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.