The decision making trial and evaluation laboratory (DEMATEL) is a pragmatic method used to construct the structural correlation of criteria in a multi-criteria decision making (MCDM) problem. This paper proposes modifications to DEMATEL. Different from the typical DEMATEL which utilizes crisp numbers, this modification introduces interval-valued intuitionistic fuzzy numbers to enhance judgements in group decision-making environment. We use the interval-valued intuitionistic fuzzy weighted averaging operator instead of the typical averaging operator to aggregate decision-makers’ preferences. This paper proposes a combination of interval-valued intuitionistic fuzzy numbers, DEMATEL and the Choquet integral to allow a strong interrelationship between the sum of rows and the sum of columns of criteria in structural correlation analysis. The feasibility and applicability of the proposed method is illustrated by a numerical example about sustainable solid waste management. The result indicates that ‘collaboration and synergy’ is the most influential criterion for sustainable solid waste management. Comparative results are presented to show the validity of the proposed method.