p-Symmetric Fuzzy Measures

Fuzzy measures are a generalization of probability measures for which additivity is removed and monotonicity is imposed instead. These measures have become a powerful tool in Decision Theory (see e.g. 12, the work of Schmeidler 21 and 3); moreover, the Choquet Expected Utility model generalizes the Expected Utility one, and this model offers a simple theoretical foundation for explaining phenomena that cannot be accounted for in the framework of Expected Utility Theory, as the well known Ellsberg’s and Allais’ paradoxes (see 3 for a survey about this topic). However, the richness of fuzzy measures has its counterpart in the complexity. If we deal with a space of n elements, a probability measure only needs n − 1 coefficients, while a fuzzy measure needs 2 − 2. In an attempt to decrease the exponential complexity of fuzzy measures in practical applications, Grabisch has