对方案有偏好的不确定语言多属性决策方法

研究了属性权重完全未知、属性值和对方案的偏好值以不确定语言变量形式给出的不确定语言多属性决策问题。首先,引入不确定语言变量的运算法则,以及不确定语言变量之间比较的可能度公式,给出了不确定语言变量间的距离的概念。针对属性权重完全未知的情形,给出了求解权重的公式。然后,利用不确定语言加权平均算子,对不确定语言决策信息进行加权集成,并利用可能度公式构造可能度矩阵(互补判断矩阵),继而利用互补判断矩阵排序公式对决策方案进行排序和择优。最后进行了实例分析。     

多属性隐式变权决策分析方法

为克服多因素变权决策方法的内在缺陷,基于Belton 和Gear提出的B/G-AHP层次分析原理给出了一种隐含式的多属性变权决策建模思想,并运用该思想给出了一种多属性变权决策新方法。它相对于多因素变权决策方法具有三方面的比较优势。其一,依赖的变权偏好信息直接由决策者给出,因而能够克服决策分析者对决策结果的主观武断性影响,更好地反映决策者的真实偏好。其二,不会受到由因素的属性值转化为偏好值所额外引入的主观测度偏差的干扰。其三,对决策者主观判断可能存在的误差予以了旨在弱化其影响的优化控制。数值分析表明新方法拥有较好的变权能力,并且相对于已有方法能够给出更易为决策者所接受的评价结论,因而具有较好的应用有效性。     

The inferring of preferences from indifferences in multicriteria decision analysis

Rivett [5] has proposed that an approximate preference ordering may be deduced from statements of pairwise indifferences between decision alternatives by using multi-dimensional scaling. In this paper it is demonstrated that much stronger evaluations of preference are possible by applying formal statistical inferential procedures to a simple parametric model, relating indifference to closeness on a scale defined by a linear function of attribute values. This can be used to screen out a considerable proportion of less desirable decision alternatives. The method is illustrated by application to Rivett's problem of the hypothetical Town of Brove, for which a satisfactory matching with Rivett's utilities is obtained. It is also shown that the method can provide useful preference orderings on the basis of less than 20% of all possible pairwise comparisons between alternatives.     

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。     

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 modified DEA model to estimate the importance of objectives with an application to agricultural economics

This paper demonstrates a connection between data envelopment analysis (DEA) and a non-interactive elicitation method to estimate the weights of objectives for decision-makers in a multiple attribute approach. This connection gives rise to a modified DEA model that allows us to estimate not only efficiency measures but also preference weights by radially projecting each unit onto a linear combination of the elements of the payoff matrix (which is obtained by standard multicriteria methods). For users of multiple attribute decision analysis the basic contribution of this paper is a new interpretation in terms of efficiency of the non-interactive methodology employed to estimate weights in a multicriteria approach. We also propose a modified procedure to calculate an efficient payoff matrix and a procedure to estimate weights through a radial projection rather than a distance minimization. For DEA users, we provide a modified DEA procedure to calculate preference weights and efficiency measures that does not depend on any observations in the dataset. This methodology has been applied to an agricultural case study in Spain.     

A case-based distance method for screening in multiple-criteria decision aid

Screening is a process of multiple-criteria decision aid (MCDA) in which a large set of alternatives is reduced to a smaller set that most likely contains the best choice. We propose screening using a distance model calibrated on the basis of the decision-maker's own judgement. Viewing MCDA as preference aggregation based on consequence data, we define consequence and preference expressions (values and weights) and describe how they are aggregated. Then we define screening and explain some of its properties. Using an appropriate definition of distance, our case-based distance method screens a set of alternatives using criterion weights and a distance threshold obtained by quadratic optimization using the decision-maker's selection of alternatives from a test set. This case-based method can elicit the decision maker's preferences more expeditiously and accurately than direct inquiry. An application in water supply planning is used to demonstrate the procedure.     

Fuzzy LINMAP approach to heterogeneous MADM considering comparisons of alternatives with hesitation degrees

Multiattribute decision making (MADM) with multiple formats of information, which is called heterogeneous MADM for short, is very complex and interesting in applications. The purpose of this paper is to extend the Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP) for solving heterogeneous MADM problems which involve intuitionistic fuzzy (IF) sets (IFSs), trapezoidal fuzzy numbers (TrFNs), intervals and real numbers. In this method, DM's preference is given through pair-wise comparisons of alternatives with hesitation degrees which are represented as IFSs. The IF consistency and inconsistency indices are defined on the basis of pair-wise comparisons of alternatives. Each alternative is assessed on the basis of its distance to a fuzzy ideal solution (FIS) unknown a priori. Based on the defined IF consistency and inconsistency indices, we construct a new fuzzy mathematical programming model, which is solved by the developed method of fuzzy mathematical programming with IFSs. Once the FIS and the attribute weights are obtained, we can calculate the distances of all alternatives to the FIS, which are used to determine the ranking order of the alternatives. A supplier selection example is presented to demonstrate the validity and applicability of the proposed method.     

挖掘客户潜在需求确定指标重要程度的证据组合方法

在现实中,属性(例如产品的各种指标)的权重常常与特定客户的需求有关,因此这些客户的偏好信息对权重的确定非常重要.这种信息不一定就直接体现在对属性的重视程度上,而可能表现在对一组具体产品的偏好关系上.在对产品的指标评价时还会存在一些无知性.针对这些情况,本文给出一个基于证据理论和目标规划、挖掘客户潜在需求的指标权重估计方法,并结合一个计算示例,给出具体的计算过程.     

Fuzzy LINMAP approach to heterogeneous MADM considering comparisons of alternatives with hesitation degrees

Multiattribute decision making (MADM) with multiple formats of information, which is called heterogeneous MADM for short, is very complex and interesting in applications. The purpose of this paper is to extend the Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP) for solving heterogeneous MADM problems which involve intuitionistic fuzzy (IF) sets (IFSs), trapezoidal fuzzy numbers (TrFNs), intervals and real numbers. In this method, DM's preference is given through pair-wise comparisons of alternatives with hesitation degrees which are represented as IFSs. The IF consistency and inconsistency indices are defined on the basis of pair-wise comparisons of alternatives. Each alternative is assessed on the basis of its distance to a fuzzy ideal solution (FIS) unknown a priori. Based on the defined IF consistency and inconsistency indices, we construct a new fuzzy mathematical programming model, which is solved by the developed method of fuzzy mathematical programming with IFSs. Once the FIS and the attribute weights are obtained, we can calculate the distances of all alternatives to the FIS, which are used to determine the ranking order of the alternatives. A supplier selection example is presented to demonstrate the validity and applicability of the proposed method.     

Evaluating airline competitiveness using multiattribute decision making

This paper presents an objective approach to the evaluation of airline competitiveness. The evaluation problem is formulated as a multiattribute decision making model and solved by three widely used methods (the simple additive weighting method, the weighted product method and the technique for order preference by similarity to ideal solution) based on multiattribute value theory. A new empirical validation procedure is developed to deal with the inconsistency problem of evaluation outcomes produced by the three methods. The procedure selects the evaluation outcome which has a minimum expected value loss. An empirical study on Taiwan's five major domestic airlines is conducted to demonstrate the effectiveness of the approach. To measure and compare overall competitiveness of the airlines, five competitiveness dimensions and their associated objective performance measures on both efficiency and effectiveness are identified. The result of empirical validation for the three methods suggests the use of the simple additive weighting method. The evaluation outcome helps an airline identify its competitive advantages relative to its competitors. The objective approach presented is particularly applicable when subjective judgements on performance ratings and attribute weights are not reliable, or suitable decision makers are not available.     

Decision Support by Interval SMART/SWING—Incorporating Imprecision in the SMART and SWING Methods

Interval judgments are a way of handling preferential and informational imprecision in multicriteria decision analysis (MCDA). In this article, we study the use of intervals in the simple multiattribute rating technique (SMART) and SWING weighting methods. We generalize the methods by allowing the reference attribute to be any attribute, not just the most or the least important one, and by allowing the decision maker to reply with intervals to the weight ratio questions to account for his/her judgmental imprecision. We also study the practical and procedural implications of using imprecision intervals in these methods. These include, for example, how to select the reference attribute to identify as many dominated alternatives as possible. Based on the results of a simulation study, we suggest guidelines for how to carry out the weighting process in practice. Computer support can be used to make the process visual and interactive. We describe the WINPRE software for interval SMART/SWING, preference assessment by imprecise ratio statements (PAIRS), and preference programming. The use of interval SMART/SWING is illustrated by a job selection example.     

群组决策中三角模糊数互补判断矩阵的相容性及方案排序研究

针对专家偏好信息为三角模糊数互补判断矩阵的群组决策问题,研究偏好信息的相容性及方案排序问题。基于Hamming 距离的概念,首先给出了衡量两个三角模糊数相容性的一个指标,并研究了该指标的相关性质;其次,根据三角模糊数互补判断矩阵的特点,给出了三角模糊数互补判断矩阵的相容性指标;以相容性指标为依据设定专家权重,进而给出了一种方案排序方法。最后,算例验证了方法的有效性。     

IMP: A decision aid for multiattribute evaluation using imprecise weight estimates

In multicriteria analysis, weights are inferred from judgements. Judgements are subject to uncertainty and the weights found depend on the method used so that weights must necessarily be imprecise. Describing weights by a suitable probability distribution captures this imprecision and leads to correspondingly imprecise estimates of the multiattribute scores given to alternatives. A method is described which enables the parameters of a Dirichlet distribution to be found from three point weight estimates and for this to be used to determine whether or not alternatives may justifiably be differentiated by their scores. A simple chart shows this information and permits easy interaction. An illustration shows the effects of different sources of imprecision and of aggregating individual assessments in a group.     

A COMPARISON OF WEIGHTING METHODS IN POWER PLANT SITING*

The insufficient attention that too often is paid to the characteristics required of attribute weights prevents multiattribute decision rules from accurately representing preferences. The weighting summation or linear model requires weights to be proportional to the relative value of unit changes in their attribute value functions. Only then will weights accurately reflect the trade-offs decision makers are willing to make. A number of methods of choosing weights are critiqued from this perspective. Applications of weighting methods in power plant siting are surveyed, and a siting study of western Maryland is presented. Two weighting methods were used, one deriving weights from trade-offs made by decision makers and the other asking decision makers to choose weights on a scale of 0 to 10. The locations picked by the two methods differ strikingly.     

目标导向层次分析方法

对含有抽象属性的多属性层次结构而言,层次分析法即AHP（包括DIS-AHP、ABS-AHP、IDE-AHP和SUP-AHP四种具体方法）会因比率比较基准缺失、权重内涵模糊不清或方案评价不保序而缺乏科学理性。为发展AHP,基于摆幅置权（SW）判断模式和多属性决策属性价值公度方法,首先给出了能为层次结构抽象属性上的SW判断提供支持的规约性多属性决策属性价值公度方法,然后由此并结合多属性价值理论给出了能够克服现有层次分析法内在缺陷的目标导向层次分析方法即ToAHP。相对于AHP,ToAHP在判断模式与权重内涵、方法建构的理论基础和相关假设检验、方案评价保序与其内在数理依据上具有明显的相对科学合理性。应用分析表明：在输入信息可比的条件下,ToAHP明显优于AHP的四种分析方法之中最具可信性的SUP-AHP方法。     

RUTA: A framework for assessing and selecting additive value functions on the basis of rank related requirements

In this paper, we present a new preference disaggregation method, called RUTA, which infers a set of additive value functions from the preference information referring to the desired ranks of some reference alternatives. Real-life experience indicates that people willingly refer to the range of allowed ranks that a particular alternative should attain, or to constraints on the final scores of the alternatives. We develop a mathematical model for incorporating such preference information via mixed-integer linear programming (MILP). Then, we discuss how decision making could be supported with the use of the already proposed extreme ranking analysis (ERA), which indicates the best and worst ranks gained by each alternative over the set of compatible preference model instances. We also introduce a new interactive UTA-like technique, which aims at selecting a single value function representing the outcomes of ERA. In the interactive process, the decision maker (DM) is assigning priorities to different pre-defined targets, which are built on results of ERA, and refer to the comparison of the best and/or worst ranks for pairs of alternatives. In particular, the DM may choose to emphasize or neglect the advantage of some alternatives over the others, in terms of results of ERA. In this way, one obtains a synthetic representation of extreme ranking analysis at a higher level of abstraction.     

权重信息完全未知的灰色多属性群决策方法研究

基于灰色系统理论的思想和方法,探讨了决策方案的属性值为区间灰数、属性权重及各决策人的权威权重完全未知的灰色多属性群决策问题。通过分析,引入了个体理想最优方案向量、理想专家、方案间优势度和方案集中方案间优势比较矩阵等概念。根据区间灰数的本质特征,定义了两区间灰数的新的相离度,构建了基于两区间灰数相离度的灰色区间关联系数公式及灰色关联度。建立了基于投影的特征向量法和模糊互补判断矩阵排序方法的两种决策算法,给出的算法避免了权重的计算。文中实例分析说明了所提出的灰色多属性群决策方法的合理性及其算法的有效性。     

Dominance intensity measure within fuzzy weight oriented MAUT: An application

We introduce a dominance intensity measuring method to derive a ranking of alternatives to deal with incomplete information in multi-criteria decision-making problems on the basis of multi-attribute utility theory (MAUT) and fuzzy sets theory. We consider the situation where there is imprecision concerning decision-makers' preferences, and imprecise weights are represented by trapezoidal fuzzy weights. The proposed method is based on the dominance values between pairs of alternatives. These values can be computed by linear programming, as an additive multi-attribute utility model is used to rate the alternatives. Dominance values are then transformed into dominance intensity measures, used to rank the alternatives under consideration. Distances between fuzzy numbers based on the generalization of the left and right fuzzy numbers are utilized to account for fuzzy weights.     

Heuristics for prioritizing pair-wise elicitation questions with additive multi-attribute value models

Additive value models are widely used in Multiple Criteria Decision Analysis. Direct elicitation of the value model preference parameters can impose excessive cognitive burden on the decision maker. Indirect techniques that employ pair-wise questions have been proposed for lowering the elicitation effort. In all practically relevant problems, more than a single question needs to be answered for arriving at a sufficiently precise outcome. The selection and ordering of questions affects the number of answers required for ranking the decision alternatives. However, evaluating all possible questions and answers is intractable due to the search space being, in the worst case, of factorial size. This paper develops heuristics for prioritizing pair-wise elicitation questions based on (1) necessary preference relations, (2) extreme ranks attained by the alternatives, (3) pair-wise preference indices, and (4) rank acceptability indices. We also introduce three metrics for assessing quality of a question prioritization heuristic. Numerical results allow us to identify a subset of heuristics that score well on our metrics in a variety of problem settings. This conclusion was validated in a real-world experiment where 101 subjects answered pair-wise questions to rank 10 mobile phone packages evaluated in terms of four criteria.