Preferences and Consistency Issues in Group Decision Making

A group selection of one alternative from a set of feasible ones should be based on the preferences of individuals in the group. Decision making procedures are usually based on pair comparisons, in the sense that processes are linked to some degree of credibility of preference. The main advantage of pairwise comparison is that of focusing exclusively on two alternatives at a time and on how they are related. However, it generates more information that needed and therefore inconsistent information may be generated. This paper addresses both preference representation and consistency of preferences issues in group decision making.

Different preference representation formats individuals can use to model or present their preferences on a set of alternatives in a group decision making situation are reviewed. The results regarding the relationships between these preference representation formats mean that the fuzzy preference relation “is preferred to” representing the strength of preference of one alternative over another in the scale [0,1] can be used as the base element to integrate these different preference representation formats in group decision making situations.

Due to the complexity of most decision making problems, individuals’ preferences may not satisfy formal properties that fuzzy preference relations are required to verify. Consistency is one of them, and it is associated with the

transitivity property.

Many properties have been suggested to model transitivity of fuzzy preference relations. As aforementioned, this paper provides an overview of the main results published in this area.