A value of a sequence of elements of a finite metric space is an element for which is minimum. The –function with domain the set of all finite sequences on and defined by is a value of is called the –function on . The and functions are the well-studied median and mean functions, respectively. In this note, simple characterizations of the –functions on the -cube are given. In addition, the center function (using the minimax criterion) is characterized as well as new results proved for the median and antimedian functions.
"Axioms for Consensus Functions on the -Cube." J. Appl. Math. 2017 1 - 5, 2017. https://doi.org/10.1155/2017/8025616