基于理想关联度的不确定多属性决策方法

针对只有部分属性权重信息且属性值以区间数形式给出的不确定多属性决策问题,提出了一种逼近理想关联度的决策分析方法。首先改进了文[4]给出的区间数决策矩阵的规范化方法;然后提出了利用期望-方差区间数排序方法求解理想最优方案;最后依据关联系数矩阵给出了属性权重信息不完全的区间数多属性决策问题的求解方法,其核心是求解线型规划得到属性权重,进而根据各个方案与理想最优方案的综合关联度大小进行排序。特别地,给出了属性权重完全未知的简洁方法,文后的实例验证了方法的可行性和有效性。     

属性和专家客观权重未知的多值中智数群决策方法

针对评价信息为多值中智数的多属性决策问题,提出基于最小最大相似度求解属性权重与标准区间求解专家权重的方法.该方法首先根据最小最大模型求解属性权重,将初始评价矩阵集结为综合决策矩阵,其次利用数字分析法求得标准区间,根据各专家与标准区间的相似度确定专家权重,再对综合评价矩阵集结得各方案的综合评价值,对综合评价值排序得最优方...     

综合主、客观权重信息的最优组合赋权方法

首先构造了一种多属性决策主观权重确定的偏好比率法,介绍了属性客观权重确定的熵值法,提出了一种基于离差平方和的最优组合赋权方法,并给出了具体算例.通过提出的方法可以将多属性决策问题中主、客观权重的信息进行有效地综合.     

政府购买公共服务的三边匹配决策模型

针对政府购买公共服务中供应商及评估方的选择决策问题,从政府服务购买、服务供应、监管评估三方的匹配视域,利用三边匹配决策与多属性决策方法,构建基于各方评价的三边匹配模型.首先,对政府购买公共服务的三边匹配问题进行了描述,并给出了三边匹配的相关概念.然后,在三边主体多属性评价信息的基础上,定义匹配效用函数,给出了标准加权效用矩阵的计算方法.进一步地,在考虑三方加权匹配效用最优的基础上,建立了累加最优效用三边匹配模型.最后,对模型进行了算例应用及分析,研究表明模型对政府选择服务供应商及监管评估机构有实践的指导意义.     

基于模糊证据推理及改进TOPSIS的多属性群决策方法

针对不同识别框架多属性群决策问题属性准则度量的不确定性、随机性,定义基于梯形模糊数表征的属性准则评价等级相似度量,求解专家决策权重的最优解。对公共识别框架备选方案属性准则采用模糊证据推理过程综合专家评价等级置信度信息;利用可严格区分属性准则评价等级的相似度量,改进TOPSIS方法中备选方案属性准则评价等级置信度距离因子,获取备选方案逼近正负理想解的贴近度。实例分析以某通信企业电信产品市场竞争力评估为例,说明基于模糊证据推理、改进TOPSIS的多属性群决策问题求解过程,从属性准则专家模糊评价等级置信度集中获取直观的待评估产品市场竞争力排序结果,验证该方法解决此类决策问题的可行性与有效性。     

基于不完全权重信息下模糊多属性决策的供应链合作伙伴选择

针对属性权重完全未知或只有部分权重信息且属性值为三角模糊数的供应链合作伙伴选择问题,给出了一种模糊多属性决策方法.提出了一种基于置信度的定性指标的量化方法,通过求解最优化决策模型确定属性的权重,然后根据各方案到模糊理想点的相对贴近度的大小选择最优的合作伙伴.     

基于区间直觉模糊集的多阶段动态双边匹配决策方法

在双边匹配问题中,偏好强度很难用具体的数值来描述,加之双边匹配具有阶段性特征,因此论文从以上两个方面提出一种新的处理多阶段双边匹配的方法。首先,依据每阶段的匹配最优信息动态分配权重;其次,提出不确定动态区间直觉模糊加权几何(UDIIFWG)算子,并用该集结算子将多个阶段的偏好信息进行集结,并基于得分函数矩阵和匹配矩阵构建以双边主体满意度最大为目标的匹配决策模型,通过求解该模型得到最优的匹配决策方案。最后,通过算例对所提方法加以验证。     

不完全信息下的区间直觉模糊数的多属性决策方法

针对属性权重信息不完全的区间直觉模糊的多属性决策问题,提出灰色关联分析的决策方法.该方法首先确定各属性下的最佳和最劣方案,确定各方案与理想方案的灰色关联系数,然后在属性权重信息不完全的情况下,建立基于理想点的最优决策模型,求出属性权重,进而根据与理想方案的相对贴近度对各方案进行排序,最后用实例对该方法进行了说明,理论分析和数据结果表明了方法的可行性和有效性.     

基于优势的双边匹配决策方法

传统的双边匹配方法根据主体双方给出的偏好序信息排序, 忽略匹配双方个体间存在的差异, 匹配结果不能很好的满足主体需求, 稳定性较差, 造成资源的错配甚至浪费。本文以人为出发点, 基于对匹配主体特征属性的优势结构识别, 提出新的序值依据, 将定性的不确定匹配标准依重视程度量化, 从而实现对人的多维度测量, 最大化个体差异, 以实现“按需匹配”的高稳定性、高满意度匹配结果。构建基于主体客观评价的优势属性量表; 引入个体综合情况的计算公式; 依托隶属度加权法把多目标优化转变成单目标优化; 运用Hungarain方法获得满意度最高且稳定匹配的指派方案; 最后通过算例证明本方法的科学性和可行性。     

属性权重信息不完全的双边匹配多目标决策模型的研究

以C2C电子商务为实际背景，研究了在商品属性权重信息不完全的情况下买卖双方的双边匹配问题。首先给出了C2C电子商务中商品属性权重信息不完全的双边匹配问题的数学描述；然后在此基础上，以最大化匹配度和交易额为目标，建立了双边匹配多目标决策模型，并依据该模型是一类多目标混合0.1整数二次规划模型的特点，设计了模型的求解方法；最后通过一个仿真实例的计算，说明了模型及求解方法的有效性和可行性。     

一种基于证据推理的多指标多标度大群体决策方法

针对多指标多标度大群体决策问题,提出了一种基于证据推理的决策方法.首先将参与决策人针对各指标给出的方案评价信息转化为关于指标评价标度的概率分布.然后运用证据推理方法将针对不同指标的概率分布形式的群体评价信息进行集结,得到关于综合评价标度分布形式的群体综合评价信息,在此基础上计算每个方案的效用值,并据此对方案进行排序.最后,通过一个实例说明了本文提出方法的可行性和有效性.本文的方法为解决大群体决策问题提供了一种新途径.具有实际应用价值.     

基于分布式序关系的双边匹配决策方法

针对分布式序关系的双边匹配问题,提出了一种基于证据推理的决策方法。首先,以双边匹配满意程度为目标,把双边的各个评价信息作为证据,并通过证据融合求出匹配的满意度;接着,构建基于满意度的决策模型来获得匹配方案。最后, 通过算例说明该方法的应用。     

An evidential reasoning based consensus model for multiple attribute group decision analysis problems with interval-valued group consensus requirements

With the aim of modeling multiple attribute group decision analysis problems with group consensus (GC) requirements, a GC based evidential reasoning approach and further an attribute weight based feedback model are sequentially developed based on an evidential reasoning (ER) approach. In real situations, however, giving precise (crisp) assessments for alternatives is often too restrictive and difficult for experts, due to incompleteness or lack of information. Experts may also find it difficult to give appropriate assessments on specific attributes, due to limitation or lack of knowledge, experience and provided data about the problem domain. In this paper, an ER based consensus model (ERCM) is proposed to deal with these situations, in which experts’ assessments are interval-valued rather than precise. Correspondingly, predefined interval-valued GC (IGC) requirements need to be reached after group analysis and discussion within specified times. Also, the process of reaching IGC is accelerated by a feedback mechanism including identification rules at three levels, consisting of the attribute, alternative and global levels, and a suggestion rule. Particularly, recommendations on assessments in the suggestion rule are constructed based on recommendations on their lower and upper bounds detected by the identification rule at a specific level. A preferentially developed industry selection problem is solved by the ERCM to demonstrate its detailed implementation process, validity, and applicability.     

A note on article “The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees”

Wang et al. use an evidential reasoning approach for solving multiple attribute decision analysis (MADA) problems under interval belief degrees [Y.M. Wang, J.B. Yang, D.L. Xu, K.S. Chin, The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees, European Journal of Operational Research 175 (2006) 35–66]. In this note it is shown some nonlinear optimization models in that paper are incorrect. The necessary corrections are proposed.     

基于证据推理的直觉模糊多属性群决策方法

针对属性值为直觉模糊数的多属性群决策问题,提出了一种证据推理的扩展方法。首先,在考虑主观因素与客观因素的基础上运用直觉模糊熵法计算出属性及专家的综合权重。其次,提出一种基于证据推理的直觉模糊信息融合方法,该方法可以避免由于评价值的隶属度为0而导致的信息丢失现象,弥补了现有直觉模糊信息融合方法存在的不足。在此基础上,集结评价信息并按照备选方案与理想方案的相对贴近度对备选方案进行比选。最后,运用实例验证了所提方法的有效性。     

An attribute weight based feedback model for multiple attributive group decision analysis problems with group consensus requirements in evidential reasoning context

In an evidential reasoning context, a group consensus (GC) based approach can model multiple attributive group decision analysis problems with GC requirements. The predefined GC is reached through several rounds of group analysis and discussion (GAD) in the approach. However, the GAD with no guidance may not be the most appropriate way to reach the predefined GC because several rounds of GAD will spend a lot of time of all experts and yet cannot help them to effectively emphasize on the assessments which primarily damage the GC. In this paper, an attribute weight based feedback model is constructed to effectively identify the assessments primarily damaging the GC and accelerate the GC convergence. Considering important attributes with the weights more than or at least equal to the mean of the weights of all attributes, the feedback model constructs identification rules to identify the assessments damaging the GC for the experts to renew. In addition, a suggestion rule is introduced to generate appropriate recommendations for the experts to renew their identified assessments. The identification rules are constructed at three levels including the attribute, alternative and global levels. The feedback model is used to solve an engineering project management software selection problem to demonstrate its detailed implementation process, its validity and applicability, and its advantages compared with the GC based approach.     

Evidential reasoning based preference programming for multiple attribute decision analysis under uncertainty

Multiple attribute decision analysis (MADA) problems having both quantitative and qualitative attributes under uncertainty can be modelled and analysed using the evidential reasoning (ER) approach. Several types of uncertainty such as ignorance and fuzziness can be consistently modelled in the ER framework. In this paper, both interval weight assignments and interval belief degrees are considered, which could be incurred in many decision situations such as group decision making. Based on the existing ER algorithm, several pairs of preference programming models are constructed to support global sensitivity analysis based on the interval values and to generate the upper and lower bounds of the combined belief degrees for distributed assessment and also the expected values for ranking of alternatives. A post-optimisation procedure is developed to identify non-dominated solutions, examine the robustness of the partial ranking orders generated, and provide guidance for the elicitation of additional information for generating more desirable assessment results. A car evaluation problem is examined to show the implementation process of the proposed approach.     

Determining attribute weights to improve solution reliability and its application to selecting leading industries

In multiple attribute decision analysis, many methods have been proposed to determine attribute weights. However, solution reliability is rarely considered in those methods. This paper develops an objective method in the context of the evidential reasoning approach to determine attribute weights which achieve high solution reliability. Firstly, the minimal satisfaction indicator of each alternative on each attribute is constructed using the performance data of each alternative. Secondly, the concept of superior intensity of an alternative is introduced and constructed using the minimal satisfaction of each alternative. Thirdly, the concept of solution reliability on each attribute is defined as the ordered weighted averaging (OWA) of the superior intensity of each alternative. Fourthly, to calculate the solution reliability on each attribute, the methods for determining the weights of the OWA operator are developed based on the minimax disparity method. Then, each attribute weight is calculated by letting it be proportional to the solution reliability on that attribute. A problem of selecting leading industries is investigated to demonstrate the applicability and validity of the proposed method. Finally, the proposed method is compared with other four methods using the problem, which demonstrates the high solution reliability of the proposed method.     

Reply to the note on article “The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees”

In a very recent note by Gao and Ni [B. Gao, M.F. Ni, A note on article “The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees”, European Journal of Operational Research, in press, doi:10.1016/j.ejor.2007.10.0381], they argued that Yen’s combination rule [J. Yen, Generalizing the Dempster–Shafer theory to fuzzy sets, IEEE Transactions on Systems, Man and Cybernetics 20 (1990) 559–570], which normalizes the combination of multiple pieces of evidence at the end of the combination process, was incorrect. If this were the case, the nonlinear programming models we proposed in [Y.M. Wang, J.B. Yang, D.L. Xu, K.S. Chin, The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees, European Journal of Operational Research 175 (2006) 35–66] would also be incorrect. In this reply to Gao and Ni, we re-examine their numerical illustrations and reconsider their analysis of Yen’s combination rule. We conclude that Yen’s combination rule is correct and our nonlinear programming models are valid.     

Inference in directed evidential networks based on the transferable belief model

Inference algorithms in directed evidential networks (DEVN) obtain their efficiency by making use of the represented independencies between variables in the model. This can be done using the disjunctive rule of combination (DRC) and the generalized Bayesian theorem (GBT), both proposed by Smets [Ph. Smets, Belief functions: the disjunctive rule of combination and the generalized Bayesian theorem, International Journal of Approximate Reasoning 9 (1993) 1–35]. These rules make possible the use of conditional belief functions for reasoning in directed evidential networks, avoiding the computations of joint belief function on the product space. In this paper, new algorithms based on these two rules are proposed for the propagation of belief functions in singly and multiply directed evidential networks.