# Group decision making

A Group Decision Making (GDM) problem is a decision situation where:

• There exists a group m of individuals or experts, E = {e1, ... ,em}, who each have their own attitudes and knowledge.
• There is a decision problem consisting of n alternatives or possible solutions to the problem, X = {x1, ... ,xn}.
• The experts try to achieve a common solution.

Each expert ei expresses his/her opinions or preferences over alternatives in X by means of a preference structure. Some examples of preference structures widely used in scientific literature related to GDM, are: fuzzy preference relations, preference orderings, utility vectors, and so on.

Some GDM problems are characterized by the existence of multiple attributes or criteria, C = {c1, ... ,cq}, and experts must assess alternatives based on each of these criteria. For instance, consider a decision problem about buying a new house; then some criteria to evalute different houses could be: location, neighbothood or size, amongst others. In these situations, we have a Multi-Criteria Group Decision Making (MCGDM) problem.

GDM problems are usually defined in environments of uncertainty, in which the information regarding the problem is vague and imprecise. These situations are also known as GDM problems under fuzzy contexts. Some information domains for expressing preferences, that have been frequently utilized by experts to deal with uncertainty, are: numerical, interval-valued or linguistic information. The solution for a GDM problem has been classically determined by applying an alternative selection process, which is composted of two phases:

1. Aggregation phase: Experts' preferences are combined, by using an aggregation operator.
2. Exploitation phase: An alternative or subset of alternatives is obtained as the solution for the GDM problem, by applying a selection criterion (e.g. dominance or non-dominance degrees).

Selection process for the resolution of GDM problems