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.     

Screening alternatives graphically by an extended case-based distance approach

Screening is a helpful process of multiple criteria decision aid (MCDA) to reduce a larger set of alternatives into a smaller one containing the best alternatives; thereby, decision makers are able to concentrate on evaluating alternatives within a smaller set. Therefore, determining how to assist decision makers in screening is an important issue for MCDA. This study proposes an extended case-based distance approach incorporating the advantages of a case-based distance method, a mixed-integer programming approach of discriminant analysis, and a multidimensional scaling technique to help decision makers screen alternatives visually in MCDA. The proposed approach can screen alternatives by evaluating sets of cases selected by decision makers, providing visual aids to observe decision context, reducing the number of misclassifications, and improving multiple solution problems. An interactive screening procedure is also developed to provide flexibility so that decision makers can check and adjust screening results iteratively.     

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.     

An exact algorithm for the multicriteria ordered clustering problem

In the context of multicriteria decision aid, we address the problem of regrouping alternatives into completely ordered categories based on valued preference degrees. We assume that the number of groups is fixed a priori. This will be referred to as the multicriteria ordered clustering problem. The model is based on the definition of an inconsistency matrix and only uses the ordinal properties of the pairwise preference relations. An exact algorithm is proposed to find the ordered partition and is applied as illustration to the Human Development Index.     

Consistency and Accuracy in Decision Aids: Experiments with Four Multiattribute Systems*

There have been a number of multiattribute decision aids developed to aid selection problems. Multiattribute value theory and the analytic hierarchy process are two commonly used techniques. Different systems can result in radically different conclusions if they inaccurately and inconsistently reflect the preference structure of decision makers, or if they are based on inappropriate theoretical models. This study examines the impact of the underlying theoretical model, the method in which preference information is elicited, and the structure of alternatives as influences on the results from using various decision aids. It was found that two systems based on the multiattribute value theory model were just as diverse in their conclusions as were results between AHP and the multiattribute value theory models. Therefore, accuracy of information reflecting decision maker preference is an important consideration. Feedback capable of assuring the decision maker that information provided is consistent is a necessary feature required of decision aids applied to selection problems. The study also found that the way in which information is elicited influenced the result more than did the underlying model. Exact numerical data for complex concepts such as attribute importance and alternative performance on attributes is not necessary, and elicitation procedures that are more natural for the user are likely to be more accurate.     

Stock Evaluation Using a Preference Disaggregation Methodology

This paper presents a real application of a multicriteria decision aid (MCDA) approach to portfolio selection based on preference disaggregation, using ordinal regression and linear programming (UTADIS method; UTilités Additives DIScriminantes). The additive utility functions that are derived through this approach have the extrapolation ability that any new alternative (share) can be easily evaluated and classified into one of several user-predefined groups. The procedure is illustrated with a case study of 98 stocks from the Athens stock exchange, using 15 criteria. The results are encouraging, indicating that the proposed methodology could be used as a tool for the analysis of the portfolio managers' preferences and choices. Furthermore, the comparison with multiple discriminant analysis (either using a stepwise procedure or not) illustrates the superiority of the proposed methodology over a well-known multivariate statistical technique that has been extensively used to study financial decision-making problems.     

RANK GENERATION,PRESERVATION, AND REVERSAL IN THE ANALYTIC HIERARCHY DECISION PROCESS

Decision making has the objective of finding the best alternative or set of alternatives by considering a number of goals, objectives, criteria, competitors, and other important factors. The analytic hierarchy process is a decision aid used to assist a decision maker in sorting out the complexity of a decision problem and making use of his or her judgments. A decision maker must be assured that the arithmetic operations of any such decision process are the right ones—that they surface the correct ranking and values of the alternatives and preserve or alter ranks appropriately when new alternatives are added or deleted. In this paper it will be shown that with absolute measurement, rank always is preserved, with relative measurement, rank changes with nspect to scveral criteria only because of the structural dependence (involving both numbers and measurements) of criteria on alternatives. A discussion of the effect on rank of replicas and near replicas of the alternatives also is given.     

Expanding the Reach of Participatory Risk Management: Testing an Online Decision‐Aiding Framework for Informing Internally Consistent Choices

This article presents research aimed at developing and testing an online, multistakeholder decision‐aiding framework for informing multiattribute risk management choices associated with energy development and climate change. The framework was designed to provide necessary background information and facilitate internally consistent choices, or choices that are in line with users’ prioritized objectives. In order to test different components of the decision‐aiding framework, a six‐part, 2 × 2 × 2 factorial experiment was conducted, yielding eight treatment scenarios. The three factors included: (1) whether or not users could construct their own alternatives; (2) the level of detail regarding the composition of alternatives users would evaluate; and (3) the way in which a final choice between users’ own constructed (or highest‐ranked) portfolio and an internally consistent portfolio was presented. Participants’ self‐reports revealed the framework was easy to use and providing an opportunity to develop one's own risk‐management alternatives (Factor 1) led to the highest knowledge gains. Empirical measures showed the internal consistency of users’ decisions across all treatments to be lower than expected and confirmed that providing information about alternatives’ composition (Factor 2) resulted in the least internally consistent choices. At the same time, those users who did not develop their own alternatives and were not shown detailed information about the composition of alternatives believed their choices to be the most internally consistent. These results raise concerns about how the amount of information provided and the ability to construct alternatives may inversely affect users’ real and perceived internal consistency.     

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。     

ASSESSMENT OF MULTIATTRIBUTED MEASURABLE VALUE AND UTILITY FUNCTIONS VIA MATHEMATICAL PROGRAMMING*

A major restriction on the use of decision analysis in practice is the frequent difficulty of determining a decision maker's multiattribute utility function. The assessment process can be complex and tedious and generally involves: (1) identifying relevant independence conditions, (2) assessing conditional utility functions, (3) assessing scaling constants, and (4) checking for consistency. Some of the assessment and modeling complexities encountered include an assessor's inability to respond in a quantitatively meaningful and consistent way to hypothetical gambles and an analyst's problem in selecting an appropriate functional form that accurately characterizes the conditional utility assessments. A simplified procedure that mitigates these difficulties is proposed. This procedure facilitates the determination of scaling constants by obtaining (via mathematical programming) a multiattributed measurable value function which is converted to a multiattributed utility function. The methodology can be developed advantageously to produce an interactive software package for use as an assessment aid.     

PAHAP: A Pairwise Aggregated Hierarchical Analysis of Ratio-Scale Preferences

In this paper, we present a Pairwise Aggregated Hierarchical Analysis of Ratio-Scale Preferences (PAHAP), a new method for solving discrete alternative multicriteria decision problems. Following the Analytic Hierarchy Process (AHP), PAHAP uses pairwise preference judgments to assess the relative attractiveness of the alternatives. By first aggregating the pairwise judgment ratios of the alternatives across all criteria, and then synthesizing based on these aggregate measures, PAHAP determines overall ratio scale priorities and rankings of the alternatives which are not subject to rank reversal, provided that certain weak consistency requirements are satisfied. Hence, PAHAP can serve as a useful alternative to the original AHP if rank reversal is undesirable, for instance when the system is open and criterion scarcity does not affect the relative attractiveness of the alternatives. Moreover, the single matrix of pairwise aggregated ratings constructed in PAHAP provides useful insights into the decision maker's preference structure. PAHAP requires the same preference information as the original AHP (or, altematively, the same information as the Referenced AHP, if the criteria are compared based on average (total) value of the alternatives). As it is easier to implement and interpret than previously proposed variants of the conventional AHP which prevent rank reversal, PAHAP also appears attractive from a practitioner's viewpoint.     

一种基于偏好分布的群决策方法

为了满足群决策的实际需求,本文提出了一种基于偏好分布的群决策方法,该方法利用完全不对称预先排序向量表示决策者的偏好,通过分析计算偏好排序向量的密度和分布结构,从可行方案集合中寻找所有决策者都能接受的优选方案集合,逐次缩小搜索空间以逼近一致满意解。该方法结合冲突分析,可进一步分析决策者之间的相互关系,集成于谈判支持系统,具有直观、实用等特点,最后给出了一个实际例子说明该方法。     

Temptation and Self‐Control

We study a two‐period model where ex ante inferior choice may tempt the decision‐maker in the second period. Individuals have preferences over sets of alternatives that represent second period choices. Our axioms yield a representation that identifies the individual's commitment ranking, temptation ranking, and cost of self‐control. An agent has a preference for commitment if she strictly prefers a subset of alternatives to the set itself. An agent has self‐control if she resists temptation and chooses an option with higher ex ante utility. We introduce comparative measures of preference for commitment and self‐control and relate them to our representations.     

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.     

一种具有不同粒度语言判断矩阵的群决策方法

针对具有不同粒度语言判断矩阵形式的偏好信息的群决策问题,提出了一种基于二元语义运算的群决策方法.在该方法中,首先给出了不同粒度语言判断矩阵的定义;然后给出了不同粒度语言判断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,并且采用近年来最新发展的关于二元语义信息集结的加权平均算子和语言优势度直接对语言短语进行运算,最终确定最优方案;最后给出了一个算例.     

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.     

Selecting sourcing partners for a make-to-order supply chain

Make-to-order manufacturers face an idiosyncratic and complex situation in the sourcing selection process. Although they can source from several key suppliers, each order requires custom key parts that cannot be stocked. Our research provides a decision model to facilitate the sourcing process for these manufacturers using information about their sourcing partners’ cost and processing time. The manufacturer can calculate the total cost and on-time probability for all possible combinations of certified suppliers and key part allotments to obtain a sourcing portfolio with several sourcing alternatives for a desired service level. The portfolio allows the manufacturer to make trade-offs between cost and reliability to finish the job on time. Additionally, the portfolio can be obtained for a given due date or for reduced due dates in a competitive bid situation. The portfolio approach allows the manufacturer to maintain control over the sourcing selection process by partnering with sourcing members to keep costs low without losing the needed flexibility to meet customer demands.     

Multi-attribute utility methods in group decision making: Past applications and potential for inclusion in GDSS

This paper reviews a variety of studies in which multi-attribute utility theory (MAU) has been used successfully to aid group decision processes and discusses the incorporation of MAU in Group Decision Support Systems (GDSS). GDSS of various levels of automation have been proposed to aid group decision making. A number of commercial GDSSs are available which are capable of aiding generation of alternatives, their evaluation, and selection. Many authors have promoted the incorporation of quantitative decision making models in GDSS. The most appropriate quantitative tool for GDSS is MAU, but MAU has rarely been utilized. The cases reviewed illustrate that the use of MAU techniques is not prohibitively difficult or complex.     

基于前景理论的多阶段随机多准则决策方法

研究一种基于动态参考点的多阶段随机多准则决策方法。考虑多阶段决策过程中决策者的风险偏好,建立了基于前景理论的多阶段随机多准则决策分析框架,提出了一种基于阶段发展特征的动态参考点设置方法;构建准则权重的目标规划模型,结合阶段参考点动态变化的特征测算各阶段备选方案的综合前景值;设计方案综合前景值的范围估算模型,以反映决策风险对评价结果的影响;案例研究验证了上述方法的可行性和实际效果。     

一种具有不确定偏好序信息的多指标群决策方法

针对具有不确定偏好序信息的多指标群决策问题,给出了一种决策分析方法。在本文中,首先对具有不确定偏好序信息的多指标群决策问题进行了描述;然后给出了将不确定偏好序转换为投票数的计算公式;进一步地,依据Bernardo方法的基本思想,根据每个专家给出的不确定偏好序信息,计算相应的投票数并构建群体投票矩阵,并基于群体投票矩阵构建0-1整数规划模型,通过求解模型可得到方案排序结果。最后,通过一个算例以及与已有方法的对比分析说明了本文给出的方法的可行性和有效性。