* Corresponding author Explaining the consensus of opinions with the vocabulary of the experts Aïda Valls * Dept. d’Enginyeria Informàtica i Matemàtiques Universitat Rovira i Virgili Carretera de Salou, s/n E-43006 Tarragona, Spain avalls@etse.urv.es Vicenç Torra Institut d’Investigació en Intel.ligència Artificial IIIA-CSIC Campus Universitat Autònoma Barcelona E-08193 Bellaterra, Spain vtorra@iiia.csic.es Abstract In a decision making framework experts often use linguistic variables to describe their opinions or preferences. When experts are allowed to use their own set of terms, syntactic and semantic differences in the vocabularies may be found. In this work we propose a method that uses clustering techniques to aggregate data, and which gives the result in terms of the vocabulary of one of the experts, after adapting it in order to better describe the result. Keywords: Linguistic labels, Decision Making, Aggregation, Cluster analysis. 1. Introduction In a typical multi-criteria decision making problem (MCDM), an alternative (or a set of alternatives) has to be selected from a larger set of them on the basis of the performace values of these alternatives according to several criteria. Knowledge in this context is usually represented by means of a function that assigns a value for each pair (alternative, criterion) [2]. Frequently, different criteria give values in different domains. Sometimes restrictions are applied to these domains to ease the process of selection of the best alternative/s. A usual restriction is that all the alternatives must be evaluated with real numbers. Other approaches [4,6] allow criteria to use linguistic values (called labels or terms), but the domain must be identical for each criterion. Others allow different linguistic domains for each criterion provided that all the terms are equally informative [5], that is, the semantics of each term is forced a priori. Finally, there are studies [3] that consider the use of both numerical and linguistic domains. This case is of particular interest because the expert has more flexibility in order to express his preferences. In [13] we introduced a methodology to deal with heterogeneous criteria: numerical, linguistic and boolean. Moreover, our proposal takes into account the semantics of the linguistic values during all the decision process. This semantics is obtained using negation functions (defined in [11]) instead of other known approximations such as fuzzy sets. In MCDM, the decision making is made in two steps [2]: (i) the rating, i.e. the aggregation of the preferences, (ii) the ranking or ordering between the alternatives with respect to the global degree of satisfaction. We propose a methodology for the rating phase. At the end we obtain a consensus criterion that corresponds to the collective opinion, which gives a linguistic preference value to each alternative. Then, the decision maker can consider other criteria and aggregate the results, or just rank the alternatives and choose the best one.