Fuzzy approaches to modelling consensus in group decision support

In this paper we introduce some models and systems we developed in the field of group decision support in fuzzy environments. The basic framework within which we operate is the following one. We have a set of individuals who present their opinions concerning an issue in question, and a moderator, who is supposed to be responsible for the session with the individuals. The individuals present their testimonies which may initially differ to a large extent, i.e. the group may be far from consensus (unanimous agreement, as traditionally meant). Then the moderator – via some exchange of information, rational argument, bargaining, etc. – tries to persuade the individuals to change their opinions. If the individuals are rationally committed to consensus, such a change usually occurs, and the group gets closer to consensus. This is repeated until the group gets sufficiently close to consensus, according to a fixed metric, or until some time limit for the process is reached. The individual testimonies are assumed to be expressed as reciprocal fuzzy preference relations and the measure of consensus depends on a function estimated for each expert according to her/his aversion to opinion changing. In order to capture the fuzzy uncertainties of human intuition we introduce a vocabulary of linguistic terms whose values are represented by fuzzy numbers. At the end of the paper an application in the field of environmental impact assessment is described.