<p>An interval-valued intuitionistic trapezoidal fuzzy set (IVITrFS) is a powerful tool for simulating uncertainty, which is able to take into account the various scenarios of the fuzzy decision-making information and to better describe the uncertainty of the fuzzy decision-making information. In this paper, we propose a new mathematical integration method for the supplier selection problem, i.e., generalized interval-valued intuitionistic trapezoidal fuzzy-weighted average (GIVITrFWA) operator and generalized interval-valued intuitionistic trapezoidal fuzzy-ordered weighted average (GIVITrFOWA) operator and explore their related properties and give specific proofs. With known experts and attribute weights, the decision matrix given by the decision-maker is transformed into a tensor structure, and the proposed operator is utilized for integration to obtain the comprehensive decision information of the alternatives and then, the interval-valued intuitionistic trapezoidal fuzzy number of the ordering method is used to obtain the relatively optimal supplier. Finally, the effectiveness and feasibility of the proposed method are verified through the analysis of the arithmetic example and the comparison analysis with other methods.</p>