Generalized interval vector spaces and interval optimization

•This paper presents a method of endowing the generalized interval space with some different structures, such as vector space, topological space, order relations and algebraic calculus.•We formulate Interval optimization problems and relate them to classic multi-objective optimization problems.•We also present a version of the Mini-max’s Theorem in the interval space context.

This paper presents a method for endowing the generalized interval space with some different structures, such as vector spaces, order relations and an algebraic calculus. With these concepts we formulate interval optimization problems and relate them to classic multi-objective optimization problems. We also present a version of the Von Neumann’s Mini-max Theorem in the interval context.