Inner Products on Intervals in R^n

Abstract

In this paper, we defined an inner product on the collection of intervals in R^n within a vector space framework, demonstrating its consistency with the properties of standard inner products. We further established that the collection of intervals in R^n forms a Hilbert space under the proposed inner product. Additionally, we explored applications of this framework to interval linear programming problems and interval support vector machines, highlighting the practical relevance and usefulness of the theoretical results.