Construction of admissible linear orders for interval-valued Atanassov intuitionistic fuzzy sets with an application to decision making

•We define an admissible linear order between pairs of intervals in terms of aggregation (fusion) functions.•We show how this order may be extended to the interval-valued Atanassov intuitionistic fuzzy setting.•We characterize these linear orders.•We apply the linear order to a decision making problem where other fuzzy approaches do not lead to a unique solution.

In this work we introduce a method for constructing linear orders between pairs of intervals by using aggregation functions. We adapt this method to the case of interval-valued Atanassov intuitionistic fuzzy sets and we apply these sets and the considered orders to a decision making problem.