Group Decision Making and a Measure of Consensus under Fuzzy Preferences and a Fuzzy Linguistic Majority

The essence of group decision making is: 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.In this paper we will survey main developments in group decision making under fuzziness, mainly under fuzzy preference relations and a fuzzy (linguistic) majority. 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. Finally, 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.

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