An analytic hierarchy process model of group consensus

Abstract

In group decision making, a certain degree of consensus is necessary to derive a meaningful and valid outcome. This paper proposes a consensus reaching model for a group by using the Analytic Hierarchy Process (AHP). It supports people to improve their group consensus level through an updating of their judgments. In this model, a moderator suggests the most discordant decision maker to update his judgment in each step. The proposed consensus reaching model allows decision makers to accept or reject the suggestion from the moderator. This model ensures that the judgment updating is effective and the final solution will be of acceptable consistency. Finally, a numerical example is given to illustrate the validity of the proposed consensus reaching model.

Keywords

Group decision making / Analytic Hierarchy Process (AHP) / consensus / judgment updating

References

[1] Aczél J, Alsina C. Synthesizing judgements: a functional equations approach. Mathematical Modelling, 1987, 9(3–5): 311-320.

[2] Aczél J, Roberts F S. On the possible merging functions. Mathematical Social Sciences, 1989, 17(3): 205-243.

[3] Aczél J, Saaty T L. Procedures for synthesizing ratio judgments. Journal of Mathematical Psychology, 1983, 27(1): 93-102.

[4] Aguarón J, Moreno-Jiménez J M a. The geometric consistency index: Approximated thresholds. European Journal of Operational Research, 2003, 147(1): 137-145.

[5] Aull-Hyde R, Erdogan S, Duke J M. An experiment on the consistency of aggregated comparison matrices in AHP. European Journal of Operational Research, 2006, 171(1): 290-295.

[6] Brock H W. The problem of “Utility Weights” in group preference aggregation. Operations Research, 1980, 28(1): 176-187.

[7] Bryson N. Group decision-making and the analytic hierarchy process: exploring the consensus — relevant information content. Computers & Operations Research, 1996, 23(1): 27-35.

[8] Chen P S, Chu P, Lin M. On Vargas’s proof of consistency test for 3x3 comparison matrices in AHP. Journal of the Operations Research Society of Japan, 2002, 45(3): 233-242.

[9] Chiclana F, Herrera-Viedma E, Herrera F, Alonso S. Some induced ordered weighted averaging operators and their use for solving group decision-making problems based on fuzzy preference relations. European Journal of Operational Research, 2007, 182(1): 383-399.

[10] Chiclana F, Mata F, Martinez L, Herrera-Viedma E, Alonso S. Integration of a consistency control module within a consensus model. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2008, 16(supp01): 35-53.

[11] Dong Y, Xu Y, Yu S. Computing the numerical scale of the linguistic term set for the 2-tuple fuzzy linguistic representation model. IEEE Transactions on Fuzzy Systems, 2009, 17(6): 1366-1378.

[12] Dong Y, Zhang G, Hong W-C, Xu Y. Consensus models for AHP group decision making under row geometric mean prioritization method. Decision Support Systems, 2010, 49(3): 281-289.

[13] Forman E, Peniwati K. Aggregating individual judgments and priorities with the analytic hierarchy process. European Journal of Operational Research, 1998, 108(1): 165-169.

[14] Forman E H, Gass S I. The Analytic Hierarchy Process — An Exposition. Operations Research, 2001, 49(4): 469-486.

[15] Fu C, Yang S. An attribute weight based feedback model for multiple attributive group decision analysis problems with group consensus requirements in evidential reasoning context. European Journal of Operational Research, 2011, 212(1): 179-189.

[16] Grošelj P, Zadnik Stirn L. Acceptable consistency of aggregated comparison matrices in analytic hierarchy process. European Journal of Operational Research, 2012, 223(2): 417-420.

[17] Herrera-Viedma E, Herrera F, Chiclana F. A consensus model for multiperson decision making with different preference structures. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans, 2002, 32(3): 394-402.

[18] Herrera-Viedma E, Martinez L, Mata F, Chiclana F. A consensus support system model for group decision-making problems with multigranular linguistic preference relations. IEEE Transactions on Fuzzy Systems, 2005, 13(5): 644-658.

[19] Herrera F, Herrera-Viedma E, Verdegay J L. A model of consensus in group decision making under linguistic assessments. Fuzzy Sets and Systems, 1996, 78(1): 73-87.

[20] Herrera F, Martínez L. A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Transactions on Fuzzy Systems, 2000, 8(6): 746-752.

[21] Hsi-Mei H, Chen-Tung C. Aggregation of fuzzy opinions under group decision making. Fuzzy Sets and Systems, 1996, 79(3): 279-285.

[22] Kacprzyk J, Fedrizzi M, Nurmi H. Group decision making and consensus under fuzzy preferences and fuzzy majority. Fuzzy Sets and Systems, 1992, 49(1): 21-31.

[23] Keeney R L. A group preference axiomatization with cardinal utility. Management Science, 1976, 23(2): 140-145.

[24] Keeney R L, Kirkwood C W. Group decision making using cardinal social welfare functions. Management Science, 1975, 22(4): 430-437.

[25] Lin R, Lin J S J, Chang J, Tang D, Chao H, Julian P C. Note on group consistency in analytic hierarchy process. European Journal of Operational Research, 2008, 190(3): 672-678.

[26] Ramanathan R, Ganesh L S. Group preference aggregation methods employed in AHP: an evaluation and an intrinsic process for deriving members’ weightages. European Journal of Operational Research, 1994, 79(2): 249-265.

[27] Saaty T L. A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology, 1977, 15(3): 234-281.

[28] Saaty T L. The Analytic Hierarchy Process: Planning, priority setting, resource allocaton, 1980, NewYork: McGraw-Hill

[29] Saaty T L. How to make a decision: the analytic hierarchy process. European Journal of Operational Research, 1990, 48(1): 9-26.

[30] Saaty T L. Fundamentals of decision making and priority theory with the Analytic Hierarchy Process, 1994, Pittsburgh: RWS Publications

[31] Saaty T L. A ratio scale metric and the compatibility of ratio scales: the possibility of arrow’s impossibility theorem. Applied Mathematics Letters, 1994, 7(6): 45-49.

[32] Saaty T L, Peniwati K. Group decision making: drawing out and reconciling differences, 2012, Pittsburgh: RWS Publications

[33] Subramanian N, Ramanathan R. A review of applications of Analytic Hierarchy Process in operations management. International Journal of Production Economics, 2012, 138(2): 215-241.

[34] Tan C. A multi-criteria interval-valued intuitionistic fuzzy group decision making with Choquet integral-based TOPSIS. Expert Systems with Applications, 2011, 38(4): 3023-3033.

[35] Tanino T. Fuzzy preference orderings in group decision making. Fuzzy Sets and Systems, 1984, 12(2): 117-131.

[36] Vaidya O S, Kumar S. Analytic Hierarchy Process: an overview of applications. European Journal of Operational Research, 2006, 169(1): 1-29.

[37] Wang R-C, Chuu S-J. Group decision-making using a fuzzy linguistic approach for evaluating the flexibility in a manufacturing system. European Journal of Operational Research, 2004, 154(3): 563-572.

[38] Wu Z, Xu J. A concise consensus support model for group decision making with reciprocal preference relations based on deviation measures. Fuzzy Sets and Systems, 2012, 206(0): 58-73.

[39] Wu Z, Xu J. A consistency and consensus based decision support model for group decision making with multiplicative preference relations. Decision Support Systems, 2012, 52(3): 757-767.

[40] Xu Y, Li K W, Wang H. Distance-based consensus models for fuzzy and multiplicative preference relations. Information Sciences, 2013, 253(0): 56-73.

[41] Xu Z. On consistency of the weighted geometric mean complex judgment matrix in AHP. European Journal of Operational Research, 2000, 126(3): 683-687.

[42] Xu Z. An automatic approach to reaching consensus in multiple attribute group decision making. Computers & Industrial Engineering, 2009, 56(4): 1369-1374.

[43] Yu P L. A class of solutions for group decision problems. Management Science, 1973, 19(8): 936-946.