On the Algebraic Properties of Intervals and Some Applications

Abstract

The algebraic properties of interval vectors (boxes) are studied. Quasilinear spaces with group structure are studied. Some fundamental algebraic properties are developed, especially in relation to the quasidistributive law, leading to a generalization of the familiar theory of linear spaces. In particular, linear dependence and basis are defined. It is proved that a quasilinear space with group structure is a direct sum of a linear and a symmetric space. A detailed characterization of symmetric quasilinear spaces with group structure is found.