A decision-making computational methodology for a class of type-2 fuzzy intervals: An interval-based approach.

•Our method maintains the flexibility of interval arithmetic and interval reasoning as major objectives where FIs are represented by their profiles, viewed as gradual numbers.•Our method is based on interval relations to determine a generic formulation of the intersection operation between type-2 fuzzy intervals (FIs).•The proposed method is applied to a risk decision-making problem.•Our method offers a convenient tool, which enables decision-makers to manage their judgment in the possible uncertain domain of decision.•The Bellman-Zadeh decision-making problem using membership functions can be transformed into an interval arithmetic problem using the FI profiles.