On Group Decision Making, Consensus Reaching, Voting and Voting Paradoxes under Fuzzy Preferences and a Fuzzy Majority: A Survey and some Perspectives

Group decision making, as meant in this chapter, is the following choice problem which proceeds in a multiperson setting. There is a group of individuals (decisionmakers, experts, ...) who provide their testimonies concerning an issue in question. These testimonies are assumed here to be individual preference relations over some set of option (alternatives, variants, ...). The problem is to find a solution, i.e. an alternative or a set of alternatives, from among the feasible ones, which best reflects the preferences of the group of individuals as a whole. We will survey main developments in group decision making under fuzziness. First, we will briefly outline some basic inconsistencies and negative results of group decision making and social choice, and show how they can be alleviated by some plausible modifications of underlying assumptions, mainly by introducing fuzzy preference relations and, to a lesser extent, a fuzzy majority. Then, we will concentrate on how to derive solutions under individual fuzzy preference relations, and a fuzzy majority equated with a fuzzy linguistic quantifier (e.g., most, almost all, ...) and dealt with in terms of a fuzzy logic based calculus of linguistically quantified statements or via the ordered weighted averaging (OWA) operators. We will briefly mention that one of solution concepts proposed can be a prototype for a wide class of group decision making choice functions. Then, we will discuss a related issue of how to define a “soft” degree of consensus in the group under individual fuzzy preference relations and a fuzzy majority. Finally, we will show how fuzzy preferences can help alleviate some voting paradoxes.