Decision Support Monte Carlo simulation techniques for group decision making with incomplete information A. Mateos * , A. Jime ´nez, S. Rı ´os-Insua Department of Artificial Intelligence, School of Computer Science, Madrid Technical University, Campus de Montegancedo s/n, 28660 Madrid, Spain Received 27 January 2004; accepted 21 February 2005 Available online 13 May 2005 Abstract In this paper we deal with group decision-making problems where several decision makers elicit their own prefer- ences separately. The decision makersÕ preferences are quantified using a decision support system, which admits incom- plete information concerning the decision makersÕ responses to the questions they are asked. Consequently, each decision maker proposes classes of utility functions and attribute weight intervals for the different attributes. We intro- duce an approach based on Monte Carlo simulation techniques for aggregating decision maker preferences that could be the starting point for a negotiation process, if necessary. The negotiation process would basically involve the decision maker tightening the imprecise component utilities and weights to output more meaningful results and achieve a con- sensus alternative. We focus on how attribute weights and the component utilities associated with a consequence are randomly generated in the aggregation process taking into account the decision-makersÕ preferences, i.e., their respec- tive attribute weight intervals and classes of utility functions. Finally, an application to the evaluation of intervention strategies for restoring a radionuclide contaminated lake illustrates the usefulness and flexibility of this iterative process. Ó 2005 Elsevier B.V. All rights reserved. Keywords: Decision analysis; Group decisions and negotiations; Multiple criteria analysis; Decision support system; Additive multi- attribute utility model 1. Introduction We consider multicriteria group decision-making problems, where the decision makers (DMs) want to identify the ÔbestÕ or Ômost preferredÕ alternative decision from a set of alternatives S ={S 1 , ... ,S s }. The 0377-2217/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2005.02.057 * Corresponding author. Tel.: +34 91 336 6596; fax: +34 91 352 4819. E-mail addresses: amateos@fi.upm.es (A. Mateos), ajimenez@fi.upm.es (A. Jime ´nez), srios@fi.upm.es (S. Rı ´os-Insua). European Journal of Operational Research 174 (2006) 1842–1864 www.elsevier.com/locate/ejor