AbstractA vector‐space approach to color systems has been shown to be useful in describing metameric effects and producing metamers under different illuminations. The vector‐space approach has also been used to describe color scanning and reproduction systems. This article extends the applications presented in previous work by introducing set theoretic concepts which allow the addition of realistic constraints. The set theoretic methods allow the full range of solutions of color problems to be explored by allowing a set of solutions to a particular problem formulation. The applications discussed here include producing realizable metamers and the design of scanning filt