An integrated method for cognitive complex multiple experts multiple criteria decision making based on ELECTRE III with weighted Borda rule

The ELECTRE (ELimination Et Choix Traduisant la REalité, in French) is an effective multiple criteria decision making method based on comparative analysis. Among the family of the ELECTRE methods and their extensions, the ELECTRE III is widely used since it can tackle uncertain and imprecise information. The hesitant fuzzy linguistic term set can represent people's perceptions more comprehensively and flexibly than exact numbers especially in cognitive complex decision-making process. In this paper, we develop an integrated method based on the ELECTRE III to handle the cognitive complex multiple experts multiple criteria decision making problems in which the cognitive complex information is represented by hesitant fuzzy linguistic term sets and the outranking relations between alternatives are calculated by a novel score-function-based distance measure between hesitant fuzzy linguistic elements. A combinative weight-determining method involving both subjective and objective opinions of experts is introduced to derive the weights of criteria. After obtaining the ranking of alternatives from each experts’ decision matrix by the distillation algorithm, the weighted Borda rule is implemented to aggregate the rankings of alternatives regarding different experts. Some ordinal consensus measures are introduced to identify the reliability of the final ranking result. An application of hospital ranking in China is provided to validate the efficiency of the proposed method.     

Robust multi-criteria sorting with the outranking preference model and characteristic profiles

We present a new multiple criteria sorting approach that uses characteristic profiles for defining the classes and outranking relation as the preference model, similarly to the Electre Tri-C method. We reformulate the conditions for the worst and best class assignments of Electre Tri-C to increase comprehensibility of the method and interpretability of the results it delivers. Then, we present a disaggregation procedure for inferring the set of outranking models compatible with the given preference information, and use the set in deriving, for each decision alternative, the necessary and possible assignments. Furthermore, we introduce simplified assignment procedures and prove that they maintain a no class jumps-property in the possible assignments. Application of the proposed approach is demonstrated by classifying 40 land zones in 4 classes representing different risk levels.     

Multiple Criteria Hierarchy Process with ELECTRE and PROMETHEE

Robust Ordinal Regression (ROR) supports Multiple Criteria Decision Process by considering all sets of parameters of an assumed preference model, that are compatible with preference information elicited by a Decision Maker (DM). As a result of ROR, one gets necessary and possible preference relations in the set of alternatives, which hold for all compatible sets of parameters, or for at least one compatible set of parameters, respectively. In this paper, we propose an extension of ELECTRE and PROMETHEE methods to the case of the hierarchy of criteria, which was never considered before. Then, we adapt ROR to the hierarchical versions of ELECTRE and PROMETHEE methods.     

An extension of the Electre I method for group decision-making under a fuzzy environment

Many real-world decision problems involve conflicting systems of criteria, uncertainty and imprecise information. Some also involve a group of decision makers (DMs) where a reduction of different individual preferences on a given set to a single collective preference is required. Multi-criteria decision analysis (MCDA) is a widely used decision methodology that can improve the quality of group multiple criteria decisions by making the process more explicit, rational and efficient. One family of MCDA models uses what is known as “outranking relations” to rank a set of actions. The Electre method and its derivatives are prominent outranking methods in MCDA. In this study, we propose an alternative fuzzy outranking method by extending the Electre I method to take into account the uncertain, imprecise and linguistic assessments provided by a group of DMs. The contribution of this paper is fivefold: (1) we address the gap in the Electre literature for problems involving conflicting systems of criteria, uncertainty and imprecise information; (2) we extend the Electre I method to take into account the uncertain, imprecise and linguistic assessments; (3) we define outranking relations by pairwise comparisons and use decision graphs to determine which action is preferable, incomparable or indifferent in the fuzzy environment; (4) we show that contrary to the TOPSIS rankings, the Electre approach reveals more useful information including the incomparability among the actions; and (5) we provide a numerical example to elucidate the details of the proposed method.     

Extreme ranking analysis in robust ordinal regression

We extend the principle of robust ordinal regression with an analysis of extreme ranking results. In our proposal, we consider the whole set of instances of a preference model that is compatible with preference information provided by the DM. We refer to both, the well-known UTA^GMS method, which builds the set of general additive value functions compatible with DM's preferences, and newly introduced in this paper PROMETHEE^GKS, which constructs the set of compatible outranking models via robust ordinal regression. Then, we consider all complete rankings that follow the use of the compatible preference models, and we determine the best and the worst attained ranks for each alternative. In this way, we are able to assess its position in an overall ranking, and not only in terms of pairwise comparisons, as it is the case in original robust ordinal regression methods. Additionally, we analyze the ranges of possible comprehensive scores (values or net outranking flows). We also discuss extensions of the presented approach on other multiple criteria problems than ranking. Finally, we show how the presented methodology can be applied in practical decision support, reporting results of three illustrative studies.     

A robust ranking method extending ELECTRE III to hierarchy of interacting criteria,imprecise weights and stochastic analysis

A great majority of methods designed for Multiple Criteria Decision Aiding (MCDA) assume that all assessment criteria are considered at the same level, however, decision problems encountered in practice often impose a hierarchical structure of criteria. The hierarchy helps to decompose complex decision problems into smaller and manageable subtasks, and thus, it is very attractive for computational efficiency and explanatory purposes. To handle the hierarchy of criteria in MCDA, a methodology called Multiple Criteria Hierarchy Process (MCHP), has been recently proposed. MCHP permits to consider preference relations with respect to a subset of criteria at any level of the hierarchy. Here, we propose to apply MCHP to the ELECTRE III ranking method adapted to handle three types of interaction effects between criteria: mutual-weakening, mutual-strengthening and antagonistic effect. We also involve in MCHP an imprecise elicitation of criteria weights, generalizing a technique called the SRF method. In order to explore the plurality of rankings obtained by the ELECTRE III method for possible sets of criteria weights, we apply the Stochastic Multiobjective Acceptability Analysis (SMAA) that permits to draw robust conclusions in terms of rankings and preference relations at each level of the hierarchy of criteria. The novelty of the whole methodology consists of a joint consideration of hierarchical assessments of alternatives performances on interacting criteria, imprecise criteria weights, and robust analysis of ranking recommendations resulting from ELECTRE III. An example regarding the multiple criteria ranking of some European universities will show how to apply the proposed methodology on a decision problem.     

基于前景理论和隶属度的混合型多属性决策方法

针对带有决策者期望的混合型多属性决策问题,提出了一种基于前景理论和隶属度的决策分析方法。首先依据决策者对各个属性的期望,将具有清晰数、区间数和语义短语三种形式的决策矩阵转化成为前景决策矩阵。然后,根据各个方案与决策期望之间的广义加权欧氏距离,建立了可变模糊模式识别模型,并通过构造拉格朗日松弛函数,进行交叉迭代计算,得到各个方案的最优隶属度以及对应的属性权重,在此基础上,通过合成各个方案的累计前景值与隶属度,得到方案的综合前景值,并依据综合前景值的大小进行方案排序。最后通过一个原油管道路线优选实例,表明了该方法的可行性与有效性。     

Beyond Markowitz with multiple criteria decision aiding

The paper is about portfolio selection in a non-Markowitz way, involving uncertainty modeling in terms of a series of meaningful quantiles of probabilistic distributions. Considering the quantiles as evaluation criteria of the portfolios leads to a multiobjective optimization problem which needs to be solved using a Multiple Criteria Decision Aiding (MCDA) method. The primary method we propose for solving this problem is an Interactive Multiobjective Optimization (IMO) method based on so-called Dominance-based Rough Set Approach (DRSA). IMO-DRSA is composed of two phases: computation phase, and dialogue phase. In the computation phase, a sample of feasible portfolio solutions is calculated and presented to the Decision Maker (DM). In the dialogue phase, the DM indicates portfolio solutions which are relatively attractive in a given sample; this binary classification of sample portfolios into ‘good’ and ‘others’ is an input preference information to be analyzed using DRSA; DRSA is producing decision rules relating conditions on particular quantiles with the qualification of supporting portfolios as ‘good’; a rule that best fits the current DM’s preferences is chosen to constrain the previous multiobjective optimization in order to compute a new sample in the next computation phase; in this way, the computation phase yields a new sample including better portfolios, and the procedure loops a necessary number of times to end with the most preferred portfolio. We compare IMO-DRSA with two representative MCDA methods based on traditional preference models: value function (UTA method) and outranking relation (ELECTRE IS method). The comparison, which is of methodological nature, is illustrated by a didactic example.     

基于交叉效率DEA与群体共识的区间乘性语言偏好关系群决策

针对区间乘性语言偏好关系群决策问题，提出了一种基于交叉效率DEA和群体共识的群决策方法。首先，提出乘性语言偏好关系导出函数的定义，并构建产出导向的DEA模型，证明了一致性乘性语言偏好关系的DEA效率得分与排序向量之间存在比例关系。在此基础上，建立基于理想值的交叉效率DEA模型，提出乘性语言偏好关系的通用排序方法。同时，基于群体共识建立目标规划模型来计算各语言偏好关系的权重系数。最后，利用Monte Carlo随机模拟的方法对群体语言偏好空间进行统计分析，得到群决策期望排序向量及其可信度。算例分析表明本文方法能够有效的避免信息损失，具有较强的适用性和较高的可信度。     

Integrated framework for robustness analysis using ratio-based efficiency model with application to evaluation of Polish airports

We consider a problem of evaluating efficiency of Decision Making Units (DMUs) based on their deterministic performance on multiple consumed inputs and multiple produced outputs. We apply a ratio-based efficiency measure, and account for the Decision Maker׳s preference information representable with linear constraints involving input/output weights. We analyze the set of all feasible weights to answer various robustness concerns by deriving: (1) extreme efficiency scores and (2) extreme efficiency ranks for each DMU, (3) possible and necessary efficiency preference relations for pairs of DMUs, (4) efficiency distribution, (5) efficiency rank acceptability indices, and (6) pairwise efficiency outranking indices. The proposed hybrid approach combines and extends previous results from Ratio-based Efficiency Analysis and the SMAA-D method. The practical managerial implications are derived from the complementary character of accounted perspectives on DMUs׳ efficiencies. We present an innovative open-source software implementing an integrated framework for robustness analysis using a ratio-based efficiency model on the diviz platform. The proposed approach is applied to a real-world problem of evaluating efficiency of Polish airports. We consider four inputs related to the capacities of a terminal, runways, and an apron, and to the airport׳s catchment area, and two outputs concerning passenger traffic and number of aircraft movements. We present how the results can be affected by integrating the weight constraints and eliminating outlier DMUs.     

基于非线性区间数风险控制的资产负债优化模型

现有研究把存、贷款利率视为常数,无法使资产配置的优化结果适应未来市场利率的变化。本文的资产负债管理优化模型通过资产与负债的区间数的持续期缺口建立了区间型利率风险免疫条件,使资产的最优配置在资产与负债的收益率变化时仍能免疫利率风险。研究表明本文引入的持效期缺口区间的偏向选择参数γ决定预留缺口是赚钱还是亏钱。γ取值0.5时缺口区间两端点的绝对值最小;γ越大于0.5时,正缺口越大,在利率下降时就越赚钱。γ越小于0.5时,负缺口越大,在利率上升时就越赚钱。而区间长度选择参数γ决定损益的大小;揭示了在积极的利率风险管理策略中,选择较小的λ会获得较多的风险收益。另一方面,本文通过相关系数组合半绝对离差建立了非线性区间型组合风险的函数表达式,改变了现有研究线性区间型算法将各笔贷款风险进行简单线性加权、进而夸大了组合信用风险的弊端。     

多标准决策表中发现概率规则的变精度粗糙集方法

用优势关系代替不可分辨关系,本文提出了一种可以从多标准决策表中获取概率规则的扩展变精度粗糙集模型,该模型能够处理多标准决策表中可能的不一相容性,获取由偏好对象组成的概率决策规则集,并导出事例决策系统的偏好模型。研究结果表明:基于优势关系,从多标准决策表中获取的最小概率规则集,使用的条件数量较少,且导出规则的数量较少、较强。     

方案有不确定偏好的区间数相对熵群决策方法

研究了属性值是区间数并且已知方案偏好信息的多属性群决策问题。建立了每个方案客观偏好值与主观偏好值偏差的相对熵测度矩阵;基于客观信息和方案偏好信息的相对熵建立了属性权重模型;建立了一个新的区间数比较的可能度公式,基于可能度公式给出了方案排序方法,算例说明方法可行性。     

An enhanced loading model for the probabilistic workload control under workload imbalance

Load-oriented manufacturing control (LOMC), a well known probabilistic approach to workload control, is based on limiting and smoothing workload using one static parameter for each workcentre, called load limit (LL). The value of this parameter is set by the shop managers based on the planned lead time at each workcentre. In this paper the use of LL is shown to be inappropriate for the smoothing of workloads when the workload is not sufficiently balanced. We propose to enhance the LOMC model by introducing two sets of parameters:

(i) limiting parameters (LPs), that are statical parameters of the workcentres, set by the shop managers. LPs are used to limit the workload released to the shop;

(ii) smoothing parameters (SPs), that are dynamical parameters of the workcentres, computed as a function of their real workload. SPs are used to smooth the jobs workload over downstream workcentres.

A simulation model was used to compare the enhanced model, based on two parameters sets, with the traditional LOMC model, based on a single parameter set. The simulation runs were earned out with different conditions of due-date assignments, dispatching rules and production mix. The statistical analysis performed on experimental results confirmed that the enhanced model achieves significantly better due dates under unbalanced workload conditions.     

对方案有偏好的区间数多属性灰色关联决策模型

针对属性值以区间数形式给出并且已知方案偏好信息的多属性决策问题,提出了一种灰色关联分析的决策方法。该方法依据一般的灰色关联分析方法的基本思路,给出了该问题的计算步骤,其核心是通过构建并求解一个单目标最优化模型,得到属性权重信息,从而计算出每个方案客观偏好值与主观偏好值的灰色关联系数,进而得到每个方案客观偏好与主观偏好的关联度,根据关联度对所有方案进行排序。最后给出了一个数值例子,结果表明方法简单,有效和易于计算。     

A classification approach based on the outranking model for multiple criteria ABC analysis

The multiple criteria ABC analysis is widely used in inventory management, and it can help organizations to assign inventory items into different classes with respect to several evaluation criteria. Many approaches have been proposed in the literature for addressing such a problem. However, most of these approaches are fully compensatory in multiple criteria aggregation. This means that an item scoring badly on one or more key criteria could be placed in good classes because these bad performances could be compensated by other criteria. Thus, it is necessary to consider the non-compensation in the multiple criteria ABC analysis. To the best of our knowledge, the ABC classification problem with non-compensation among criteria has not been studied sufficiently. We thus propose a new classification approach based on the outranking model to cope with such a problem in this paper. However, the relational nature of the outranking model makes the search for the optimal classification solution a complex combinatorial optimization problem. It is very time-consuming to solve such a problem using mathematical programming techniques when the inventory size is large. Therefore, we combine the clustering analysis and the simulated annealing algorithm to search for the optimal classification. The clustering analysis groups similar inventory items together and builds up the hierarchy of clusters of items. The simulated annealing algorithm searches for the optimal classification on different levels of the hierarchy. The proposed approach is illustrated by a practical example from a Chinese manufacturer. Furthermore, we validate the performance of the approach through experimental investigation on a large set of artificially generated data at the end of the paper.     

An approach to consensus measurement of linguistic preference relations in multi-attribute group decision making and application

This paper studies the group decision making problem with linguistic preference relations. We first study the consensus measure between the individual preference relations and the collective (group) preference relation by defining the concept of degree of similarity between two linguistic values and two linguistic preference relations. Then we propose a concept of the acceptance consensus threshold value for group decision making with linguistic preference information. We show that the consensus between individual preference relations and the collective (group) preference relation is greater than the weighted similarity degree of a given individual preference relation with respect to other individual preference relations in group decision making with linguistic preference relations. The results will help in the analysis of crucial issues of conflict and agreement among preferences of decision-makers, which affect the consensus of group decision making with linguistic preference relations. Theoretical foundations are then established for the proposed method. Finally, the proposed method is applied to evaluate the degree of consensus of individual overall preference values with respect to the collective overall preference values for multi-attribute group decision making with linguistic information. The main contribution of this paper is twofold. One is to present a new way to measure the consensus between the individual preference relations and the collective (group) preference relation in group decision making with linguistic preference information. Another is to provide an effective approach to evaluating individual overall preference values with respect to the collective overall preference values in multi-attribute group decision making with linguistic information.     

使用者形象一致性及形象强度对品牌延伸的影响

运用2个实验探讨了延伸产品与母品牌"使用者形象一致性"对消费者评价品牌延伸产生的影响。实验1表明,"使用者形象一致性"与"产品相似性"之间存在交互作用:当延伸产品使用者形象与母品牌使用者形象一致时,消费者根据延伸产品与"原产品"的相似性或延伸产品的"远"、"近"对品牌延伸做出评价;此时,"近"的延伸较"远"的延伸获得更高评价。当延伸产品使用者形象与母品牌使用者形象不一致时,"远"的延伸反而比"近"的延伸获得更高评价。实验2表明,母品牌使用者刻板印象的强、弱,会调节"使用者形象一致性"对延伸评价的影响。具体来说,对于使用者刻板印象强的品牌,形象不一致会对延伸评价产生较大的负面影响;对于使用者刻板印象较弱的品牌,形象不一致不会对延伸评价形成负面影响。     

超效率DEA模型的区间扩展

将一种改进的DEA模型-超效率DEA(SE-DEA)模型[1]拓展到区间投入产出情形,得到区间SE-DEA模型。定义了一种反映决策者满意度的区间数序关系。当决策者给定一满意度水平,将区间SE-DEA中的区间不等式约束转化为确定型约束。研究了该满意度水平的另一层含义,即决策者对除被评价决策单元外的其它决策单元的偏好程度,据此将区间SE-DEA中的区间等式约束和区间目标函数转化为确定型。最终将区间SE-DEA转化为某一满意度水平下的确定型SE-DEA,并进行求解。最后将文中方法应用于天津市某4家科研所的效率预测问题之中。     

When are two multivariate random processes indistinguishable

Prediction error identification methods have been recently the objects of much study, and have wide applicability. The maximum likelihood (ML) identification methods for Gaussian models and the least squares prediction error method (LSPE) are special cases of the general approach. In this paper, we investigate conditions for distinguishability or identifiability of multivariate random processes, for both continuous and discrete observation time T. We consider stationary stochastic processes, for the ML and LSPE methods, and for large observation interval T, we resolve the identifiability question. Our analysis begins by considering stationary autoregressive moving average models, but the conclusions apply for general stationary, stable vector models. The limiting value for T → ∞ of the criterion function is evaluated, and it is viewed as a distance measure in the parameter space of the model. The main new result of this paper is to specify the equivalence classes of stationary models that achieve the global minimization of the above distance measure, and hence to determine precisely the classes of models that are not identifiable from each other. The new conclusions are useful for parameterizing multivariate stationary models in system identification problems. Relationships to previously discovered identifiability conditions are discussed.