Using the Analytic Hierarchy Process as a Two-phase Integrated Decision Approach for Large Nominal Groups

When decision makers who comprise a large nominal group face an unstructured decision problem and no simultaneous interactive communications are available, problem identification and consensus building are difficult, if not impossible. Few tools are available to assist decision makers in this situation. The Analytic Hierarchy Process (AHP) has typically been used to evaluate a set of alternatives after a decision problem has been structured as a hierarchy with various levels of criteria above the alternatives. With a group of decision makers, AHP has been used to evaluate those alternatives either by consensus building or by combining judgments or priorities using the geometric mean to aggregate their preferences. In this paper, we extend the use of AHP to a situation involving a large nominal group of dispersed decision makers where the entire hierarchy is not defined at the outset. In particular, we use the AHP as an integrative approach to identify the priorities of the various criteria and then use those priorities to screen and consolidate a large set of potential alternatives. This results in considering a reduced set of alternatives that will be affected by the more important criteria. The consolidated set of alternatives is evaluated by each individual in the group using AHP, combined using the geometric mean, and the results are synthesized to obtain the overall priorities of the alternatives. The approach is demonstrated and evaluated in a case study to select an alunmi anniversary gift to the U.S. Coast Guard Academy with a large nominal group of decision-makers dispersed throughout the United States.     

A Distance-Based Collective Weak Ordering

A group decision-making approach can be seen as a two stage process. The first stage allows for multi-cirteria evaluation of the alternatives and the second aims at deriving a collective weak ordering from the partial orderings supplied by the members after the first stage. The problem of combining the weak orderings to form a collective ranking is investigated. An axiomatic structure relating to the concept of distance between binary relations is developed. An algorithm for deriving the collective weak ordering is proposed, based on the idea of ranking first the least dominated alternatives.     

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 Use of Ranking Veto Concept to Mitigate the Compensatory Effects of Additive Aggregation in Group Decisions on a Water Utility Automation Investment

The use of additive models for aggregating group decisions implies they have a compensatory effect in the process of aggregating all decision makers’ (DMs’) preferences. In this kind of model, the final result may produce some extremely undesirable alternatives for one or more DMs. Such alternatives may emerge with a higher ranking than desirable ones, thus generating conflicts and regrets. To overcome this problem the concept of ranking veto is introduced based on a reduction factor combined with the utility of the alternative in order to penalize conflicting alternatives and reduce disagreements in an additive model. A water utility problem was considered as a numerical application to illustrate the model. A decision group method based on MAUT, utility thresholds and a reduction factor is proposed to support group decision in selecting regions that will receive investments in automation over the next 4 years.     

A note on the relationships between some risk‐adjusted performance measures

Assuming portfolio returns are normally distributed, it is shown that both Sortino ratio (SR) and upside potential ratio (UPR) are monotonically increasing functions of the Sharpe ratio. As a result, all three risk‐adjusted performance measures provide identical ranking among investment alternatives. The effects of skewness and kurtosis are then evaluated within the Edgeworth‐Sargan density family. For the Sortino ratio, the above conclusion remains valid in the presence of negative skewness or excessive kurtosis. Similar results apply to the UPR with modifications. For all other cases, both SR and UPR provide exactly opposite ranking among investment alternatives to that suggested by the Sharpe ratio when the Sharpe ratio is large. Applications to futures hedging are discussed. Specifically, it is found that the Sharpe ratio may frequently lead to a smaller futures position than the other two ratios. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:483–495, 2002     

Development of a media selection model using the analytic network process

The authors develop and test a comprehensive model for media selection utilising the Analytic Network Process (ANP). ANP is a flexible and powerful multi-attribute decision aid developed by Saaty (1996) for solving complex decision-making problems. It is aimed at integrating different measures (both qualitative/intangible and quantitative/tangible) into a single overall score for ranking decision alternatives. In applying the ANP method, the authors specifically incorporate web/internet media advertising into their list of media alternatives, using many of the same standard media attributes that have typically been employed in comparing more traditional media. The result is a model that may be utilised by expert and/or novice media planners with equal effectiveness.     

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.     

Multicriteria Group Decision-Making Method Using Vector Similarity Measures For Trapezoidal Intuitionistic Fuzzy Numbers

Based on the extension of the Jaccard, Dice, and cosine similarity measures, three vector similarity measures between trapezoidal intuitionistic fuzzy numbers (TIFNs) are proposed in the vector space and are applied to the fuzzy multicriteria group decision-making problem, in which the criteria weights and the evaluated values in decision matrix are expressed by TIFNs. Through the weighted similarity measures between each alternative and the ideal alternative, the ranking order of all the alternatives can be determined and the best one(s) can be easily identified as well. A practical example of the developed approaches is given to select the investment alternatives. The decision results of different similarity measures demonstrate that the three similarity measures have better similarity identification. The illustrative example shows that the proposed methods are applicable.     

The Majority Rule with Arbitrators

The majority rule with arbitrators is the (relative) majority rule supplemented by the indifference-breaking rule according to which, in case of social indifference under the majority rule, the social preference coincides with the preference of the non-indifferent individual ranked higher in an exogenous ranking of the individuals. For the case of preferences over two alternatives, a characterization of this rule is suggested that relies on axioms of efficiency, inter-anonymity, intra-anonymity, parity, and reducibility. It is also provided a characterization of the set of rules consisting of the majority rule and the majority rule with arbitrators.     

模糊多属性决策法在配送中心选址中的应用

依据配送中心选址的主要因素,从基础设施、自然环境、社会效益、费用以及服务水平等几个方面建立多级评判指标体系,并提供两种模糊多属性决策法对备选配送中心进行优选和排序。最后一个算例方法客观反映实际情况,具有可行性。     

A Distance-Based Consensus Model with Flexible Choice of Rank-Position Weights

In this paper we propose a preference aggregation procedure for those cases in which the decision-makers express their preferences by means of a ranking of alternatives. Among the most applied methods for this purpose are those inspired by the Borda–Kendall rule, which attach to each alternative an aggregated value of the votes received in the different rank positions, and those based on distance measures between individual and collective preferences, which look for the solution that maximizes the consensus. The main idea here is to integrate these two approaches. Taking into account that the information about the values of weights or utilities assigned to each rank position is imprecise, we propose an evaluation of the alternatives using that vector of weights that minimizes the disagreement between DMs. In order to solve the problem, mixed-integer linear programming models are constructed. Two numerical examples are examined to illustrate the applicability of the proposed procedure.     

On the Use of Paired Comparisons to Construct Group Preference Scales for Decision Making

Polling opinion is a common group activity. Scaling tools can be used to provide a more precise presentation of opinions than traditional polling/voting. The interval scale of items constructed by scaling tools can aid participants in finding the current disposition of a group. We consider Thurstone’s law of comparative judgment as well as a weighted digraph ranking system for building group scales from pairwise comparisons. Assumptions for computing scales are reviewed together with issues and limitations of applying these scaling methods in groups. Results from a classic experiment and simulations by both methods are compared. We also made recommendations on choosing scaling method based on theoretic and practical consideration.     

Selecting Pesticides and Nonchemical Alternatives: Green Thumbs' Rules of Thumb Decision Tools

This study of a sample of home gardeners indicates that rules of thumb, or heuristics, are used to select between chemical pesticides and nonchemical alternatives. Such rules of thumb serve to simplify otherwise complicated choice decisions. Heuristics commonly used to choose pesticides include how safe, effective, efficacious, and economical they are, whereas for alternative products consumers more often take into account convenience, efficiency, competency, and handiness. Generally, in an overall ranking of 24 individual choice attributes, pesticies rank low on these attributes where alternatives rank high and vice versa. Gender, age, and years using pesticides are significantly correlated with pesticide selection.     

A Deviation-Based Approach to Intuitionistic Fuzzy Multiple Attribute Group Decision Making

The aim of this article is to investigate the approach to multiple attribute group decision making (MAGDM) with intuitionistic fuzzy information. We first introduce a deviation measure between two intuitionistic fuzzy numbers, and then utilize the intuitionistic fuzzy hybrid aggregation operator to aggregate all individual intuitionistic fuzzy decision matrices into a collective intuitionistic fuzzy decision matrix. Based on the deviation measure, we develop an optimization model by which a straightforward formula for deriving attribute weights can be obtained. Furthermore, based on the intuitionistic fuzzy weighted averaging operator and information theory, we utilize the score function and accuracy function to give an approach to ranking the given alternatives and then selecting the most desirable one(s). In addition, we extend the above results to MAGDM with interval-valued intuitionistic fuzzy information.     

A logistic regression-based pairwise comparison method to aggregate preferences

In a group decision making process, several individuals or a committee have the responsibility to choose the best alternative from a set. The problem addressed in this paper is how to aggregate personal preferences to arrive at an optimal group decision. New technologies allow individuals that may seldom or never meet to make group decisions. This paper proposes a methodology to obtain the group preference ordering in two steps. Firstly, each individual studies the problem isolated, and then, in a possibly virtual meeting, the group must agree on the preferences on some pairs of alternatives. Then, the group criterion is achieved by using a logistic regression model within the pairwise comparison framework proposed here. Properties of the procedure are studied and two illustrative examples are presented.     

An Extended PROMETHE II Multi-Criteria Group Decision Making Technique Based on Intuitionistic Fuzzy Logic for Sustainable Energy Planning

The implementations of Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE) category to complex multi-criteria group decision making (MCGDM) scenarios have been included in thousands areas. Outranking methods such as PROMETHEE II are also greatly employed in energy planning application. In MCGDM methods if decision makers (DMs) are not able to treat precise data in order to define their preferences, the intuitionistic fuzzy set (IFS) theory enables them. IFS attributes are connected with the degree of membership and non-membership, and can be used to draw uncertainty in group decision-making situations. In this paper, a new version of the PROMETHEE II method is proposed, aiming at solving MCGDM problems. Linguistic variables are expressed in the membership function and non-membership function of IFS which are used to assess the weights of all criteria and the ratings of each alternative with respect to each criteria. Conditional normalized Euclidean distance measure is adopted to measure deviations between alternatives on intuitionistic fuzzy set. Then, a ranking algorithm is applied to indicate the order of superiority of alternatives. Finally, a practical example is given to an application of sustainable energy planning to verify our proposed method. Additionally, a comparative analysis is done among the proposed PROMETHEE II method and the intuitionistic fuzzy technique for order preference by similarity to ideal solution (IF-TOPSIS) method and elimination and choice translating reality method (IF-ELECTRE).     

Social Planner’s Solution for the Caspian Sea Conflict

This paper evaluates the proposed alternatives for sharing the Caspian Sea from the social planner’s or systems-level perspective with respect to the stakeholders’ utilities from the oil and natural gas resources of the sea. Different multi-criteria decision-making methods, namely dominance, maximin, lexicography, simple additive weighting, and TOPSIS are applied to determine the social planner’s ranking of these alternatives. Results suggest the Condominium governance regime as the most promising division method. Bankruptcy rules and cooperative game theory methods can be considered as the other socially optimal resolutions to the conflict over sharing the Caspian Sea energy resources among its five littoral countries. Consideration of these methods in negotiations may help with resolving the existing deadlock, which has been in place for two decades.     

Ordered Weighted Disagreement Functions

In this paper a preference aggregation procedure is proposed for those cases in which decision-makers express their preferences by means of a ranking of alternatives. Among the most commonly applied methods for this purpose are those based on distance measures between individual and collective preferences, which look for the solution that minimizes the disagreement across decision-makers. Some models based on the minimization of the distance between rankings include weights to adjust the relative importance of the agents in the final decision, although in those cases, the weights are related with an a priori evaluation of the individuals and not with the behaviour of the agents in the group decision making process. In the model proposed here, a weighted disagreement function whose emphasis is on the ordered position of the individuals’ disagreement values is developed. In order to solve the problem, a mixed-integer linear programming model is constructed.     

A Multicriteria Selection System Based on Player Performance: Case Study—The Spanish ACB Basketball League

In this paper, we describe an approach to rank sport players based on their efficiency. Although is extremely useful to analyze the performance of team games there is no unanimity on the use of a single index to perform such a ranking. We propose a method to summarize the huge amount of information collected at different aspects of a sport team which is almost daily publicly available. The tool will allow agents involved in a player’s negotiation to show the strengths (and weaknesses) of the player with respect to other players. The approach is based on applying a multicriteria outranking methodology using as alternatives the potential players and as criteria different efficiency indices. A novel automatic parameter tuning approach is detailed that will allow coaches and sports managers to design templates and sports strategies that improve the efficiency of their teams. We report the results performed over the available information on the ACB Basketball League, and we show how it can be easily implemented and interpreted in practice by decision-makers non familiar with the mathematical side of the methodology.     

Benchmarking Indian banks using DEA in post-reform period: a progressive time-weighted mean approach

The ranking of banks based on single period data could mislead the management as well as customers, as many one-time influences may wrongly portray banks with lasting strategy. This study uses data envelopment analysis (DEA) models to rank Indian banks based on their performance over 13 years of post-reform period by using the progressive time-weighted means of variable benchmarking super-efficiency scores. Furthermore, the relative performances of these banks are evaluated against the ‘best practice’ bank by using the fixed benchmarking DEA model. The results show no statistical evidence of dominance of either public sector banks over private sector banks or vice-versa when their efficiencies are evaluated with the common frontier. However, the variations in efficiency across the public sector banks are comparatively less as compared with private sector banks. The efficiency based on the ownership frontier further supports our argument that the public sector banks are relatively more consistent in their performance over the years as well as across the banks. The results show a huge difference in the ranking of some of the banks when the usual method of ranking is compared with progressive time-weighted mean approach, where the performance of the banks over the years is taken into account.