A Majority Guided Aggregation Operator in Group Decision Making

This chapter is about majority modelling in the context of group (multi-expert) decision making, to the aim of defining 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 experts. The reduction of the individual experts' opinions into a representative value (which we call the majority opinion) is usually performed through an aggregation process. In this chapter we describe two distinct approaches to the definition and consequent computation of a majority opinion within fuzzy set theory, where majority can be expressed by a linguistic quantifier (such as most). We first consider the case where linguistic quantifiers are associated with aggregation operators; in this case a majority opinion is computed by aggregating the individual opinions. To model this semantics of linguistic quantifiers the Induced Ordered Weighted Averaging operators (IOWA) are used with a modified definition of their weighting vector. We then consider a second case where the concept of majority is modelled as a vague concept. Based on this interpretation a formalization of a fuzzy majority opinion as a fuzzy subset is described.