间权重优化模型,并运用最大偏差法的基本思想获得属性权重.其次,基于三角模糊数提出一种新的MULTIMOORA扩展形式,并结合占优理论对备选方案进行比选.最后,通过实例证明了所提方法是可行的,也是有效的.【期刊名称】《运筹与管理》【年(卷),期】2018(027)003【总页数】8页(P74-81)【关键词】前景理论;三角模糊数;MLTIMOORA;占优理论【作者】代文锋;仲秋雁;齐春泽【作者单位】大连理工大学管理与经济学部,辽宁大连116024;兰州财经大学信息工程学院,甘肃兰州730020;大连理工大学管理与经济学部,辽宁大连116024;兰州财经大学信息工程学院,甘肃兰州730020【正文语种】中文【中图分类】C9340 引言多属性决策是指决策者在现有决策信息的基础上，采用特定的方法对具有多个属性的备选方案进行比较与选择的过程。
毕达哥拉斯犹豫模糊集多属性决策研究
第４６卷 第３期２０２４年３月系统工程与电子技术ＳｙｓｔｅｍｓＥｎｇｉｎｅｅｒｉｎｇａｎｄＥｌｅｃｔｒｏｎｉｃｓＶｏｌ．４６ Ｎｏ．３Ｍａｒｃｈ２０２４文章编号：１００１ ５０６Ｘ（２０２４）０３ ０９８２ １０ 网址：ｗｗｗ．ｓｙｓ ｅｌｅ．ｃｏｍ收稿日期：２０２２０７０４；修回日期：２０２２０９２６；网络优先出版日期：２０２３０５２３。
网络优先出版地址：ｈｔｔｐ：∥ｌｉｎｋ．ｃｎｋｉ．ｎｅｔ／ｕｒｌｉｄ／１１．２４２２．ＴＮ．２０２３０５２３．１３２５．０１０基金项目：泰山学者工程专项经费（ｔｓ２０１７１２０７２）资助课题 通讯作者．引用格式：关欣，刘赢．毕达哥拉斯犹豫模糊集多属性决策研究［Ｊ］．系统工程与电子技术，２０２４，４６（３）：９８２ ９９１．犚犲犳犲狉犲狀犮犲犳狅狉犿犪狋：ＧＵＡＮＸ，ＬＩＵＹ．Ｒｅｓｅａｒｃｈｏｎｍｕｌｔｉ ａｔｔｒｉｂｕｔｅｄｅｃｉｓｉｏｎ ｍａｋｉｎｇｆｏｒＰｙｔｈａｇｏｒｅａｎｈｅｓｉｔａｔｉｏｎｆｕｚｚｙｓｅｔｓ［Ｊ］．ＳｙｓｔｅｍｓＥｎｇｉ ｎｅｅｒｉｎｇａｎｄＥｌｅｃｔｒｏｎｉｃｓ，２０２４，４６（３）：９８２ ９９１．毕达哥拉斯犹豫模糊集多属性决策研究关 欣，刘 赢（海军航空大学，山东烟台２６４０００） 摘 要：针对属性间相互关联，评价信息为毕达哥拉斯犹豫模糊信息的多属性决策问题，首先通过研究犹豫度对决策结果的影响，提出一种新的毕达哥拉斯犹豫模糊集得分函数，解决了现有得分函数中存在的不足。
其次，提出一种最小公倍数规范化原则，解决了现有方法容易引入误差的缺陷。
最后，针对属性关联的多属性决策问题，基于λ 模糊测度与Ｃｈｏｑｕｅｔ积分，提出了一种拓展交互式多准则决策（ｉｎｔｅｒａｔｉｖｅｍｕｌｔｉ ｃｒｉｔｅｒｉａｄｅｃｉｓｉｏｎ ｍａｋｉｎｇ，ＴＯＤＩＭ）方法，既解决了属性关联的问题，又通过前景理论反映了决策者的心理行为特征。
实例分析与敏感性分析验证了所提算法的正确性与有效性。
三角模糊数在多属性决策中的建模
三角模糊数在多属性决策中的建模廖勇;陈华群【摘要】In order to obtain the mathematical model of Multi-Attribute Decision Making(MADM)under condition of group decision making, linguistic variable and triangular fuzzy number is introduced into MADM in this research. The entries in decision matrix and weights of all attributes are represented by triangular fuzzy number or linguistic variable. The final evaluation value of each alterative is achieved by means of Simple Additive Weighting method(SAW). The degree of dominance between alternatives is defined by the way of difference of two triangular fuzzy numbers. The complementary judgment matrix is built up on degree of dominance between alternatives. The ordering vector of alternatives is figured out by using the least-square method. The order of alternatives is gained according to the value of element of the order vector.%为了获得三角模糊数的多属性决策数学模型，将语言变量和三角模糊数引入到多属性决策中，用语言变量或三角模糊数表示多属性决策中的属性值和各属性的权重，采用加权和法求得每个备选方案的三角模糊数最终评价值，并应用三角模糊数的减法运算定义任意两个三角模糊数的优越度，在方案两两对比求得优越度后建立方案的互补判断矩阵，采用最小平方法求得方案排序向量，根据排序向量元素的大小进行方案排序。
计量决策方法
计量决策方法
计量决策方法是指根据定量数据和计量模型来进行决策的方法。
这种方法基于数理统计、优化理论和模型建立、求解技术等方法，通过对问题进行定量分析和量化评估，从而在各种可行的方案中选择最优方案。
常见的计量决策方法包括：
1. 线性规划（Linear Programming，LP）：线性规划是一种用
于解决最优化问题的数学方法，它可以找到一组最优的决策变量值，使得目标函数达到最大或最小值。
2. 整数规划（Integer Programming，IP）：整数规划是线性规
划的一种扩展，它在决策变量的取值上增加了整数约束条件，适用于决策变量需要取整数值的问题。
3. 动态规划（Dynamic Programming，DP）：动态规划是一种
基于多期决策的分析方法，通过将大问题划分为一系列小问题，并逐步求解这些小问题，最终得到全局最优解。
4. 多属性决策（Multi-attribute Decision Making，MADM）：
多属性决策方法是用于解决多属性决策问题的方法，通过对不同属性进行量化评估和加权，找到最佳方案。
5. 灰色系统理论（Grey System Theory，GST）：灰色系统理
论是一种用于处理信息不完全、未知或不确定的系统的理论方法，它通过分析和预测灰色数据的变化趋势，为决策提供参考。
6. 模糊决策（Fuzzy Decision Making，FDM）：模糊决策方法是一种用于处理信息模糊性和不确定性的方法，它通过模糊数学理论和模糊推理，对问题进行模糊评估和模糊决策。
这些计量决策方法在不同的决策问题中具有广泛的应用，可以帮助决策者做出更合理、更科学的决策。
几种模糊多属性决策方法及其应用
几种模糊多属性决策方法及其应用一、本文概述随着信息时代的快速发展，决策问题日益复杂，涉及的属性越来越多，决策信息的不确定性也越来越大。
在这种背景下，模糊多属性决策方法应运而生，成为解决复杂决策问题的重要工具。
本文旨在探讨几种典型的模糊多属性决策方法，包括模糊综合评价法、模糊层次分析法、模糊集结算子等，并分析它们在实际应用中的优势和局限性。
本文首先介绍了模糊多属性决策方法的基本概念和理论基础，为后续研究提供必要的支撑。
接着，详细阐述了三种常用的模糊多属性决策方法，包括它们的原理、步骤和应用范围。
在此基础上，通过案例分析，展示了这些方法在实际应用中的具体运用和取得的效果。
通过本文的研究，读者可以深入了解模糊多属性决策方法的原理和应用，掌握其在实际问题中的使用技巧，为解决复杂决策问题提供有力支持。
本文也为进一步研究和改进模糊多属性决策方法提供了参考和借鉴。
二、模糊多属性决策方法概述模糊多属性决策（Fuzzy Multiple Attribute Decision Making，FMADM）是一种处理不确定性、不精确性和模糊性的决策分析方法。
在实际问题中，由于信息的不完全、知识的局限性或环境的动态变化，决策者往往难以获取精确的属性信息和权重信息，这使得传统的多属性决策方法难以应用。
模糊多属性决策方法通过引入模糊集理论，能够更好地处理这种不确定性和模糊性，为决策者提供更合理、更可靠的决策支持。
模糊多属性决策方法的核心思想是将决策问题中的属性值和权重视为模糊数，利用模糊集理论中的运算法则进行决策分析。
根据不同的决策目标和背景，模糊多属性决策方法可以分为多种类型，如模糊综合评价、模糊多目标决策、模糊群决策等。
这些方法在各自的领域内都有着广泛的应用，如企业管理、项目管理、环境评估、城市规划等。
在模糊多属性决策方法中，常用的模糊数有三角模糊数、梯形模糊数、正态模糊数等。
这些模糊数可以根据实际问题的需要选择合适的类型，以更好地描述属性值的不确定性和模糊性。
多属性决策的敏感性分析方法及在评标管理中的应用
AbstractSensitivity analysis is an important tache of using models and making quantitative decisions.People will be affected by the uncertain decision parameters when they are devoted to the study on multi-attribute decision making to obtain optimal solutions.Due to the influence of the uncertain problems or parameters on the results of the evaluation,the reliability of evaluation results is often a problem for the decision makers. Sensitivity analysis can reflect the degree of influence on the decision from uncertainty factors, and decision makers can know which parameters are most sensitive, so as to turn their attention more effectively on the key part, which has important practical significance for the multi-attribute decision making.Based on the National Natural Science Foundation of China and the Hubei Electric Power Commission project "Research on the methods and mechanism of bidding and purchasing of electric power materials", the following research work has been carried out: First of all, we discuss the common methods of multi-attribute decision making, and analyze their advantages and disadvantages as well as the future development.Then we research sensitivity measurements based on distance measure and vectorial angle measure,and test the sensitivity of the project by the minimum variation of the local parameters and the vector angle of the global parameters separately.Next,we regard the bidding as multi-attribute decision making under SAW, establish the model and analyze the sensitivity of attribute value,attribute weights and expert weights individually.We put forward the concept and calculation method of minimum variation and sensitivity coefficient when analyzing the sensitivity of attribute value.While introducing the vectorial angle to analyze the sensitivity of attribute weights and expert weights.We give some definitions ,geometric representation and solving methods and then discuss the rationality and validity.Combining with the specific bidding example and datas,we verify and compare the methods of sensitivity analysis,then give some suggestions for experts.The methods of sensitivity analysis in this paper extend the range of sensitivity analysis on multi-attribute decision making to a certain degree,which have theoretical significance and application value on research of decision making theory.Keywords：Multi-attribute Decision Making; Sensitivity Analysis; Angle Measure; Electric Power Materials Bid; Simple Additive Weighting目录摘要 (I)Abstract ........................................................................................................... I I 1 绪论.. (1)1.1 研究背景、目的及意义 (1)1.2多属性决策的敏感性分析及研究概况 (2)1.3 电力物资评标及研究概况 (7)1.4 研究内容与结构安排 (9)2 多属性决策及敏感性分析方法研究 (11)2.1 多属性决策方法研究 (11)2.2 敏感性分析方法研究 (16)2.3 本章小结 (20)3 基于多属性决策的评标模型及其敏感性分析 (22)3.1 评标模型的建立 (22)3.2 方案排序关于属性值的敏感性分析 (25)3.3 方案排序关于属性权重的敏感性分析 (30)3.4 方案排序关于专家权重的敏感性分析 (34)3.5 本章小结 (37)4 湖北电力公司评标结果的敏感性分析 (39)4.1 案例背景 (39)4.2 专家评价及各方案排序 (41)4.3 排序结果的敏感性分析 (43)4.4 本章小结 (49)5 总结与展望 (50)5.1 主要结论与创新点 (50)5.2 研究展望 (51)致谢 (52)参考文献 (53)附录1 攻读硕士学位期间参加的科研项目 (57)附录2 技术专家和商务专家的评分表 (58)1 绪论1.1研究背景、目的及意义作为决策科学的一个重要研究领域[1]，多属性决策（Multiple Attribute Decision Making，MADM）方法，是指决策者在考虑多个属性的情况下对有限个备选方案进行科学合理排序的理论和方法。
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P. Liu et al. / A method of multi-attribute decision making under risk based on interval probability
1. Introduction The multi-attribute decision making is widely used in the areas of society, economy, management, military affairs and engineering technology, such as investment decision making, alternative evaluation, economic benefit evaluation and staff evaluation etc. In the realistic decision making, the decision makers sometimes face the uncertain condition. The attribute values are random variables and they can be changed with natural state. The decision makers do not know the real state in the future, but they can know the possible natural states and can qualify the randomness through setting the probability distribution. This decision making problem is called multi-attribute decision making under risk [1]. So, it has the important theoretic and real meaning to study the multi-attribute decision making problem under risk.
Journal of Intelligent & Fuzzy Systems 26 (2014) 3005–3011 DOI:10.3233/IFS-130966 IOS Press
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A method of multi-attribute decision making under risk based on interval probability
a Soft
Abstract. This paper investigates the multi-attribute decision making (MADM) problems under risk based on the interval probability in which the attribute values take the form of uncertain linguistic variables and the attribute weights are crisp numbers. Based on the probability theory and the projection theory, a decision making method is proposed. Firstly, based on the projection method, the optimization model is constructed, and the optimal closeness degree is calculated. Then, based on the optimal closeness degree, the order of the alternatives can be ranked. Finally, an illustrative example is provided to demonstrate the steps and verify the effectiveness of this method. Keywords: Interval probability, uncertain linguistic variables, projection method, the optimization closeness degree, multi-attribute decision making (MADM) under risk
Xiao [5] proposed a new decision making method based on the grey relative degree for the dynamic hybrid multiattribute decision making problems under risk, in which the attribute values take the forms of the precision number, the interval number and the fuzzy number, and the attribute weights are unknown. Wang and Gong [6] proposed a method of the expectation and hybrid entropy with respect to the problems of dynamic hybrid multi-attribute decision making under risk in which the attribute values take the form of interval probability fuzzy random variables and the attribute weights are precisely known. In this method, the measurement of expectation-hybrid entropy for interval probability fuzzy random variable is defined. By constructing the optimization model, the interval of expectation-hybrid entropy of each alternative is obtained. Then the possibility degree is utilized to rank all the alternatives. He [7] solved the problems of the multi-attribute decision making under risk in the condition of the interval probability by transforming the interval probability to the point probability on the basis of the probability mathematical properties and the maximum entropy principle. Chen and zhu [8] solved the problems of multi-attribute decision making (MADM) under risk in the condition of the interval probability. Firstly, the interval probability is transformed to the point probability by the operator C-OWA, so, this problem is transformed to the traditional problem of MADM under risk. Liu and Wang [9] proposed a new decision approach based on entropy weight and projection theory to solve the hybrid multiple attribute decision-making under risk of interval probability with weight unknown. Han and Liu [10] proposed a new decision approach based on entropy weight and TOPSIS to solve the hybrid multiple attributes decision-making problems under risk with attribute weight known. However, in the real situation, the precise number may not express the evaluation precisely, instead of this, we can use the linguistic terms to describe the evaluation information (e.g., when we evaluate the “comfort” or “design” of a car, the linguistic terms like “bad”, “poor”, “average” or “good” can be used.). Sometimes, the linguistic terms value given by the decision makers can not match the linguistic term in the linguistic term set, but it can lie between the two linguistic terms in the linguistic term set. In order to solve these problems, we can use the uncertain linguistic variables to describe the decision making information. Liu et al. [11] proposed an extended TOPSIS method based on the probability theory and uncertain linguistic variables to solve the risk multiple attribute decision making problems