In this paper, we analyze several classes of functions proposed in the literature to simultaneously generalize weighted means and ordered weighted averaging (OWA) operators: weighted OWA (WOWA) operators, hybrid weighted averaging (HWA) operators, and ordered weighted averaging-weighted average (OWAWA) operators. Since, in some cases, the results provided by these operators may be questionable, we introduce functions that also generalize both operators and characterize those satisfying a condition imposed to maintain the relationship among the weights
