<p>Transportation problems (TP) have wide-ranging impacts on the economy, and the environment. If efficient transportation planning is not done beforehand, it can lead to increased costs for businesses as well as consumers, and in some cases, it can also become a reason for disruptions in supply chains. Further, this can result in decreased productivity and higher prices for goods and services. Thus, there is always a need for proper transportation planning. However, while modeling a real-life transportation scenario, the parameters do not always have a precise value. The uncertainty in parameters is based on the linguistic description given by the decision-makers and is because of various influential factors. To address them, various forms representing different types of uncertainties have been widely proposed and used in modeling realistic situations. In this paper, interval-valued triangular neutrosophic numbers (IVTNN) with some basic definitions and arithmetic operations are proposed. Further, expected interval and expected value functions are proposed for defuzzification of IVTNNs. Considering this type of uncertainty, a model of TP in an interval-valued triangular neutrosophic environment is formulated and a solution approach is proposed for it. Further, using the defined expected value and definitions related to IVTNNs, the uncertain model is transformed into a crisp model and a standard linear programming algorithm is applied to find the optimum transportation cost using LINGO. Also, two numerical examples are presented to demonstrate the feasibility of the proposed method. The advantages of our model over certain existing approaches in the literature are also highlighted. Furthermore, we discuss some limitations of the proposed model. At last, conclusions with the future research scope of this study are presented.</p>