This paper proposes a new effective tool to address complex multicriteria decision-making problems where all decision-making information is provided by decision makers in both the trapezoidal neutrosophic environment and the bipolar neutrosophic environment. Relatedly, the concepts and operating laws of the bipolar trapezoidal neutrosophic set are defined. Some priority aggregate operators for the aggregation of bipolar trapezoidal neutrosophic information are discussed. In addition, priority aggregation operators based on Dombi operations are developed: bipolar trapezoidal neutrosophic Dombi weighted averaging operator and bipolar trapezoidal neutrosophic Dombi weighted geometric operator. The desirable properties of these operators and the relationship between them are investigated. Two approaches are proposed to address multiple criteria for decision-making problems in the bipolar trapezoidal neutrosophic environment. The sensitivity of the proposed approaches is analyzed using examples, and a multiple comparison test is conducted to demonstrate their effectiveness.