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).     

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.     

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).     

TOPSIS Based Approach to Scoring Negotiating Offers in Negotiation Support Systems

In this paper we analyze the possibility of applying the technique for order preferences by similarity to ideal solution (TOPSIS) to building the scoring system for negotiating offers. TOPSIS is a multiple criteria decision making method that is based on measuring distances between alternatives under consideration and two bipolar reference alternatives, a positive and negative ideal. Thus the criteria used for the evaluation of alternatives should be described using strong scales. However, in the negotiation, the issues are very often described qualitatively, which results in ordinal or even nominal variables that must be taken into consideration in offers’ evaluation process. What is more, TOPSIS may be applied to solving the discrete decision problems while the negotiation space may be defined by the means of continuous variables too. In this paper we try to modify the TOPSIS algorithm to make it applicable to negotiation support and, moreover, discuss the following methodological issues: using TOPSIS for a negotiation problem with continuous negotiation space; selecting the distance measure for adequate representation of negotiator’s preferences and measuring distances for qualitative issues. Finally, we propose a simple additional mechanism that allows for building the TOPSIS-based scoring system for negotiating offers and does not involve negotiators in time consuming and tiresome preference elicitation process. This mechanism requires from negotiators to construct examples of offers that represent some categories of quality and then by using a goal programming approach it infers all the parameters required by the TOPSIS algorithm. We also show a simple prototype software tool that applies the TOPSIS modified algorithm and may be used in electronic negotiation support.     

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.     

Deriving Weights from Interval Multiplicative Preference Relations in Group Decision Making

In this article, we investigate group decision making problems with interval multiplicative preference relations (including complete interval multiplicative preference relations and incomplete interval multiplicative preference relations). On the basis of the number of judgments and the consistency degree of each interval multiplicative preference relation, we first give a combined weighting method to derive the weights of decision makers. Then, we establish two linear programming models to derive the weight intervals of alternatives from all individual consistent interval multiplicative preference relations and utilize the continuous ordered weighted averaging operator or the continuous ordered weighted geometric operator to aggregate all the values in each weight interval. In addition, we establish a more general model to check the consistency of all individual interval multiplicative preference relations. In the cases where the optimal objective value of the model is not zero, we can get the optimal weights of alternatives directly, and then utilize these optimal weights and the optimal deviation values derived from the model to construct consistent interval multiplicative preference relations. Furthermore, we discuss some special cases of the established models and illustrate our models with a practical example.     

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.     

A Hierarchical Clustering Approach Based on Three-Dimensional Gray Relational Analysis for Clustering a Large Group of Decision Makers with Double Information

Two types of information, collectively referred to as double information, are usually required in management decision-making. The first is preference information expressed in a judgment matrix. The second is reference information expressed in a multi-attribute decision matrix. In this paper, we investigate large-scale group clustering problems with double information in group decision-making. We first establish a novel three-dimensional gray correlation degree index, which integrates the alternative decision-making vector, index vector and alternative preference vector, to fully excavate the correlation between decision makers with double information. We then develop a new clustering procedure combining three-dimensional gray relational analysis and the concept of hierarchical clustering. Moreover, a model for determining clustering centers is established on the basis of the maximum gray correlation degree within each cluster and minimum gray correlation degree among clusters. A heuristic algorithm for the model to identify the core decision maker in each cluster is proposed. Finally, we illustrate the applications of the developed procedures with a practical case. The rationality of the proposed method is demonstrated by comparing results with results obtained using other methods, including the traditional gray clustering method and hierarchical clustering method with single information; i.e., preference information or reference information.     

Multi-criteria Group Decision-Making Method Based on Intuitionistic Interval Fuzzy Information

For problems in multi-criteria group decision-making (MCGDM), this paper defines intuitionistic interval numbers, and the operational laws and comparison method of it. Some intuitionistic interval information aggregation operators are proposed, such as intuitionistic interval weighted arithmetic averaging operator, intuitionistic interval weighted geometric averaging operator, intuitionistic interval ordered weighted averaging operator, intuitionistic interval heavy averaging operator and intuitionistic interval aggregating operator. Then, based on intuitionistic interval fuzzy information, a method is developed to handle the problems in MCGDM. In this method, by applying the knowledge level of the experts to the decision making problem, the model of maximizing comprehensive membership coefficient is constructed to determine the weights of decision makers. By calculating the distances to the ideal and negative ideal solutions, the comprehensive attribute values and the rank of the alternatives can be obtained. Finally, an example is provided to demonstrate the feasibility and effectiveness of the proposed method.     

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.     

A Mixed-Data Evaluation in Group TOPSIS with Differentiated Decision Power

This main objective of this paper is to provide decision support for mixed data in group Technique for Order Preference by Similarity to Idea Solution (TOPSIS) with differentiated decision power. We use a signum function to compare the ordinal performance of alternatives on any qualitative criterion, or the partial information provided by decision makers. The proposed process for ordinal information is uniformly coherent with the traditional TOPSIS steps, preserving the characteristic of distance-based utilities. Ordinal weights are also considered herein, and the decision power of the group members is formulated by their weights under an agreement in the group. Two examples demonstrate that the proposed approach has some benefits and achieves robustness with two types of sensitivity analyses. Some discussions and their limitations to the approach are also provided.     

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.     

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.     

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.     

Type-2 TOPSIS: A Group Decision Problem When Ideal Values are not Extreme Endpoints

In the traditional TOPSIS, the ideal solutions are assumed to be located at the endpoints of the data interval. However, not all performance attributes possess ideal values at the endpoints. We termed performance attributes that have ideal values at extreme points as Type-1 attributes. Type-2 attributes however possess ideal values somewhere within the data interval instead of being at the extreme end points. This provides a preference ranking problem when all attributes are computed and assumed to be of the Type-1 nature. To overcome this issue, we propose a new Fuzzy DEA method for computing the ideal values and distance function of Type-2 attributes in a TOPSIS methodology. Our method allows Type-1 and Type-2 attributes to be included in an evaluation system without compromising the ranking quality. The efficacy of the proposed model is illustrated with a vendor evaluation case for a high-tech investment decision making exercise. A comparison analysis with the traditional TOPSIS is also presented.     

Systems analysis: Aid to decision making: A method of investigation

Decision makers today face constraints that did not exist in the early part of this century-constraints related to labor, consumerism, and ecology, for example. The decision making process is also complicated by the number of alternatives available to attain a certain objective. This article describes the systems analysis approach to decision making and explains why it is needed. The approach involves nine basic steps and, finally, identification of the best solution by considering the facts, assumptions, and uncertainties for the problem. Systems analysis is not a panacea for the decision maker; it is a method of investigating, not solving.     

Reaching informed agreement in multispecialist cooperation

Very often, complex decisions must be made by a group of specialists rather than a single decision maker. To make an effective decision, the combination of the group's expertise must be brought to bear on the situation. Fusing expertise where individuals have very detailed knowledge in their own areas and much weaker understanding of others is characterized by many difficulties: (1) agents cannot communicate their expertise in an intelligible way to nonexperts because of differences in vocabulary and conceptual content; (2) the process allows for incorrect inferences; and (3) no one knows what anyone else needs to know. This impasse cannot be broken until shared mental models are developed to provide a level of agreement in evaluating alternatives needed to focus the activity of the group. This article presents a model of decision making by teams of specialists in which agents' evaluations confound expert and naive inferences in judging alternatives. A partitioning of agent knowledge into expert and naive models is proposed. The naive portion of agents' models provides both a common language and the inferential skeleton needed for the development of shared models. Communications are categorized into types of evaluation or justification based on their form and the entities they involve within the agent models. A process of model refinement is outlined, linking communications among agents to modifications of the naive/ shared portions of their models. The process of cooperative problem solving by a team of specialists is characterized as a search among alternatives in which model refinement continually alters the agents' evaluations, leading to progressively greater accuracy and more precisely directed search. The model is intended as a research tool for investigating multiagent problem solving among people and machines.     

Fuzzy Group Decision Making for the Selection of Facility Location

In this paper, fuzzy group decision making based on extension of TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method which was proposed by Chen (Fuzzy Sets Syst, 114:1–9, 2000) is adopted for facility location selection. In this method, the ratings of various alternatives versus various subjective criteria and the weights of all criteria are assessed in linguistic variables represented by fuzzy numbers. By fuzzy numbers, it has been tried to resolve the ambiguity of concepts that are associated with human being’s judgments. To determine the order of the alternatives, closeness coefficient is defined by calculating the distances to the fuzzy positive ideal solution (FPIS) and fuzzy negative ideal solution (FNIS). In Chen’s approach, the distance between two fuzzy numbers is calculated with vertex method. But in this study, different distance measurement methods are used and the results are compared. Finally the proposed method has been applied to a facility location selection problem of a textile company in Turkey.     

A framework for interactive multiple criteria group decision support

An interactive framework is developed for multiple criteria group decision support. Decision makers are asked to specify aspiration and reservation levels to establish a preferred range for the value of each objective for each decision maker. Group and individual solutions are generated as a function of these levels. Decision makers are asked to react to current solutions by revising their aspiration and reservation levels and additional solutions are generated. The framework is both simpler and more flexible than previous approaches.     

A Note on Linguistic Hybrid Arithmetic Averaging Operator in Multiple Attribute Group Decision Making with Linguistic Information

In this paper, we propose a linguistic hybrid arithmetic averaging (LHAA) operator, which is based on linguistic weighted arithmetic averaging (LWAA) operator and extended ordered weighted averaging (EOWA) operator, and study some desirable properties of the LHAA operator. The LHAA operator can not only reflect the importance degrees of both the given argument and its ordered position, but also relieve the influence of unfair arguments on the decision results by weighting these arguments with small values. Based on the LWAA and LHAA operators, we develop a practical approach to multiple attribute group decision making under linguistic environment. The approach first aggregates the individual linguistic preference values into a collective linguistic preference value for each alternative by using the LWAA and LHAA operators (it is worth pointing out that the aggregation process does not produce any loss of linguistic information), and then orders the collective linguistic preference values to obtain the best alternative(s). Finally, an illustrative example is also given to verify the approach and to demonstrate its feasibility and practicality.