Modeling the concept of majority opinion in group decision making

In this paper the problem of group decision making is studied. One of the main issues in this context is to define a decision strategy which takes into account the individual opinions of the decision makers. The concept of majority plays in this context a key role: what is often needed is an overall opinion which synthesizes the opinions of the majority of the decision makers. The reduction of the individual values into a representative value (which we call the majority opinion) is usually performed through an aggregation process. Within fuzzy set theory the concept of majority can be expressed by a linguistic quantifier (such as most), which is formally defined as a fuzzy subset. In this paper we propose two distinct approaches to the definition of a majority opinion. We first consider the case where linguistic quantifiers are associated with aggregation operators which allow us to compute a majority opinion by aggregating the individual opinions. In this case the majority opinion corresponds to the aggregated value. To model this semantics of linguistic quantifiers the IOWA operators are used and a new proposal of definition of their weighting vector is presented. A second method is based on the consideration of the concept of majority as a vague concept. Based on this interpretation we propose a formalization of a fuzzy majority opinion as a fuzzy subset.