The role of betweenness relations, monometrics and penalty functions in data aggregation

Penalty functions have been used for data aggregation since Yager introduced his “general theory of information aggregation” back in 1993. Obviously, the ideas of Yager have long time been surpassed. However, over the years, the use of penalty functions has shifted towards the aggregation of values in a closed interval. Here, we propose to return to the origin of penalty-based data aggregation and to expand the current definition of penalty functions beyond the confinement to closed intervals. We do this by bringing to the field of data aggregation an old acquaintance of the early scholars of geometry: betweenness relations.