The goal of this work is to introduce the concept of interval metric in a
compact way by modifying the existing definitions of interval metric. Then,
a result regarding the necessary and sufficient criterion for interval
metric is established. Thereafter, to illustrate the idea of interval
metric, a set of examples is provided. Then, several results regarding the
formation of interval metric are derived. Also, the concept of interval
diameter, boundedness of a set under interval metric and interval distance
are introduced. All the theoretical results are illustrated with the help of
some numerical examples. Finally, as an application of interval metric, all
the theoretical developments of transformation of multi-objective interval
optimization problem into interval single objective optimization problem by
Global criterion method, Tchebycheff method and Weighted Tchebycheff method
are established.