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The dynamics of consensus in group decision making: investigating the pairwise interactions between fuzzy preferences

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  • Mario Fedrizzi

    (DISA, Faculty of Economics, Trento University)

  • Michele Fedrizzi
  • Ricardo Alberto Marques Pereira

    (DISA, Faculty of Economics, Trento University)

  • Matteo Brunelli

Abstract

In this paper we present an overview of the soft consensus model in group decision making and we investigate the dynamical patterns generated by the fundamental pairwise preference interactions on which the model is based. The dynamical mechanism of the soft consensus model is driven by the minimization of a cost function combining a collective measure of dissensus with an individual mechanism of opinion changing aversion. The dissensus measure plays a key role in the model and induces a network of pairwise interactions between the individual preferences. The structure of fuzzy relations is present at both the individual and the collective levels of description of the soft consensus model: pairwise preference intensities between alternatives at the individual level, and pairwise interaction coefficients between decision makers at the collective level. The collective measure of dissensus is based on non linear scaling functions of the linguistic quantifier type and expresses the degree to which most of the decision makers disagree with respect to their preferences regarding the most relevant alternatives. The graded notion of consensus underlying the dissensus measure is central to the dynamical unfolding of the model. The original formulation of the soft consensus model in terms of standard numerical preferences has been recently extended in order to allow decision makers to express their preferences by means of triangular fuzzy numbers. An appropriate notion of distance between triangular fuzzy numbers has been chosen for the construction of the collective dissensus measure. In the extended formulation of the soft consensus model the extra degrees of freedom associated with the triangular fuzzy preferences, combined with non linear nature of the pairwise preference interactions, generate various interesting and suggestive dynamical patterns. In the present paper we investigate these dynamical patterns which are illustrated by means of a number of computer simulations.

Suggested Citation

  • Mario Fedrizzi & Michele Fedrizzi & Ricardo Alberto Marques Pereira & Matteo Brunelli, 2010. "The dynamics of consensus in group decision making: investigating the pairwise interactions between fuzzy preferences," DISA Working Papers 1004, Department of Computer and Management Sciences, University of Trento, Italy, revised 29 Jul 2010.
    • Handle: RePEc:trt:disawp:1004
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    References listed on IDEAS

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    1. Mario Fedrizzi & Michele Fedrizzi & R. A. Marques Pereira, 2007. "Consensus Modelling In Group Decision Making: Dynamical Approach Based On Fuzzy Preferences," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 3(02), pages 219-237.
    2. French, Simon, 1981. "Consensus of opinion," European Journal of Operational Research, Elsevier, vol. 7(4), pages 332-340, August.
    3. F. J. Cabrerizo & S. Alonso & E. Herrera-Viedma, 2009. "A Consensus Model For Group Decision Making Problems With Unbalanced Fuzzy Linguistic Information," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 109-131.
    4. Carlsson, Christer & Ehrenberg, Dieter & Eklund, Patrik & Fedrizzi, Mario & Gustafsson, Patrik & Lindholm, Paul & Merkuryeva, Galina & Riissanen, Tony & G.S. Ventre, Aldo, 1992. "Consensus in distributed soft environments," European Journal of Operational Research, Elsevier, vol. 61(1-2), pages 165-185, August.
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