OM3: Ordered maxitive, minitive, and modular aggregation operators: Axiomatic analysis under arity-dependence (I)

Recently, a very interesting relation between symmetric minitive, maxi-tive, and modular aggregation operators has been shown. It turns out that the intersection between any pair of the mentioned classes is the same. This result introduces what we here propose to call the OM3 operators. In the first part of our contribution on the analysis of the OM3 operators we study some properties that may be useful when aggregating input vectors of varying lengths. In Part II we will perform a thorough simulation study of the impact of input vectors’ calibration on the aggregation results.