基于比较可能度的多属性决策方法

围绕多等级上同时考虑优于、劣于、无差异和不确定等四种成对方案间关系的不同分布式偏好关系（DPR）,提出一种基于其比较可能度的属性权重未知的多属性决策方法。首先,利用各等级的得分值将分布式偏好关系转为得分值区间,并基于得分值区间构造服从均匀分布的分布式偏好关系比较可能度;其次,通过理论分析证明其与未考虑分布的比较可能度间的大小关系及其取值差异范围;最后运用提出的比较可能度形成属性权重未知的多属性决策流程,产生高辨识度的决策解。将提出的方法运用于求解芜湖市战略性新兴产业的评估问题,验证了方法的正确性和有效性。     

加型Pythagorean模糊偏好关系的多属性决策方法

考虑Pythagorean模糊偏好关系的多属性决策问题,提出了加性Pythagorean模糊偏好关系的多属性决策方法。基于加性一致性Pythagorean模糊偏好关系提出一种新的Pythagorean模糊权重确定模型。给出了可接受加性一致性Pythagorean模糊偏好关系的定义,并针对不满足可接受加性一致性的Pythagorean模糊偏好关系,提出一种加性一致性调整算法。给出基于Pythagorean模糊偏好关系加性一致性的多属性决策方法,并通过实例分析提出的新方法的可行性和合理性。     

基于多等级方案成对比较的决策方法

为了解决现有的方案两两比较方法一般构建单等级上的比较关系, 且不能同时表达多种不同偏好关系的不足, 提出一种新的基于多等级方案成对比较的决策方法, 构建方案集上基于对称框架的分布式多等级偏好关系. 通过设定各等级的得分值, 计算分布式偏好关系的得分矩阵, 并基于此矩阵构建成对优化模型, 求取各方案的优先权区间, 进而产生决策结果. 将所提出的方法应用于某制造企业云服务供应商的选择问题, 验证了所提出方法的应用性和有效性.

     

基于乘法偏好关系的群一致性偏差熵多属性群决策方法研究

在多属性群决策中, 针对每一个属性下决策者都有一个关于决策方案的乘法偏好关系的决策问题, 提出一种基于乘法偏好关系的群一致性偏差熵多属性群决策方法. 此方法考虑到不同属性下的决策者具有不同的权重, 并通过迭代运算可以达到群一致性水平, 从而得出最终的不同属性下决策者的权重; 同时, 可以利用偏差熵模型来求解属性权重, 利用这两个权重最终获得一个综合各方意见的群一致性乘法偏好关系. 最后通过算例分析验证了所提出方法的有效性.     

基于后悔理论的图模糊LINMAP多属性决策方法及应用

针对图模糊多属性决策方法基于未知属性权重且往往只考虑客观属性信息的不足,提出一种基于后悔理论的图模糊LINMAP多属性决策方法.首先,依据后悔理论的思想,定义图模糊后悔-欣喜函数,给出方案感知效用值的计算方法;然后,设计图模糊偏好信息集,用其表示属性间的相互影响关系,并提出方案对序列和决策者事先给定偏好信息的图模糊一致性程度和非一致性程度;接着,通过图模糊得分函数和精确度函数构建含有参数的目标函数,并设置图模糊阈值,使得非一致性程度最小化且一致性程度与非一致性程度差别至少不小于该图模糊阈值,据此建立新的优化模型,获得备选方案的属性权重向量和模糊理想点,进而利用感知效用值对备选方案进行排序择优;最后,通过算例分析验证所提出方法的合理性,并通过灵敏度分析和对比分析表明所提出方法的灵活性和优点.     

一种多属性决策问题的分类方法研究

针对多属性决策的分类问题,基于方案间的赋值级别高于关系,提出一种多属性决策分类法．首先描述了多属性决策的分类问题;然后通过方案间赋值的级别高于关系和线性规划模型,得到一种符合决策者偏好的多属性决策分类方法,从而对方案进行归类．该方法克服了使用传统的ELECTRE Ⅱ方法时,定义的有序方案对之间的赋值级别高于关系导出属性权重的困难,并将否决因素考虑进来．最后通过一个数值例子说明了该方法的有效性．     

基于理想点—矢量余弦投影的多属性决策方法

针对现有的多属性问题决策过程大多无法体现决策者对产品的个人多等级偏好以及缺乏一个客观合理的多属性评价基准的不足,提出一种基于矢量余弦投影的多属性偏好决策方法。通过多等级成对比较法来确定决策者对各项属性的偏好度;再根据理想点来确定理想评价对象各项属性的理想值;利用矢量余弦投影法计算一般多属性问题矢量在理想多属性问题矢量方向上的投影强度,根据强度的大小确定各个方案的优先级排序结果。通过一个算例验证了所提方法的有效性和可行性。     

基于模糊偏好关系的多智能主体决策

多智能主体决策在决策支持系统中的应用越来越广泛,但也带来了各智能主体决策一致性,以及选择最优决策方案的问题,为解决以上问题,该文提出了基于模糊偏好关系的多智能主体决策方法,该方法利用模糊聚合算子对多智能主体的决策结果进行聚合,并利用模糊偏好关系对决策方案进行排序,从而选择最优决策方案。     

基于模糊语言偏好关系一致性改进的决策方法

针对决策者提供的偏好信息为语言标量的决策问题,首先引入了语言偏好关系的有序一致性和加性一致性的定义,研究了语言偏好关系加性一致性的判定方法,构建了满足加性一致性的诱导语言偏好关系,提出一致性指数和满意一致性的概念;然后建立了基于语言偏好关系一致性改进的决策算法,并证明了算法的收敛性,同时通过该算法改进后的语言偏好关系满足满意一致性条件。最后通过数据库系统的选择实例说明提出的决策算法是合理的和有效的。     

偏好关系粗近似的一种新方法

提出一种多准则方案对偏好程度粗度量的一般方法。构造了一种从参考方案集中获取偏好规则并用于全体方案排序和优选的算法。将参考方案对的偏好关系定量分级表示,应用粗集理论的近似原理对综合偏好关系进行粗近似以获取基于偏好信息的决策规则。计算实例表明新方法能充分表示决策者的偏好,有效避免了规则不一致性。     

Integrated evidential reasoning approach in the presence of cardinal and ordinal preferences and its applications in software selection

A combination of cardinal and ordinal preferences in multiple-attribute decision making (MADM) demonstrates more reliability and flexibility compared with sole cardinal or ordinal preferences derived from a decision maker. This situation occurs particularly when the knowledge and experience of the decision maker, as well as the data regarding specific alternatives on certain attributes, are insufficient or incomplete. This paper proposes an integrated evidential reasoning (IER) approach to analyze uncertain MADM problems in the presence of cardinal and ordinal preferences. The decision maker provides complete or incomplete cardinal and ordinal preferences of each alternative on each attribute. Ordinal preferences are expressed as unknown distributed assessment vectors and integrated with cardinal preferences to form aggregated preferences of alternatives. Three optimization models considering cardinal and ordinal preferences are constructed to determine the minimum and maximum minimal satisfaction of alternatives, simultaneous maximum minimal satisfaction of alternatives, and simultaneous minimum minimal satisfaction of alternatives. The minimax regret rule, the maximax rule, and the maximin rule are employed respectively in the three models to generate three kinds of value functions of alternatives, which are aggregated to find solutions. The attribute weights in the three models can be precise or imprecise (i.e., characterized by six types of constraints). The IER approach is used to select the optimum software for product lifecycle management of a famous Chinese automobile manufacturing enterprise.     

A Problem-based Selection of Multi-attribute Decision-making Methods

Different multi-attribute decision-making (MADM) methods often produce different outcomes for selecting or ranking a set of decision alternatives involving multiple attributes. This paper presents a new approach to the selection of compensatory MADM methods for a specific cardinal ranking problem via sensitivity analysis of attribute weights. In line with the context-dependent concept of informational importance, the approach examines the consistency degree between the relative degree of sensitivity of individual attributes using an MADM method and the relative degree of influence of the corresponding attributes indicated by Shannon's entropy concept. The approach favors the method that has the highest consistency degree as it best reflects the decision information embedded in the problem data set. An empirical study of a scholarship student selection problem is used to illustrate how the approach can validate the ranking outcome produced by different MADM methods. The empirical study shows that different problem data sets may result in a different method being selected. This approach is particularly applicable to large-scale cardinal ranking problems where the ranking outcome of different methods differs significantly.     

基于可能度矩阵的概率语言多属性决策方法

为解决两个概率语言术语集之间的优劣比较这一基本问题,在已有可能度计算方法的基础上,提出一种改进的可能度公式.该可能度公式能够克服已有可能度公式的缺点,具有计算过程简单、区分能力强、易于拓展应用等特点.进一步研究发现:基于该可能度公式对多个评估对象进行两两比较得到的可能度矩阵,具有加性一致性的模糊互补偏好关系;将多个可能度矩阵加权平均得到的综合可能度矩阵,也具有加性一致性的模糊互补偏好关系.据此,构建一种概率语言多属性决策方法,并将其应用于军队院校教育教学质量评价.数值实验表明,所提出的概率语言多属性决策方法结构简单、计算过程清晰且具有较强的自检能力,能够通过确保计算过程的正确性来保证决策结果的有效性.     

Fuzzy LINMAP method for multiattribute decision making under fuzzy environments

The Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP) developed by Srinivasan and Shocker [V. Srinivasan, A.D. Shocker, Linear programming techniques for multidimensional analysis of preference, Psychometrika 38 (1973) 337–342] is one of the existing well-known methods for multiattribute decision making (MADM) problems. However, the LINMAP only can deal with MADM problems in crisp environments. Fuzziness is inherent in decision data and decision making processes, and linguistic variables are well suited to assessing an alternative on qualitative attributes using fuzzy ratings. The aim of this paper is further extending the LINMAP method to develop a new methodology for solving MADM problems under fuzzy environments. In this methodology, linguistic variables are used to capture fuzziness in decision information and decision making processes by means of a fuzzy decision matrix. A new vertex method is proposed to calculate the distance between trapezium fuzzy number scores. Consistency and inconsistency indices are defined on the basis of preferences between alternatives given by the decision maker. Each alternative is assessed on the basis of its distance to a fuzzy positive ideal solution (FPIS) which is unknown. The FPIS and the weights of attributes are then estimated using a new linear programming model based upon the consistency and inconsistency indices defined. Finally, the distance of each alternative to the FPIS can be calculated to determine the ranking order of all alternatives. A numerical example is examined to demonstrate the implementation process of this methodology. Also it has been proved that the methodology proposed in this paper can deal with MADM problems under not only fuzzy environments but also crisp environments.     

A fully fuzzy best–worst multi attribute decision making method with triangular fuzzy number: A case study of maintenance assessment in the hospitals

This paper introduces the best–worst method to solve multi-attribute decision-making (MADM) problems in the fuzzy environment. In the proposed method, there is no need to do all the possible pairwise comparisons. In other words, only reference comparisons should be done. Reference comparisons consist of assessing the relative fuzzy preference of the best criterion (alternative) over others and all the criteria (alternatives) over the worst one. Afterward, a fully fuzzy linear mathematical model will be formulated and solved to determine the weight of the criteria. The same action will be performed to find the score of alternatives. This method has some interesting and valuable characteristics: (a) less required data for pairwise comparison, (b) high ability to provide a reliable solution, (c) it is an autonomous method along with its high capability to accompany another method. To evaluate the performance, it is compared with another fuzzy MADM method in an example. Furthermore, we apply this method for the maintenance evaluation of hospitals in Bojnord. The computational study confirms the high efficiency and satisfactory performance of the method, and results are validated by a low consistency ratio. Furthermore, the suggested methodology outperforms fuzzy AHP and well verified in the test instance.     

A new hesitant fuzzy linguistic approach for multiple attribute decision making based on Dempster–Shafer evidence theory

Hesitant fuzzy linguistic term sets (HFLTSs) are useful tool to represent qualitative information in multiple attribute decision making (MADM), and Dempster–Shafer evidence theory (DSET) has some advantages in denoting and fusing uncertain information. The goal of this paper is to develop a new hesitant fuzzy linguistic (HFL) MADM approach based on the DSET. To realize this goal, we propose a method of converting the original decision matrix expressed by HFLTSs into the evidence matrix with HFLTSs, and develop a weight-determining model for MADM problems with HFL information. Further, in order to integrate the evidences with HFLTSs under all attributes, we propose a combination algorithm for MADM problems based on the combination rule of DSET. Based on these studies, we develop a HFL-DSET approach for MADM problems with unknown weights. Furthermore, an applicable example for supplier selection is used to illustrate the proposed approach. Lastly, some comparative analyses with other HFL-MADM methods are conducted to show the feasibility and superiority of the proposed approach.     

Existence and construction of weight-set for satisfying preferenceorders of alternatives based on additive multi-attribute valuemodel

Based on the additive multi-attribute value model for multiple attribute decision making (MADM) problems, the paper investigates how the set of attribute weights (or weight-set thereafter) is determined according to the preference orders of alternatives given by decision makers. The weight-set is a bounded convex polyhedron and can be written as a convex combination of the extreme points. We give the sufficient and necessary conditions for the weight-set to be not empty and present the structures of the weight-set for satisfying the preference orders of alternatives. A method is also proposed to determine the weight-set. The structure of the weight-set is used to determine the interval of weights for every attribute in the decision analysis and to judge whether there exists a positive weight in the weight-set. The research results are applied to several MADM problems such as the geometric additive multi-attribute value model and the MADM problem with cone structure     

A method for multiple attribute decision-making with the fuzzy preference relation on alternatives

This paper investigates the multiple attribute decision-making (MADM) problem with preference information on alternatives. A new method is proposed to solve the MADM problem, where the decision maker (DM) gives his/her preference on alternatives in a fuzzy relation. To reflect the DM's subjective preference information, a linear goal programming model is constructed to determine the weight vector of attributes and then to rank the alternatives. Finally, a numerical example is used to illustrate the use of the proposed method.     

Method and system for Multi-Attribute Market Value Assessment in analysis of construction and retrofit projects

Multi-Attribute Decision-Making (MADM) methods prioritize the alternatives of comparative projects quite accurately. Problems arise when there is a need to determine the utility degrees and market values of the project alternatives. This becomes especially important for establishing the market value of real estate property in tender offers. However, the available MADM methods cannot accomplish this. Thus the authors of this article developed the MAMVA method, which permits determining the utility degrees and market values of project alternatives, and also developed a system on the basis of this developed method. This article presents the proposed Multi-Attribute Market Value Assessment (MAMVA) Method and the Decision Support System for Construction and Retrofit Projects (DSS-CRP). It also presents a case study to demonstrate the effectiveness of this method and system. The application of the MAMVA Method and DSS-CRP System for prioritizing and for determining the utility degrees and market values of construction and retrofit projects under consideration for financing by the European Economic Area (EEA) and Norway Financial Mechanism Grant made it possible to decrease the amount of requested support.This article also presents the analysis and comprehensive assessment of the noted construction and retrofit projects. These were performed in consideration of the entire life cycle of a project and of needs satisfaction relevant to all the groups interested in a project. The developed MAMVA Method and DSS-CRP System permit assessing the appropriateness of projects under analysis in conceptual and qualitative forms. This method and system automatically submit the values of the project alternatives.     

Fuzzy heterogeneous multiattribute decision making method for outsourcing provider selection

One of the critical activities for outsourcing success is outsourcing provider selection, which may be regarded as a type of fuzzy heterogeneous multiattribute decision making (MADM) problems with fuzzy truth degrees and incomplete weight information. The aim of this paper is to develop a new fuzzy linear programming method for solving such MADM problems. In this method, the decision maker’s preferences are given through pair-wise alternatives’ comparisons with fuzzy truth degrees, which are expressed with trapezoidal fuzzy numbers (TrFNs). Real numbers, intervals, and TrFNs are used to express heterogeneous decision information. Giving the fuzzy positive and negative ideal solutions, we define TrFN-type fuzzy consistency and inconsistency indices based on the concept of the relative closeness degrees. The attribute weights are estimated through constructing a new fuzzy linear programming model, which is solved by using the developed fuzzy linear programming method with TrFNs. The relative closeness degrees of alternatives can be calculated to generate their ranking order. An example of the IT outsourcing provider selection problem is analyzed to demonstrate the implementation process and applicability of the method proposed in this paper.