Strict monotonicity Strict monotonicity is desired in applications where the number of items to be shown to the user is limited. Weighted arithmetic means and
OWA functions are strictly monotone when w j > 0, ∀ j, while geometric and
harmonic means are strict for x ∈]0, 1]n. Aggregation functions which are not
strict, the maximum function for instance, could not distinguish between an item
d1 = (0.3, 0.8) and another d2 = (0.8, 0.8).