Comparison of first aggregation and last aggregation in fuzzy group TOPSIS

The Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS), one of the major multi attribute decision making (MADM) techniques, ranks the alternatives according to their distances from the ideal and the negative ideal solution. In real evaluation and decision making problems, it is vital to involve several people and experts from different functional areas in decision making process. Also under many conditions, crisp data are inadequate to model real-life situations, since human judgments including preferences are often vague and cannot estimate his preference with an exact numerical value. Therefore aggregation of fuzzy concept, group decision making and TOPSIS methods that we denote “fuzzy group TOPSIS” is more practical than original TOPSIS.     

Extension of VIKOR method for decision making problem based on hesitant fuzzy set

The multiple criteria decision making (MCDM) methods VIKOR and TOPSIS are all based on an aggregating function representing “closeness to the ideal”, which originated in the compromise programming method. The VIKOR method of compromise ranking determines a compromise solution, providing a maximum “group utility” for the “majority” and a minimum of an “individual regret” for the “opponent”, which is an effective tool in multi-criteria decision making, particularly in a situation where the decision maker is not able, or does not know to express his/her preference at the beginning of system design. The TOPSIS method determines a solution with the shortest distance to the ideal solution and the greatest distance from the negative-ideal solution, but it does not consider the relative importance of these distances. And, the hesitant fuzzy set is a very useful tool to deal with uncertainty, which can be accurately and perfectly described in terms of the opinions of decision makers. In this paper, we develop the E-VIKOR method and TOPSIS method to solve the MCDM problems with hesitant fuzzy set information. Firstly, the hesitant fuzzy set information and corresponding concepts are described, and the basic essential of the VIKOR method is introduced. Then, the problem on multiple attribute decision marking is described, and the principles and steps of the proposed E-VIKOR method and TOPSIS method are presented. Finally, a numerical example illustrates an application of the E-VIKOR method, and the result by the TOPSIS method is compared.     

基于Vague集信息的多属性群决策专家水平评判方法

针对基于Vague集信息的多属性群决策专家水平评判问题提出了两种评判方法.首先引进了基于Vague集信息的多属性群决策信息体(即决策信息体)的相关概念,通过决策信息体构造了基于Vague集信息的一致性决策矩阵及模糊熵,其次利用Vague集信息的相似度量以及Vague集信息的模糊熵两种信息不确定性度量方法,对基于Vague集信息的多属性群决策专家水平评判问题提出了两种评判方法,即统计分析方法和模糊熵分析方法,对专家的评判水平进行排序.最后,通过一个算例说明两种方法的一致性、有效性和实用性.     

改进型双基点多指标多方案排序法

本文针对双基点法及其一系列改进方法的不足,借鉴DEA方法的“相对效率”和变权思想,对一类多指标多方案评价与排序问题给出了一种合理的评价方法并得出了排序结果.双基点法中权值的设定反映了决策者对评价指标的偏好,但在某种程度上而言,这样的设定过于依赖决策者的主观判断,其合理性和公平性有待商榷.而DEA方法不受任何人为因素的影响,仅依赖被评价方案对应于所考虑因素的状态值,其特点是它在评价某个方案时,从该方案在方案集中的相对效率出发,选择最有利于该方案的权,若变动这组权,只会使该方案在方案集中的排序结果要么不变要么更差.文章进一步对多个方案的相对效率为1的情形给出改进方法,最后选用两个实例加以说明.     

一种Vague偏好群体决策方法

采用 Vague集理论来描述和处理不确定信息或含糊信息 ,比采用模糊集理论描述和处理不确定信息或含糊信息在很多情况下更贴近客观现实 .在诸学者对模糊群体决策研究的基础上 ,提出一种 Vague群体决策方法 ,采用 Vague值作为决策者对备选方案的评估值 ,通过对决策者的各备选方案偏好值的集结 ,最后根据集结值的效用值对备选方案排序 ,进行决策 .     

区间数多属性决策的Vague集方法

对属性值为区间数的多属性决策问题,采用Vague集方法进行处理.首先利用区间数决策矩阵的规范化把区间评价值转化为Vague值,然后利用Vague集方法对方案进行排序并选出最优方案.实例分析阐明了本文方法的有效性和实用性.     

一种基于不同粒度且属性权重未知的群决策方法

针对具有不同粒度语言评价矩阵和属性未知的群决策问题,给出了一种基于二元语义和TOPSIS算法的群决策方法。在该方法中,首先给出了不同粒度语言评价矩阵一致化为由基本语言评价集表示的二元语义信息的方法;然后引入TOPSIS的方法,结合二元语义形式计算规则,确定未知的属性客观权重,利用二元语义集结算子,得到单个决策者对方案的评价值;再通过T-OWA算子对各决策者给出的评价信息进行集结和方案选优;最后给出了一个算例。     

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。     

一种基于TOPSIS法的单值中智多属性决策新方法

单值中智集(SVNS)是中智集(NS)的一种特殊情况,它可以描述现实世界中大量存在的不精确、不确定和不一致信息。由于语言评价的模糊性,传统的模糊评价方法在解决多属性决策(MADM)问题上效果不佳。针对这种情况,提出了一种基于TOPSIS法的单值中智多属性决策新方法。首先介绍了中智集的一些基本概念和运算规则,给出了两个单值中智集之间的广义距离公式;然后构建了聚合专家权重的单值中智决策矩阵,把TOPSIS法推广到单值中智集的环境下;接着通过偏好排序确定了最佳的决策方案。最后通过一个仿真实例,说明了该方案的有效和实用性。     

淘汰式变权TOPSIS法

传统的TOPSIS法不能直接用于常见的淘汰选优的实际决策.提出淘汰式变权TOPSIS法,通过逐步淘汰明显较劣方案,调整符合决策人偏好的权重,可以更好地反映实际决策行为.实例分析表明该法是简单实用的.     

两两比较的TOPSIS法

TOPSIS法是一种常用的多目标决策方法,它以正负理想解作为统一的参照基准来比较方案的优劣.并不适用于常见的两两比较的决策行为.运用最小二乘法解决判别一致性问题,从而建立了两两比较的TOPSIS法,并进行了实例分析.     

A fuzzy closeness approach to fuzzy multi-attribute decision making

The aim of this paper is to develop a new fuzzy closeness (FC) methodology for multi-attribute decision making (MADM) in fuzzy environments, which is an important research field in decision science and operations research. The TOPSIS method based on an aggregating function representing “closeness to the ideal solution” is one of the well-known MADM methods. However, while the highest ranked alternative by the TOPSIS method is the best in terms of its ranking index, this does not mean that it is always the closest to the ideal solution. Furthermore, the TOPSIS method presumes crisp data while fuzziness is inherent in decision data and decision making processes, so that fuzzy ratings using linguistic variables are better suited for assessing decision alternatives. In this paper, a new FC method for MADM under fuzzy environments is developed by introducing a multi-attribute ranking index based on the particular measure of closeness to the ideal solution, which is developed from the fuzzy weighted Minkowski distance used as an aggregating function in a compromise programming method. The FC method of compromise ranking determines a compromise solution, providing a maximum “group utility” for the “majority” and a minimum individual regret for the “opponent”. A real example of a personnel selection problem is examined to demonstrate the implementation process of the method proposed in this paper.     

The SIR method: A superiority and inferiority ranking method for multiple criteria decision making

In this paper, a superiority and inferiority ranking (SIR) method is proposed. This new method uses two types of information, the superiority and the inferiority information, to derive two types of flows, the superiority flow and the inferiority flow, by which the set of alternatives are ranked partially or completely. Relationships between the SIR method and some of the classical multiple criteria decision making (MCDM) methods (such as SAW, TOPSIS and PROMETHEE) are explored. It is proved that the SIR method is a significant extension of the well-known PROMETHEE method.     

基于Vague集的群决策方法研究

首先介绍了Vague集的基本概念,将直觉模糊集的一些运算规则重新在Vague集上作了定义,提出用Vague值表示的九级语言术语集.接着指出衡量Vague集(值)相似度要考虑的三个因素,提出了新的度量方法.在同时考虑专家决策结果的一致性和专家权重的基础上,提出了汇总各专家Vague意见的方法.最后以一个案例说明了所提出的方法.     

基于Vague集的模糊多目标决策方法及应用

针对目前基于Vague集多目标决策中Vague值计算困难以及确定目标满意度的下界和不满意度的上界存在主观随意性问题.提出了一种基于Vague集的模糊多目标决策方法.利用属性数学中的属性集和属性测度理论构造目标的真隶属度函数、假隶属度函数和犹豫度函数,从而可计算出目标的Vague值;采用记分函数计算方案的多目标评分值,从而可以对方案进行排序并选择出最优方案.应用实例验证了该方法的有效性和实用性.     

基于Fuzzy-Rough-TOPSIS的工程项目投标风险评价模型研究

在工程项目招投标阶段,项目风险评价是建筑施工企业进行投标决策和作出项目选择的重要依据.基于理想化与主客观相结合的思想,提出了一种确定风险评价指标综合权重的方法;采用梯形模糊数处理模糊性信息,并将其与粗集理论和TOPSIS(a technique for order preference by similarity to ideal solution)方法相融合,建立了工程项目风险评价的Fuzzy-Rough-TOPSIS模型.实例运行表明,模型可操作性强,适用于多个项目的风险分析和比较,并能够在一定程度上克服以往模型存在的主观性强、应用条件限制严格等不足.     

基于vague集投影及距离的模糊多指标决策

提出了两个vague值投影和距离的概念,并在此基础上给出了考虑指标权重影响的基于vague集投影和距离的多指标模糊决策方法.在这个方法中,利用候选方案在理想方案上的投影和距离来求出最佳方案.此方法与文献现有的应用vague集相似度度量进行决策的方法相比较,新方法更加合理且弥补了现有方法的不足之处.最后对实例进行分析计算,算例验证了该方法的有效性.     

基于TOPSIS思想的技术创新方案的Vague集评价方法及其应用

为了得到理想的技术创新选择方案,论文从技术创新的实际出发,从实力、潜力和外部环境三个角度选择了一组反映技术创新项目实际情况的评价指标。并借助Vague集理论,通过TOPSIS中正负理想解的思想定义了任意创新方案的评价指标值,运用Vague集理论中距离的概念构建了新的评价方法,进而得到了满意的评价结果。该方法一方面体现了Vague集理论描述不确定性问题的优点,另一方面借助TOPSIS思想满足了方案评价的基本准则。这一思想和方法的提出不仅为Vague集理论研究提供了新的应用领域,也为技术创新的研究提供了新的思路和方法。     

基于联系数贴近度的区间数多属性决策方法

利用集对分析和联系数学理论对区间数多属性决策方法进行了研究.首先给出了联系数贴近度的定义和性质;然后在将区间数决策矩阵转化为联系数决策矩阵的基础上,依据传统的逼近理想解的排序方法(TOPSIS)的基本思路,基于联系数贴近度提出了一种区间数多属性决策新方法.该方法简洁直观,易于计算,无需对区间数进行排序;最后,通过算例表明了它的有效性和实用性.     

Approach to group decision making based on determining the weights of experts by using projection method

The aim of this paper is to present a new approach for determining weights of experts in the group decision making problems. Group decision making has become a very active research field over the last decade. Especially, the investigation to determine weights of experts for group decision making has attracted great interests from researchers recently and some approaches have been developed. In this paper, the weights of experts are determined in the group decision environment via projection method. First of all, the average decision of all individual decisions is defined as the ideal decision. After that, the weight of expert is determined by the projection of individual decision on the ideal decision. By using the weights of experts, all individual decisions are aggregate into a collective decision. Then an ideal solution of alternatives of the collective decision, expressed by a vector, is determined. Further, the preference order of alternatives are ranked in accordance with the projections of alternatives on the ideal solution. Comparisons with an extended TOPSIS method are also made. Finally, an example is provided to illustrate the developed approach.