Abstract As an uncertain programming model with multiple conflicting performance indices and bounded uncertain parameter(s), multiobjective interval number programming is a daunting topic in the fields of mathematics and intelligent optimization. Despite its comprehensive engineering application background, it is still open, and further studies are needed on basic theory, model transformation and intelligent optimizers. Therein, this work not only gropes a new shortcut to tackling one such model, but also proposes a novel multiobjective interval number immune optimization algorithm. The intrinsic solution relation between the model and a related natural interval extension one is discovered in terms of the new concept of optimal-value vector solution, by which a fast interval nondominated sorting approach is acquired. The algorithm mainly consists of population division, proliferation, evolution, selection and memory update, in which a co-evolutionary mechanism is designed to promote the current population to move quickly towards the Pareto front with the assistance of the sorting approach and an external archive set. The algorithm's resource consumption depends mainly on the archive's size. Comparative experiments have validated that the optimizer can effectively perform well over the compared approaches and is significantly superior to them with regard to efficiency.