Group Aggregation Techniques for Analytic Hierarchy Process and Analytic Network Process: A Comparative Analysis

The analytic hierarchy process (AHP) and the analytic network process are important multiple criteria decision making methods for supporting complex, discrete strategic management decision problems. In order to exploit a broader information basis as well as to achieve a sufficient degree of objectivity strategic decision settings are mostly embedded into a multi-personal decision context to which different individuals with expert status contribute. Owing to the fact that there is a vast number of different methods and further internal possibilities (derivation of means) to aggregate the individual expert preferences to a group consensus, the first aim of this paper is to present a comprehensive literature review on various aggregation possibilities. The second aim is the conduction of a transparent comparative analysis of selected approaches and methods (geometric/arithmetic aggregation of individual judgments, geometric/arithmetic aggregation of individual priorities, geometric/arithmetic loss function approach and Group AHP model). Therefore, we use four different evaluation scenarios and point out under which assumptions which solution is suitable. Starting from these results, the aggregation techniques adequate to a specific decision context are provided.     

Group Decision Making with Dispersion in the Analytic Hierarchy Process

With group judgments in the context of the Analytic Hierarchy Process (AHP) one would hope for broad consensus among the decision makers. However, in practice this will not always be the case, and significant dispersion may exist among the judgments. Too much dispersion violates the principle of Pareto Optimality at the comparison level and/or matrix level, and if this happens, then the group may be homogenous in some comparisons and heterogeneous in others. The question then arises as to what would be an appropriate aggregation scheme when a consensus cannot be reached and the decision makers are either unwilling or unable to revise their judgments. In particular, the traditional aggregation via the geometric mean has been shown to be inappropriate in such situations. In this paper, we propose a new method for aggregating judgments when the raw geometric mean cannot be used. Our work is motivated by a supply chain problem of managing spare parts in the nuclear power generation sector and can be applied whenever the AHP is used with judgments from multiple decision makers. The method makes use of principal components analysis (PCA) to combine the judgments into one aggregated value for each pairwise comparison. We show that this approach is equivalent to using a weighted geometric mean with the weights obtained from the PCA.     

The Secretary Problem Revisited - The Group Decision-Making Perspective

We consider a decision situation where there is an initial set of alternatives that may be augmented, a variant of the problem known in the literature as the "secretary problem". We focus the discussion on the special case of group decision-making, where a group or committee is charged with the responsibility of negotiating the decision. We investigate situations of explicitly stated (multiple) criteria and the simpler situation of no such stated criteria. The former case includes the congenial, the mixed, and the uncongenial cases, where the individuals agree on the direction of all, some, or none of the criteria, respectively. We offer a framework within which a group of individuals can be supported in such a decision process. In the case of explicit criteria, we provide the decision-makers with probability information of the likelihood of finding more preferred alternatives provided the initial set of alternatives is expanded. The framework is tested using a simulated real-world choice situation.     

Analysis of multiple criteria decision support systems for cooperative groups

This article reviews research on multiple criteria decision support systems for cooperative groups. The systems included in this survey integrate concepts from group decision theory, multiple criteria decision methodology, and decision support system technology. Three dimensions are considered in the analysis of existing research: the multiple criteria decision technique used to generate decision alternatives or to choose from a given set; the method used to facilitate individual compromise and group consensus; and the application category, if any.     

A Study on Aggregation of TOPSIS Ideal Solutions for Group Decision-Making

The technique for order preference by similarity to ideal solution (TOPSIS) has become a popular multi-criteria decision making (MCDM) technique, since it has a comprehensible theoretical structure and is able to provide an exact model for decision making. For the use of TOPSIS in group decisions, the common approaches in aggregating individual decision makers’ judgments are the geometric and the arithmetic mean methods, although these are too intuitive and do not consider either preference levels or preference priorities among alternatives for individual decision makers. In this paper, a TOPSIS group decision aggregation model is proposed in which the construction consists of three stages: (1) The weight differences are calculated first as the degrees of preferences among different alternatives for each decision maker; (2) The alternative priorities are then derived, and the highest one can be denoted as the degree to which a decision maker wants his most favorite alternative to be chosen; (3) The group ideal solutions approach in TOPSIS is used for the aggregation of similarities obtained from different decision makers. A comparative analysis is performed, and the proposed aggregation model seems to be more satisfactory than the traditional aggregation model for solving compromise-oriented decision problems.     

The Role of the DS/AHP in Identifying Inter-Group Alliances and Majority Rule Within Group Decision Making

DS/AHP is a nascent method of multi-criteria decision-making, based on the Dempster-Shafer theory of evidence and indirectly the Analytic Hierarchy Process. It is concerned with the identification of the levels of preference that decision makers have towards certain decision alternatives (DAs), through preference judgements made over a number of different criteria. The working result from a DS/AHP analysis is the body of evidence (BOE), which includes a series of mass values that represent the exact beliefs in the best DA(s) existing within certain subsets of DAs. This paper considers the role of DS/AHP as an aid to group decision-making, through the utilisation of a distance measure (between BOEs). Here, the distance measure enables the identification of the members of the decision-making group who are in most agreement, with respect to the judgements they have individually made. The utilisation of a single linkage dendrite approach to clustering elucidates an appropriate order to the aggregation of the judgements of the group members. This develops the DS/AHP method as a tool to identify inter-group alliances, as well as introduce a ‘majority rule’ approach to decision-making through consensus building.     

A Calibrated Group Decision Process

In practice most organisational decisions are made by groups that bring into the problem multiple perspectives, both complementary and contradictory. When having a group of decision makers, usually individuals’ preferences are either led to consensus or are aggregated with the use of some function like the median, the arithmetic or geometric mean. We focus in the second case, where individual’s preferences need to be aggregated. Our approach is based on the fact that when two decision makers are asked to give their preference between a pair of criteria using a specific scale, it is possible that they will give slightly different answers, even when they actually have the same opinion. This difference will not affect the case of a single decision maker, as it will be consistent throughout the whole process. However, it can affect a group decision when the values will be used as an input for the aggregation function. A novel approach is presented that enhances group decision making through a group calibration process. The proposed process adjusts individuals’ preferences based on their answers on a set of standardized questions prior to the aggregation phase. The method focuses The whole concept is applied to the group analytical network process method and it is illustrated through a telecommunications project case. The decision under examination concerns the selection of the right place for deploying a new telecom service of a multinational-based telecommunications company where a group of geographically dispersed decision makers form an ad-hoc virtual team in order to select the location for a new technical support centre.     

AHP-Group Decision Making: A Bayesian Approach Based on Mixtures for Group Pattern Identification

This paper proposes a Bayesian estimation procedure to determine the priorities of the Analytic Hierarchy Process (AHP) in group decision making when there are a large number of actors and a prior consensus among them is not required. Using a hierarchical Bayesian approach based on mixtures to describe the prior distribution of the priorities in the multiplicative model traditionally used in the stochastic AHP, this methodology allows us to identify homogeneous groups of actors with different patterns of behaviour for the rankings of priorities. The proposed procedure consists of a two-step estimation algorithm: the first step carries out a global exploration of the model space by using birth and death processes, the second concerns a local exploration by means of Gibbs sampling. The methodology has been illustrated by the analysis of a case study adapted from a real experiment on e-democracy developed for the City Council of Zaragoza (Spain). Partially funded under the research project Electronic Government. Internet-based Complex Decision Making: e-democracy and e-cognocracy (Ref. PM2004-052) approved by the Regional Government of Aragon (Spain) as part of the multi-disciplinary projects programme.     

Evaluating a Framework for Multi-Stakeholder Decision Support in Water Resources Management

In this paper we describe a framework for multicriteria modeling and support of multi-stakeholder decision processes. We report on its testing in the development of a new water level management policy for a regulated lake-river system in Finland. In the framework the stakeholders are involved in the decision process from the problem structuring stage to the group consensus seeking stage followed by a stage of seeking public acceptance for the policy. The framework aims at creating an evolutionary learning process. In this paper we also focus on the use of a new interactive method for finding and identifying Pareto-optimal alternatives. Role playing experiments with students are used to test the practical applicability of a negotiation support procedure called the method of improving directions. We also describe the preference programming approach for the aggregation of the stakeholder opinions in the final evaluation of alternatives and consensus seeking.     

Multiple Criteria Decision Making Models in Group Decision Support

Use of multiple criteria decision making (MCDM) models to aid the group decision process was tested. Two multiple criteria group decision support systems (MCGDSS) were studied, one using the AHP/Tchebycheff method of Iz and the other using Kersten's NEGO system. These systems were compared with a commercial GDSS, VisionQuest. VisionQuest does not include multiple criteria tools. To make the study comparable, VisionQuest was augmented with an ad hoc linear programming model that could generate solutions with specified characteristics requested by the using group. The three systems were compared on the dimensions of solution quality and decision support effectiveness.One of the hypotheses was that MCDM models would force participants to examine criteria, preferences, and aspirations more thoroughly, thus leading to decisions of better quality. Subjects using the MCGDSSs were expected to have higher mean quality and effectiveness values. However, the quality and effectiveness values of the VisionQuest/ad hoc system were found to be better on the dimension of effectiveness. Explanations for this result are included in the paper.Another hypothesis was that the AHP/Tchebycheff method of Iz, a value-oriented system, would yield more effective group support than the goal-oriented NEGO system. However, the NEGO system was found to yield solutions with better quality measures than the solutions obtained with the AHP/Tchebycheff system.Observation of the groups using the MCDM systems indicate that both the AHP/Tchebycheff and NEGO methods can be revised to enhance their effectiveness. The primary difficulty encountered with the AHP/Tchebycheff method was in the large number of pairwise comparisons required by AHP. The NEGO method can be enhanced by including specification of desired attainment levels in the first stage of the method. Both MCDM techniques have potential to benefit group decision support by giving using groups a means to design better solutions.     

利益相关者财务治理的一致性聚类分析

本文利用聚类分析方法研究利益相关者参与企业财务治理的决策机制,以融资决策为例,将内部融资、债务融资、股权融资三种不同的融资类型作为决策者判断的方案,不同类型融资的具体数值作为三角模糊数,考虑决策者的权重对决策者一致度计算的影响,计算不同决策者之间的一致度距离,进行决策者聚类,依据聚类的结果,计算一致性相同的决策者集合的最终方案集,最后通过实例演示了上述的计算过程。     

Aggregation of Individual Preference Structures in Ahp-Group Decision Making

This paper presents a new procedure, to which we have given the name Aggregation of Individual Preference Structures (AIPS), whose objective is to deal with multiactor decision making when using Analytic Hierarchy Process (AHP) as the methodological support. This procedure incorporates ideas similar to Borda count methods and transfers to the case of preference structures the principle of aggregation employed in the two approaches traditionally followed in AHP-group decision making (aggregation of individual judgments and aggregation of individual priorities). The new aggregation method allows us to capture: (i) the richness of uncertainty inherent to human beings; (ii) the vision of each decision maker within the context of the problem; (iii) the interdependencies between the alternatives being compared and (iv) the intensities of the preferences that each decision maker gives to these interdependencies. From the preference structure distribution associated to each decision maker, this new approach (AIPS) provides the holistic importance of each alternative and ranking, as well as the most representative preference structure distribution for the group. The knowledge derived from these could be employed as an initial step in the search for consensus, which characterises the negotiation processes followed by the actors involved in the resolution of decisional problems. An earlier version of this paper was presented at the GDN2005 Conference held at Vienna. The work has been partially funded under Research Projects “Electronic Government. Internet-based Complex Decision Making: e-democracy and e-cognocracy” (Ref. PM2004-052) and “Internet-based Complex Decision Making. Decisional Tools for e-cognocracy” (Ref. TSI2005-02511).     

An Integrated Group Decision-Making Method Dealing with Fuzzy Preferences for Alternatives and Individual Judgments for Selection Criteria

Organizations often require decisions to be made by a group, and decision makers often have fuzzy preferences for alternatives and individual judgments when attempting to reach an optimal solution. In order to deal with the fuzziness of preference of decision makers, this paper proposes an integrated fuzzy group decision-making method. This method allows group members to express fuzzy preferences for alternatives and individual judgments for solution selection criteria. It also allowed for the weighting of group members. The method then aggregates these elements into a compromise group decision which is the most acceptable for the group as a whole. This method has been implemented and tested. An example is presented to illustrate the method.     

伦理问题、道德强度与供应商伦理管理

供应商的伦理问题涉及人权、环境、多样化、慈善与安全等方面,不同伦理问题的道德强度不同,企业决策者对供应商不同伦理问题的重视程度也不同。运用层次分析法,给出道德强度的结果严重度、社会共识、结果发生可能性、时间急迫性、接近性、结果集中度等六个维度的相对权重,根据道德强度各维度的相对重要性,对供应商不同的伦理权重进行排序。     

Multiple‐criteria approach to ranking medical tourism destinations

The characteristics of the medical tourism industry are described. Multiple criteria are used to evaluate several popular medical tourism destinations. The analytic hierarchy process (AHP) is shown to be the appropriate methodology for evaluating and ranking medical tourism destinations because it can incorporate input from multiple decision makers as well as handle both tangible and intangible criteria. The ranking of medical tourism destinations will enable administrators at companies that specialize in arranging the logistics of obtaining medical care at foreign facilities to better advise patients regarding their choice of medical tourism destinations. This will result in patients who are more satisfied with their choice of a foreign medical facility. © 2011 Wiley Periodicals, Inc.     

Fair and Fast Convergence on Islands of Agreement in Multicriteria Group Decision Making by Logical Navigation

Reasoning on multiple criteria is a key issue in group decision to take into account the multidimensional nature of real-world decision-making problems. In order to reduce the induced information overload, in multicriteria decision analysis, criteria are in general aggregated, in many cases by a simple discriminant function of the form of a weighted sum. It requires to, a priori and completely, elicit preferences of decision makers. That can be quite arbitrary. In everyday life, to reduce information overload people often use a heuristic, called “Take-the-best”: they take criteria in a predefined order, the first criterion which discriminates the alternatives at stake is used to make the decision. Although useful, the heuristic can be biased. This article proposes the Logical Multicriteria Sort process to support multicriteria sorting within islands of agreement. It therefore does not require a complete and consistent a priori set of preferences, but rather supports groups to quickly identify the criteria for which an agreement exists. The process can be seen as a generalization of Take-the-best. It also proposes to consider one criterion at a time but once a criterion has been found discriminating it is recorded, the process is iterated and relevant criteria are logically combined. Hence, the biases of Take-the-best are reduced. The process is supported by a GDSS, based on Logical Information Systems, which gives instantaneous feedbacks of each small decision and keeps tracks of all of the decisions taken so far. The process is incremental, each step involves low information load. It guarantees some fairness because all considered alternatives are systematically analyzed along the selected criteria. A successful case study is reported.     

Voting Paradoxes and MCDM

Many, if not most, problems in group decision making can be translated into MCDM problems by substituting criteria for voters. Yet, there has been very little discussion about the implications of various types of voting paradoxes to MCDM. The classic voting paradoxes, viz. Borda's and Condorcet's, have obvious implications for certain MCDM situations. The latter implies that the notion of the best alternative, given a set of criteria and information about the ordinal ranking of the alternatives on those criteria, can be essentially arbitrary. The former, in turn, demonstrates a particularly clear case of conflict between reasonable intuitions. Completely unexplored are implications of compound majority paradoxes to MCDM. The paper deals with Ostrogorski's and Anscombe's paradoxes which result from non-bisymmetry and non-associativity of the majority relation. Moreover, we shall discuss the implications of paradox of multiple elections which is a situation where the result of multiple-item election may be a policy alternative that nobody voted for.     

Developing a Group Decision Support System for Advertising Media Evaluation: A Case in the Middle East

The importance of advertising media evaluation as a multifaceted problem is well known by both academics and practitioners. Although previous studies tried to optimize media evaluation, there still are some gaps and problems to address, particularly in areas of flexibility of models/frameworks, decision making quality, tension management, and agility of the evaluation process. Most of previous studies are based on inflexible models/frameworks that have limitations on number of criteria/alternatives they can consider and type of data they can process. A great volume of the work used arbitrary decision making; arbitrary decision making regarding criteria and media importance may reduce effectiveness of advertising campaigns. Furthermore, the academic literature offers little guidance on group decision aggregation, and tension management during decision making is neglected. Media evaluation is a time taking process and any acceleration will reduce pre-campaign costs. The main aim of this paper is to illustrate how a group decision support system (GDSS) can assist media planners to overcome mentioned problems more systematically. For this purpose, we developed a GDSS that is an integration of three well-known multi-criteria decision making techniques. With a real world case study, we illustrate the performance of the proposed GDSS. Results of our quantitative assessments indicate that the GDSS is flexible, allows decision makers to express their opinions, reduces tension among decision makers, and saves time.     

Characterization of the Row Geometric Mean Ranking with a Group Consensus Axiom

An axiomatic approach is applied to the problem of extracting a ranking of the alternatives from a pairwise comparison ratio matrix. The ordering induced by row geometric mean method is proved to be uniquely determined by three independent axioms, anonymity (independence of the labelling of alternatives), responsiveness (a kind of monotonicity property) and aggregation invariance, which requires the preservation of group consensus, that is, the pairwise ranking between two alternatives should remain unchanged if unanimous individual preferences are combined by geometric mean.