Measurements of Consensus in Multi-granular Linguistic Group Decision-Making

The reaching of consensus in group decision-making (GDM) problems is a common task in group decision processes. In this contribution, we consider GDM with linguistic information. Different experts may have different levels of knowledge about a problem and, therefore, different linguistic term sets (multi-granular linguistic information) can be used to express their opinions. The aim of this paper is to present different ways of measuring consensus in order to assess the level of agreement between the experts in multi-granular linguistic GDM problems. To make the measurement of consensus in multi-granular GDM problems possible and easier, it is necessary to unify the information assessed in different linguistic term sets into a single one. This is done using fuzzy sets defined on a basic linguistic term set (BLTS). Once the information is uniformed, two types of measurement of consensus are carried out: consensus degrees and proximity measures. The first type assesses the agreement among all the experts’ opinions, while the second type is used to find out how far the individual opinions are from the group opinion. The proximity measures can be used by a moderator in the consensus process to suggest to the experts the necessary changes to their opinions in order to be able to obtain the highest degree of consensus possible. Both types of measurements are computed in the three different levels of representation of information: pair of alternatives, alternatives and experts.