Fuzzy set approach to the utility, preference relations, and aggregation operators

Score x = (x1, … , xn) describing an alternative α is modelled by means of a continuous quasi-convex fuzzy quantity μα = μx, thus allowing to compare alternatives (scores) by means of fuzzy ordering (comparison) methods. Applying some defuzzification method leads to the introduction of operators acting on scores. A special stress is put on the Mean of Maxima defuzzification method allowing to introduce several averaging aggregation operators. Moreover, our approach allows to introduce weights into above mentioned aggregation, even in the non-anonymous (non-symmetric) case. Finally, Ordered Weighted Aggregation Operators (OWAO) are introduced, generalizing the standard OWA operators.