Normalized WDpWAM and WDpOWA spread measures

Aggregation theory often deals with measures of central tendency of quantitative data. As sometimes a different kind of information fusion is needed, an axiomatization of spread measures was introduced recently. In this contribution we explore the properties of WDpWAM and WDpOWA operators, which are defined as weighted Lp-distances to weighted arithmetic mean and OWA operators, respectively. In particular, we give forms of vectors that maximize such fusion functions and thus provide a way to normalize the output value so that the vector of maximal spread always leads to a fixed outcome, e.g., 1 if all the input elements are in [0, 1]. This might be desirable when constructing measures of experts’ opinions consistency or diversity in group decision making problems.