Metrics Based on Average Distance Between Sets

TL;DR

This paper introduces a new set distance metric based on average element distances, applicable to finite and infinite sets, with potential uses in analyzing complex data in computer and information sciences.

Contribution

It proposes a novel average-distance-based metric for sets, including generalizations to Hausdorff and fuzzy sets, expanding tools for data analysis.

Findings

The metric is valid for non-empty finite subsets of metric spaces.

Extensions to Hausdorff and fuzzy sets are discussed.

Applicable to complex data analysis in computer and information science.

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.