Characterization of fuzzy integrals viewed as aggregation operators

As it is known that fuzzy integrals cover a wide range of aggregation operators of the averaging type, such as the weighted average, medians, a large part of generalized means, and weighted minimum and maximum OWA (ordered weighted averaging) operators, it would be of valuable interest to try to characterize them. Recently, Fodor et al. have succeeded in characterizing OWA. As OWA is a particular case of fuzzy integral, their results can serve as a basis for the problem addressed here. We show several results on characterization of different kinds of fuzzy integrals. The proofs of all these results are merely a generalisation to the ones presented by Fodor, and for space limitations, are not all presented here