Metrics Based on Average Distance Between Sets

Abstract

This paper presents a distance function between sets based on an average of distances between their elements. The distance function is a metric if the sets are non-empty finite subsets of a metric space. It can be applied to produce various metric spaces on collections of sets and will be useful for analyzing complex data sets in the fields of computer science and information science. Its generalizations to include the Hausdorff metric and extensions to infinite sets for treating fuzzy sets are also discussed.