Some properties of linguistic preference relation and its ranking in group decision making

The group decision making problem with linguistic pref- erence relations is studied. The concept of additive consistent linguistic preference relation is defined, and then some properties of the additive consistent linguistic preference relation are studied. In order to rank the alternatives in the group decision making with the linguistic preference relations, the weighted average is first utilized to combine the group linguistic preference relations to one linguistic preference relation, and then the transformation function is proposed to transform the linguistic preference relation to the multiplicative preference relation, and thus the Saaty＇s eigenvec- tor method （EM） of multiplicative preference relation is utilized to rank the alternatives in group decision making with the linguistic preference relations. Finally, an illustrative numerical example is given to verify the proposed method. A comparative study to the linguistic ordered weighted averaging （LOWA） operator method is also demonstrated.

Ranking environmental projects model based on multicriteria decision-making and the weight sensitivity analysis

With the fast growth of Chinese economic, more and more capital will be invested in environmental projects. How to select the environmental investment projects （alternatives） for obtaining the best environmental quality and economic benefits is an important problem for the decision makers. The purpose of this paper is to develop a decision-making model to rank a finite number of alternatives with several and sometimes conflicting criteria. A model for ranking the projects of municipal sewage treatment plants is proposed by using exports＇ information and the data of the real projects. And, the ranking result is given based on the PROMETHEE method. Furthermore, by means of the concept of the weight stability intervals （WSI）, the sensitivity of the ranking results to the size of criteria values and the change of weights value of criteria are discussed. The result shows that some criteria, such as “proportion of benefit to project cost”, will influence the ranking result of alternatives very strong while others not. The influence are not only from the value of criterion but also from the changing the weight of criterion. So, some criteria such as “proportion of benefit to project cost” are key critera for ranking the projects. Decision makers must be cautious to them.

Application of Interval Multi-attribute Decision-Making Method to Aeroengine Performance Ranking

In view of the uncertainty of the monitored performance parameters of aeroengines, the fluctuating scope of the monitored infurmation during a period is taken as interval numbers, and the interval multi-attribute decision-making method is employed to predict the performance of aeroengine, The synthetic weights of interval numbers are obtained by calculating deviation degree and possibility degree. As an example of application, 5 performance parameters monitored on 10 CF6 aeroengines of China Eastern Airlines Co., Ltd are adopted as decision attributes to verify the algorithm. The obtained synthetic ranking result shows the effectiveness and rationality of the proposed method in reflecting the performance stares of aeroengins.

Decision making with fuzzy probability assessments and fuzzy payoff

A novel method for decision making with fuzzy probability assessments and fuzzy payoff is presented. The consistency of the fuzzy probability assessment is considered. A fuzzy aggregate algorithm is used to indicate the fuzzy expected payoff of alternatives. The level sets of each fuzzy expected payoff are then obtained by solving linear programming models. Based on a defuzzification function associated with the level sets of fuzzy number and a numerical integration formula (Newton-Cotes formula), an effective approach to rank the fuzzy expected payoff of alternatives is also developed to determine the best alternative. Finally, a numerical example is provided to illustrate the proposed method.

Using Mathematical Models in Decision Making Methodologies to Find Key Nodes in the Noordin Dark Network

A Dark Network is a network that cannot be accessed through tradition means. Once uncovered, to any degree, dark network analysis can be accomplished using the SNA software. The output of SNA software includes many measures and metrics. For each of these measures and metric, the output in ORA additionally provides the ability to obtain a rank ordering of the nodes in terms of these measures. We might use this information in decision making concerning best methods to disrupt or deceive a given dark network. In the Noordin Dark network, different nodes were identified as key nodes based upon the metric used. Our goal in this paper is to use methodologies to identify the key players or nodes in a Dark Network in a similar manner as we previously proposed in social networks. We apply two multi-attribute decision making methods, a hybrid AHP & TOPSIS and an average weighted ranks scheme, to analyze these outputs to find the most influential nodes as a function of the decision makers’ inputs. We compare these methods by illustration using the Noordin Dark Network with seventy-nine nodes. We discuss sensitivity analysis that is applied to the criteria weights in order to measure the change in the ranking of the nodes.

Application of Operational Approaches to Solving Decision Making Problem Using Z-Numbers

The combination of fuzzy logic tools and multi-criteria decision making has a great relevance in literature. Compared with the classical fuzzy number, Z-number has more ability to describe the human knowledge. It can describe both restraint and reliability. Prof. L. Zadeh introduced the concept of Z-numbers to describe the uncertain information which is a more generalized notion closely related to reliability. Use of Z-information is more adequate and intuitively meaningful for formalizing information of a decision making problem. In this paper, Z-number is applied to solve multi-criteria decision making problem. In this paper, we consider two approaches to decision making with Z-information. The first approach is based on converting the Z-numbers to crisp number to determine the priority weight of each alternative. The second approach is based on Expected utility theory by using Z-numbers. To illustrate a validity of suggested approaches to decision making with Z-information the numerical examples have been used.

New approach to multiple attribute decision making with interval numbers

In an ambiguous decision domain, the evaluation values of alternatives against attributes would be interval numbers because of the inherent, uncertain property of the problems. By using a number of linear programming models, Bryson and Mobolurin propose an approach to compute attribute weights and overall values of the alternatives in the form of interval numbers. The intervals of the overall values of alternatives are then transformed into points or crisp values for comparisons among the alternatives. However, the attribute weights are different because of the use of linear programming models in Bryson and Mobolurin＇s approach. Thus, the alternatives are not comparable because different attribute weights are employed to calculate the overall values of the alternatives. A new approach is proposed to overcome the drawbacks of Bryson and Mobolurin＇s approach. By transforming the decision matrix with intervals into the one with crisp values, a new linear programming model is proposed, to calculate the attribute weights for conducting alternative ranking.

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.

Robust data envelopment analysis based MCDM with the consideration of uncertain data

The application of data envelopment analysis （DEA） as a multiple criteria decision making （MCDM） technique has been gaining more and more attention in recent research. In the practice of applying DEA approach, the appearance of uncertainties on input and output data of decision making unit （DMU） might make the nominal solution infeasible and lead to the efficiency scores meaningless from practical view. This paper analyzes the impact of data uncertainty on the evaluation results of DEA, and proposes several robust DEA models based on the adaptation of recently developed robust optimization approaches, which would be immune against input and output data uncertainties. The robust DEA models developed are based on input-oriented and outputoriented CCR model, respectively, when the uncertainties appear in output data and input data separately. Furthermore, the robust DEA models could deal with random symmetric uncertainty and unknown-but-bounded uncertainty, in both of which the distributions of the random data entries are permitted to be unknown. The robust DEA models are implemented in a numerical example and the efficiency scores and rankings of these models are compared. The results indicate that the robust DEA approach could be a more reliable method for efficiency evaluation and ranking in MCDM problems.

Multi-attributed decision making for mining methods based on grey system and interval numbers

In the case of unknown weights, theories of multi-attributed decision making based on interval numbers and grey related analysis were used to optimize mining methods. As the representative of independence for the indicator, the smaller the correlation of indicators is, the greater the weight is. Hence, the weights of interval numbers of indicators were determined by using correlation coefficient. Relative closeness based on positive and negative ideal methods was calculated by introducing distance between interval numbers, which made decision making more rational and comprehensive. A new method of ranking interval numbers based on normal distribution was proposed for the optimization of mining methods, whose basic properties were discussed. Finally, the feasibility and effectiveness of this method were verified by theories and practice.

Viability decision of linear discrete-time stochastic systems with probability criterion

In this paper, the optimal viability decision problem of linear discrete-time stochastic systems with probability criterion is investigated. Under the condition of sequence-reachable discrete-time dynamic systems, the existence theorem of optimal viability strategy is given and the solving procedure of the optimal strategy is provided based on dynamic programming. A numerical example shows the effectiveness of the proposed methods.

Method for Risky Multiobjective Group Decision-Making and Its Application

The multiobjective group decision-making problem under risk is common in reality. This paper focuses on the study about risky multiobjective group decision-making problem where the index value is not certain. We give indexes classifying method and index normalizing formula of this type problem. By building objective function that minimizes general weighted distance from every alternative to the relatively best and worst alternative, the optimal membership degree of every decision-maker to every alternative can be obtained, and by building another objective function that minimizes general weighted distance from the optimal membership degree of every decision-maker to every alternative to the group optimal alternative and the group inferior alternative, the optimal membership degree of every decision-maker to every alternative can be obtained, which are both based on probability theory and fuzzy theory. Aftermost a model is established which collects group preferences. This method provides a new idea and approach for solving multiobjective decision-making problem among uncertain system, which is applicable for practical problem. Finally a case study shows a satisfactory result.

Application of Intuitionistic Z-Numbers in Supplier Selection

Intuitionistic fuzzy numbers incorporate the membership and non-membership degrees.In contrast,Z-numbers consist of restriction components,with the existence of a reliability component describing the degree of certainty for the restriction.The combination of intuitionistic fuzzy numbers and Z-numbers produce a new type of fuzzy numbers,namely intuitionistic Z-numbers(IZN).The strength of IZN is their capability of better handling the uncertainty compared to Zadeh's Z-numbers since both components of Z-numbers are charac-terized by the membership and non-membership functions,exhibiting the degree of the hesitancy of decision-makers.This paper presents the application of such numbers in fuzzy multi-criteria decision-making problems.A decision-making model is proposed using the trapezoidal intuitionistic fuzzy power ordered weighted average as the aggregation function and the ranking function to rank the alternatives.The proposed model is then implemented in a supplier selection problem.The obtained ranking is compared to the existing models based on Z-numbers.The results show that the ranking order is slightly different from the existing models.Sensitivity analysis is performed to validate the obtained ranking.The sensitivity analysis result shows that the best supplier is obtained using the proposed model with 80%to 100%consistency despite the drastic change of criteria weights.Intuitionistic Z-numbers play a very important role in describing the uncertainty in the decision makers’opinions in solving decision-making problems.

情绪卷入程度和期望价值对道德决策的交互影响

本研究采用道德两难困境故事,考察了在不同情绪卷入程度下,量级和概率变化对道德决策的交互影响。结果发现,在低情绪卷入条件下,随着量级的增大和概率的减小,被试的功利性倾向升高;在高情绪卷入下,在遇难者人数较多且幸存概率较高时,功利性倾向的差异不再显著。该结果表明在高情绪卷入时由于情绪加工占主导,期望价值的影响被削弱。本研究证实了情绪卷入程度和期望价值对道德决策的交互影响,对双加工模型进行了较好的补充。

PROMETHEE优先函数选择与参数配置方法

偏好顺序结构评估(preference ranking organization methods for enrichment evaluations,PROMETHEE)-Ⅱ方法是一种重要的多属性决策(mutiattribute decision making,MADM)方法。提出一种基于经典规划的鲁棒性分析方法用于解决PROMETHEE-Ⅱ参数求解问题,提供在信息条件不完全情况下的鲁棒性判别条件和设计步骤,并通过分析计算验证了这种方法的有效性。为PROMETHEE-Ⅱ权重的设置提供了新的思路,这种方法同时也可用于解决其他多属性决策问题。

优化逆序发生率的RED-TOPSIS模型

为解决TOPSIS模型中存在的逆序问题,本文提出一种基于纪录值的TOPSIS模型,称为RED-TOPSIS模型,该模型针对有纪录值数据的多属性决策问题,采用区间化公式或最大最小化公式作无量纲化处理,利用纪录值构造理想解。由于纪录客观存在且有不易打破的特点,以此确定的理想解具有近似于绝对理想解的稳定性兼具相对理想解的客观性,使得RED-TOPSIS模型理论上仅当纪录被打破时才可能产生逆序,从而在实际应用中易于操作且能大幅降低逆序现象的发生。

基于可能度的语言直觉模糊PROMETHEE多属性群决策

针对权重信息未知的语言直觉模糊多属性群决策问题,提出了一种基于改进的可能度和偏好顺序结构评估法(preference ranking organization method for enrichment evaluations, PROMETHEE)的语言直觉模糊多属性群决策方法。首先,基于Atanassov偏序和犹豫度,改进语言直觉模糊数的可能度,并证明其具有互补性、传递性等良好性质。其次,基于改进的可能度,通过最大化决策者在属性上的加权平方可能度,构造多目标规划模型,求得每位决策者的属性权重。然后,建立群体共识反馈模型,提高群体共识度,结合修正的偏好关系和决策者主观权重,提出修正系数来确定决策者权重。最后,通过实证分析验证该方法的可行性和有效性。

Model of interval multi-attribute optimization for overseas oil-gas projects

Because of the incompleteness and uncertainty in the information on overseas oil-gas projects, project evaluation needs models able to deal with such problems. A new model is, therefore, presented in this paper based on interval multi-attribute decision-making theory. Analysis was made on the important attributes （index） and the re- lationships affecting the basic factors to the project eco- nomic results were described. The interval numbers are used to describe the information on overseas oil and gas projects. On these bases, an improved TOPSIS model is introduced for the evaluation and ranking of overseas oil and gas projects. The practical application of the new model was carried out for an oil company in selecting some promising blocks from 13 oil and gas blocks in eight dif- ferent countries in the Middle East. Based on these inno- vative studies, some conclusions are given from theoretical and application aspects. The practical application shows that the introduction of interval numbers into the evaluation and ranking of the overseas oil and gas projects can lead to more reasonable decisions. The users can do the project evaluation based on the comprehensive values as well as based on some preferred index in the project evaluation and ranking.

基于Z-number的PROMETHEE多属性决策方法

针对Z-number能够模拟带有不确定信息的自然语言,却没有有效的应用方法这一问题,提出了已知部分权重时以Z-number为信息环境的多属性决策方法。首先,在Z-number理论基础上利用模糊性限制和可靠性限制之间的关系,建立了两个非线性模型计算Z-number的潜在概率;其次,结合模糊数的交叉熵和KL散度,构造了离散Z-number交叉熵公式,并且提出了基于Z-number的PROMETHEE多属性决策方法;该方法结合级别高于关系理论,建立了取值为0~1的优先函数,利用优先函数公式获得优先指数矩阵,进一步计算出净流,然后根据净流大小对各方案进行排序;最后,通过一个实例的应用与分析说明提出方法的有效性和可行性。

Classifying and ranking DMUs in interval DEA

During efficiency evaluating by DEA, the inputs and outputs of DMUs may be intervals because of insufficient information or measure error. For this reason, interval DEA is proposed. To make the efficiency scores more discriminative, this paper builds an Interval Modified DEA (IMDEA) model based on MDEA. Furthermore, models of obtaining upper and lower bounds of the efficiency scores for each DMU are set up. Based on this, the DMUs are classified into three types. Next, a new order relation between intervals which can express the DM’s preference to the three types is proposed. As a result, a full and more convictive ranking is made on all the DMUs. Finally an example is given.