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• 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. This paper proposes an interval-based computational formulation of the Bellman-Zadeh decision-making approach when the handled information (goals and constraints) is represented by type-2 fuzzy intervals (FIs). Our method, which maintains the flexibility of interval arithmetic and interval reasoning as major objectives, consists of representing an FI by its profiles, which are considered gradual numbers. The developed reflection is based on interval relations to determine a generic formulation of the intersection operation between type-2 FIs, where a computational mechanism can be easily derived. This intersection area is considered an uncertain decision domain that is represented by lower type-1 FI situations and upper type-1 FI bounds that are considered extreme situations in adverse situations and favorable situations, respectively. In this framework, any FI between these FI bounds can be chosen by decision makers as an optimal solution according to a specified decision criterion. In this paper, a risk decision-making criterion is considered; however, other decision criteria can be employed in a similar manner. The proposed vision offers a convenient tool that enables decision makers to manage their judgment in the possible uncertain domain of a decision. The interest of the proposed approach is the extension of inter-interval relations to type-1 and type-2 FIs, where the Bellman-Zadeh decision-making problem using membership functions can be transformed into an interval arithmetic problem using the FI profiles. [ABSTRACT FROM AUTHOR]