Strict valued preference relations and choice functions in decision-making procedures

Fuzzy (valued) preference relations (FPR) give possibility to take into account the intensity of preference between alternatives. The refinement of crisp (non-valued) preference relations by replacing them with valued preference relations often transforms crisp preference relations with cycles into acyclic FPR. It gives possibility to make decisions in situations when crisp models do not work. Different models of rationality of strict FPR defined by the levels of transitivity or acyclicity of these relations are considered. The choice of the best alternatives based on given strict FPR is defined by a fuzzy choice function (FCF) ordering alternatives in given subset of alternatives. The relationships between rationality of strict FPR and rationality of FCF are studied. Several valued generalizations of crisp group decision-making procedures are proposed. As shown on examples of group decision-making in multiagent systems, taking into account the preference values gives possibility to avoid some problems typical for crisp procedures.