The main purpose of this article is to utilize mathematical tools to rank alternatives for a decision making problem. In this regard, we developed different types of interval-valued intuitionistic fuzzy (IVIF) score ideals through unit-valued score (accuracy) functions. We used IVIF-score left (right) ideals to characterize an intra-regular class of an ordered Abel-Grassmann's-grououpoid (AG-groupoid) which is a semilattice of left simple AG-groupoids. We also established a connection between IVIF-score (0, 2)-ideals and IVIF-score left (right) ideals. Finally, we demonstrated how to use the interval valued intuitionistic fuzzy score $(0,2)$-ideals to identify the most suitable alternative in a decision making problem, and also explain how it can be applied to a problem of selecting a warehouse.