Decision situations in which several individual are involved are known as group decision-making (GDM) problems. In such problems, each member of the group, recognizing the existence of a common problem, tries to come to a collective decision. A high level of consensus among experts is needed before reaching a solution. It is customary to construct consensus measures by using similarity functions to quantify the closeness of experts preferences. The use of a metric that describes the distance between experts preferences allows the definition of similarity functions. Different distance functions have been proposed in order to implement consensus measures. This paper examines how the use of different aggregation operators affects the level of consensus achieved by experts through different distance functions, once the number of experts has been established in the GDM problem. In this situation, the experimental study performed establishes that the speed of the consensus process is significantly affected by the use of diverse aggregation operators and distance functions. Several decision support rules that can be useful in controlling the convergence speed of the consensus process are also derived.

In Group Decision Making (GDM) problems before to obtain a solution a high level of consensus among experts is required. Consensus measures are usually built using similarity functions measuring how close experts’ opinions or preferences are. Similarity functions are defined based on the use of a metric describing the distance between experts’ opinions or preferences. In the literature, die rent distance functions have been proposed to implement consensus measures. This paper presents analyzes the effect of the application of some die rent distance functions for measuring consensus in GDM. By using the nonparametric Wilcoxon matched-pairs signed-ranks test, it is concluded that die rent distance functions can produce significantly die rent results. Moreover, it is also shown that their application also has a significant elect on the speed of achieving consensus. Finally, these results are analyzed and used to derive decision support rules, based on a convergent criterion, that can be used to control the convergence speed of the consensus process using the compared distance functions