Using distance functions to solve representation choice problems

A representation choice problem is based on the selection of an object (or objects), which should at best represent a given set of objects. In this paper we propose to solve this problem by using distance functions between objects. These distance functions are used to define representation choice functions. Six postulates for representation choice functions are given and their analysis is presented. The theoretical results provide us with some interesting relationships between classes of choice functions specified by the accepted postulates. They a] so make it possible to specify essential properties of considered choice functions. In particular, it has been proved that in practical settings it is suggested to use functions from two particular classes, for they preserve important features. Less popular representation choice functions are also pointed at and analyzed.