We study a family of n-way metrics that generalize the usual two-way metric. The n-way metrics are totally symmetric maps from En into ℝ≥0. The three-way metrics introduced by Joly and Le Calvé (1995) and Heiser and Bennani (1997) and the n-way metrics studied in Deza and Rosenberg (2000) belong to this family. It is shown how the n-way metrics and n-way distance measures are related to (n - 1)-way metrics, respectively, (n - 1)-way distance measures.
- n-Way distance measure
- Parametrized inequality
- Tetrahedron inequality;Polyhedron inequality
- Triangle inequality