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

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Abstract

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.

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References

  • Ali, I., W. D. Cook, and M. Kress. (1986). “Ordinal Ranking and Intensity or Preference: A Linear Programming Approach,” Management Science 32, 1642–1647.

    Google Scholar 

  • Armacost, R. L., J. C. Hosseini, and J. Pet-Edwards. (1999). “Using the Analytic Hierarchy Process as a Two-phase Integrated Decision Approach for Large Nominal Groups,” Group Decision and Negotiation 8, 535–555.

    Google Scholar 

  • Arrow, K. J. (1950). “Difficulty in the Concept of Social Welfare,” Journal of Political Economy 58, 328–346.

    Google Scholar 

  • Arrow, K. J. (1963). Social Choice and Individual Values, 2nd ed., Yale University press, New Haven – London.

  • Bana, E., C. A. Costa, T. J. Stewart, and J.-C. Vansnick. (1997). “Multicriteria Decision Analysis: Some Thoughts Based on the Tutorial and Discussion Sessions of the ESIGMA Meetings,” European Journal of Operational Research 99, 28–37.

    Google Scholar 

  • Bard, J. F. (1992). “A Comparison of the Analytic Hierarchy Process with Multiattribute Utility Theory: A Case Study,” IIE Transactions 24, 111–121.

    Google Scholar 

  • Bauer, M. (1997). “Approximation Algorithms and Decision Making in the Dempster-Shafer Theory of Evidence – an Empirical Study,” International Journal of Approximate Reasoning 17(2-3), 217–237.

    Google Scholar 

  • Bell, D. E., H. Raiffa, and A. Tversky. (1988). Decision Making: Descriptive, Normative and Prescriptive Interactions, Cambridge University Press, Cambridge.

  • Belton, V. and J. Pictet. (1997). “A Framework for Group Decision Using a MCDA Model: Sharing, Aggregating or Comparing Individual Information?,” Journal of Decision Systems 6(3), 283–303.

    Google Scholar 

  • Ben Khélifa, S. and J.-M. Martel. (2001). “A Distance-Based Collective Weak Ordering,” Group Decision and Negotiation 10, 317–329.

  • Beynon, M. J., B. Curry, and P. H. Morgan. (2000). “The Dempster-Shafer Theory of Evidence: An Alternative Approach to Multicriteria Decision Modelling,” OMEGA 28(1), 37–50.

    Google Scholar 

  • Beynon, M. (2002). “DS/AHP method: A Mathematical Analysis, Including an Understanding of Uncertainty,” European Journal of Operational Research 140(1), 149–165.

    Google Scholar 

  • Beynon, M. J. (2005a). “Understanding Local Ignorance and Non-Specificity in the DS/AHP Method of Multi-Criteria Decision Making,” European Journal of Operational Research 163, 403–417.

    Google Scholar 

  • Beynon, M. J. (2005b). “A Method of Aggregation in DS/AHP for Group Decision-Making with the Non-Equivalent Importance of Individuals in the Group,” Computes & Operations Research 32, 1881–1896.

  • Bonissone, P. P. and R. M. Tong. (1985). “Editorial: Reasoning with Uncertainty in Expert Systems,” International Journal of Man Machine Studies 22, 241–250.

    Google Scholar 

  • Bryson, N. (1996). “Group Decision-Making and the Analytic Hierarchy Process: Exploring the Consensus-Relevant Information Content,” Computers & Operations Research 23(1), 27–35.

    Google Scholar 

  • Bryson, N. and A. Joseph. (1999). “Generating Consensus Priority Point Vectors: A Logarithmic Goal Programming Approach,” Computers & Operations Research 26, 637–643.

  • Carlsson, C., D. Ehrenberg, P. Eklund, M. Fedrizzi, P. Gustafsson, P. Lindholm, G. Merkuryeva, T. Riisanen, and A. G. S. Ventre. (1992). “Consensus in Distributed Soft Environments,” European Journal of Operational Research 12, 391–404.

    Google Scholar 

  • Cartwright, D. and A. Zander. (eds) (1968). Group Dynamics (3rd Ed.) Row, Peterson, Evanston, IL.

  • Cook, W. D. and M. Kress. (1985). “Ordinal Ranking with Intensity of Preference,” Management Science 31, 26–32.

    Google Scholar 

  • Crott, H. W. and J. A. Zuber. (1983). “Biases in Group Decision Making, Decision Making Under Uncertainty,” in R. W. Scholz ed., Amsterdam: North-Holland, pp. 229–252.

  • Davis, J. H., W. T. Au, L. Hulbert, X. P. Chen, C. Parks, and P. Zarnoth. (1997) “Effects of Group Size and Procedural Influence on Consensual Judgements of Quantity: The example of Damage Awards and Mock Civil Juries,” Journal of Personality and Social Psychology 73, 703–718.

    Google Scholar 

  • Dempster, A. P. (1968). “A Generalization of Bayesian Inference (with Discussion),” J Roy Stat Soc Series B 30(2), 205–247.

  • DeSanctis, G. and R. B. Gallupe. (1987). “A Foundation for the Study of Group Decision Support Systems,” Management Science 33(5), 589–609.

    Google Scholar 

  • Fixsen, D. and R. P. S. Mahler. (1997). “The Modified Dempster-Shafer Approach to Classification,” IEEE Transaction on Systems, Man and Cybernetics – part A 27(1), 96–104.

  • Forman E. and K. Peniwati. (1998). “Aggregating Individual Judgements and Priorities with the AHP,” European Journal of Operational Research 108, 165–169.

    Google Scholar 

  • Fox, C. R. and A. Tversky. (1998). “A Belief-Based Account of Decision Under Uncertainty,” Management Science 44(7), 879–895.

    Google Scholar 

  • George, T. and N. R. Pal. (1996). “Quantification of Conflict in Dempster-Shafer Framework: A New Approach,” International Journal of General Systems 24(4), 407–423.

    Google Scholar 

  • Gowda, K. C. and G. Krishna. (1978). “Dissaggregative Clustering Using the Concept of Mutual Nearest Neighbourhood,” IEEE Transaction on Systems, Man and Cybernetics 8, 883–895.

    Google Scholar 

  • Hegarat-Mascle, S., I. Bloch and D. Vidal-Madjar. (1997). “Application of Dempster-Shafer Evidence Theory to Unsupervised Classification in Multisource Remote Sensing,” IEEE Transaction on Systems, Man and Cybernetics - Part A: Systems and Humans 35(4), 1018–1031.

  • Hinsz, V. B. (1999). “Group Decision Making with Responses of a Quantitative Nature: The Theory of Social Decision Schemes for Quantities,” Organizational Behaviour and Human Decision Processes 80(1), 28–49.

  • Hollingshead, A. B. (1996). “The Rank-Order Effect in Group Decision Making,” Organizational Behaviour and Human Decision Processes 68(30), 181–193.

    Google Scholar 

  • Jousselme, A-L., D. Grenier and É. Bossé. (2001). “A New Distance Between two Bodies of Evidence,” Information Fusion 2, 91–101.

  • Kemeny, J. G. and L. J. Snell. (1962). “Preference Ranking: An Axiomatic Approach,” in Mathematical Models in Social Sciences, Ginn, New York, pp. 9–23.

  • Lai, V. S., B. K. Wong and W. Cheung. (2002). “Group Decision Making in a Multiple Criteria Environment: A Case Using the AHP in Software Selection,” European Journal of Operational Research 137(1), 134–144.

    Google Scholar 

  • Lei, Y. and X. Youmin. (1996). “A View of Group Decision Making Process and Bivoting Approach,” Computer Industrial Engineering 31(3/4), 945–948.

    Google Scholar 

  • Lipshitz, R. and O. Strauss. (1997). “Coping with Uncertainty: a Naturalistic Decision-Making Analysis,” Organisational Behaviour and Human Decision Processes 69(2), 149–163.

  • Matsatsinis, N. F. and A. P. Samaras. (2001). “MCDA and Preference Disaggregation in Group Decision Support Systems,” European Journal of Operational Research 130, 414–429.

    Google Scholar 

  • Mehrez, A. (1997). “The Interface Between OR/MS and Decision Theory,” European Journal of Operational Research 99, 38–47.

    Google Scholar 

  • Murnighan, J. K. (1978). “Models of Coalition Behaviour: Game Theoretic, Social Psychological, and Political Perspectives,” Psychological Bulletin 84, 1130–1153.

  • Murphy, C. K. (2000). “Combining Belief Functions when Evidence Conflicts,” Decision Support Systems 29, 1–9.

  • Noori, H. (1995). “The Design of An Integrated Group Decision Support System for Technology Assessment,” R&D Management 25(3), 309–322.

  • Ozdemir, M. S. and T. L. Saaty. (2005). “The Unknown in Decision Making What to do About it,” European Journal of Operational Research, in press.

  • Ramanathan, R. and L. S. Ganesh. (1994). “Group Preference Aggregation Methods Employed in AHP: An Evaluation and an Intrinsic Process of Deriving Member' Weightages,” European Journal of Operational Research 79, 249–265.

    Google Scholar 

  • Ray, T. G. and E. Triantaphyllou. (1998). “Evaluation of Rankings with Regard to the Possible Number of Agreements and Conflicts,” European Journal of Operational Research 106, 129–136.

    Google Scholar 

  • Roy, B. (1989). “Main Sources of Inaccurate Determination, Uncertainty and Imprecision in Decision Models,” Mathematical and Computer Modelling 12, 1245–1254.

  • Roy, B. and R. Slowinski. (1993). “Criterion of Distance Between Technical Programming and Socio-Economic Priority,” RA-IRO Recherche Opéationneller 27, 45–60.

  • Saaty, T. L. (1977). “A Scaling Method for Priorities in Hierarchical Structures,” Journal of Mathematical Psychology 15, 59–62.

    Google Scholar 

  • Saaty, T. L. (1980). The Analytic Hierarchy Process. New York, McGraw-Hill.

  • Shafer, G. (1976). A Mathematical theory of Evidence. Princeton, Princeton University Press.

  • Smets, P. (1991). “Varieties of Ignorance and the Need for Well-Founded Theories,” Information Sciences 57–58, 135–144.

    Google Scholar 

  • Van Den Honert, R. C. and F. A. Lootsma. (1996). “Group Preference Aggregation in the Multiplicative AHP: The Model of the Group Decision Process and Pareto Optimality,” European Journal of Operational Research 96, 363–370.

  • Von Winterfeldt, D. and W. Edwards. (1986). Decision Analysis and Behavioral Research. Cambridge University Press. Cambridge.

  • Xu, X., J.-M. Martel and B. F. Lamond. (2001). “A Multiple Criteria Ranking Procedure Based on Distance Between Partial Preorders,” European Journal of Operational Research 133, 69–80.

    Google Scholar 

  • Wasil, E. and B. Golden. (2003). “Editorial: Celebrating 25 years of AHP-based Decision Making,” Computers & Operations Research 30, 1419–1420.

  • Zouhal, L. M. and T. Denoeux. (1998). “An Evidence-Theoretic k-NN Rule with Parameter Optimization,” IEEE Transactions on Systems, Man and Cybernetics – Part C 28(2), 263–271.

    Google Scholar 

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Correspondence to Malcolm J. Beynon.

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Beynon, M.J. The Role of the DS/AHP in Identifying Inter-Group Alliances and Majority Rule Within Group Decision Making. Group Decis Negot 15, 21–42 (2006). https://doi.org/10.1007/s10726-005-1159-9

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