Abstract: Recently, a very interesting relation between symmetric minitive, maxitive, 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.
Abstract: This article is a second part of the contribution on the analysis of the recently-proposed class of symmetric maxitive, minitive and modular aggregation operators. Recent results (Gagolewski, Mesiar, 2012) indicated some unstable behavior of the generalized h-index, which is a particular instance of OM3, in case of input data transformation. The study was performed on a small, carefully selected real-world data set. Here we conduct some experiments to examine these phenomena more extensively.