On fuzzy tournaments and their solution concepts in group decision making

Assuming as the point of departure a set of individual or collective fuzzy tournaments (complete and reciprocal binary relations)-representing the preferences of the particular individuals or their group as a whole, respectively-the authors define some new solution concepts in group decision making as counterparts of the respective solution concepts in the case of nonfuzzy tournaments (complete and asymmetric binary relations). Basically, the new solution concepts are mainly counterparts of some sets of undominated options, uncovered sets, and Banks sets. The authors consider the cases of both the conventional (nonfuzzy) and fuzzy majorities.