<p>Trapezoidal-valued intuitionistic fuzzy numbers are important in modelling and solving many real-life decision-making problems in the area of engineering and Management. Decision-making algorithms modelled under a trapezoidal-valued intuitionistic fuzzy environment will be suitable for solving problems modelled under various types of intuitionistic fuzzy numbers. The study of aggregation operators on the set of trapezoidal-valued intuitionistic fuzzy numbers is essential for solving decision-making problems modelled under a trapezoidal-valued intuitionistic fuzzy environment, and hence the main aim of this paper is to introduce the idea of Dombi t-norm and Dombi t-conorm-based aggregate operators on trapezoidal-valued intuitionistic fuzzy numbers. In this work, firstly, we develop a Trapezoidal-Valued Intuitionistic Fuzzy Dombi Weighted Averaging operator, Trapezoidal-Valued Intuitionistic Fuzzy Dombi Order Weighted Averaging operator, Trapezoidal-Valued Intuitionistic Fuzzy Dombi Hybrid Averaging operator with the assistance of Dombi operations to combine the information of trapezoidal-valued intuitionistic fuzzy numbers and study their mathematical properties by establishing various theorems. Secondly, we propose two multi-attribute group decision-making algorithms, namely a trapezoidal-valued intuitionistic fuzzy Combined Compromise Solution technique and a trapezoidal-valued multi-attribute group decision-making algorithm that utilizes the proposed aggregation operators. Thirdly, we show the applicability of the proposed decision-making methods in solving a multiattribute group decision-making problem using illustrative examples. Furthermore, we conduct a sensitivity analysis of the proposed algorithms to demonstrate their stability and reliability. Finally, we demonstrate the efficacy of the proposed decision-making approach by comparing it with several familiar group decision-making methods.</p>