The quadripartitioned single-valued neutrosophic set (QSVNS) is developed to understand the concept of indeterminacy more clearly. It takes care of the diverse approaches while dealing with uncertainty under single-valued neutrosophic environment. To make the QSVNS more functional and logical, the notion of quadripartioned single-valued neutrosophic Pythagorean set (QSVNPS) is introduced. In QSVNPS, the components T C U F , , , are dependent in such a manner that T F  1, C U 1 , and 2 2 2 2 T C U F     2 . So, the QSVNPS is a powerful framework for modeling the imprecise human knowledge in a specific manner. To calculate the arithmetic operations, we consider the quadripartitioned single-valued neutrosophic Pythagorean numbers (QSVNPNs) associated with QSVNPSs. The main advantage of using QSVNPNs is that it allows the decision-makers to carry out the calculation on uncertain parameters. The present paper aims to study Dombi operators and to establish some new Dombi weight aggregate operators and develop some properties under QSVNPN environment for solving multi-criteria decision-making(MCDM) problems that we encounter in our day-to-day life process. Then we define the score and accuracy functions for ranking the QSVNPNs to choose the best-preferred alternative that goes through under a set of certain criteria. A model for MCDM problems based on Dombi operators under QSVNPNs has been introduced. To check the feasibility of the new approach, a numerical example is demonstrated that shows the effectiveness of the proposed model for multi-criteria decision-making. Finally, a comparative analysis between the rankings, obtained by using the proposed model, of the given set of alternatives under a certain set of criteria gives the optimal choice.