On some theoretical developments of interval metric space

Abstract

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.