<p>Neutrosophic soft rough sets are a valuable mathematical tool for dealing with uncertainty, inconsistency and ambiguity. The aim of this paper is to develop new decision-making methods to deal with uncertainties in real-world problems using neutrosophic soft rough sets. First, this paper defines several concepts used in decision-making methods on neutrosophic soft rough sets, including neutrosophic soft rough matrices, neutrosophic soft rough numbers, sum of neutrosophic soft rough numbers, cumulative geometric operators, discriminant measures and ranking concepts. Furthermore, using these newly defined concepts, we develop two different algorithms for decision-making methods. First, we introduce the multi-criteria decision-making method (MCDM) to determine the best option among several alternatives. In this method, we present an algorithm that uses the sum operator and ranking concepts associated with neutrosophic soft rough numbers. Traditional sharp techniques are generally ineffective in solving multi-criteria decision-making (MCDM) problems due to language and interpretation issues. To address this, we propose an alternative method known as the Technique for Similarity to Ideal Solution Rank Preference (TOPSIS). This method helps to identify the decision option that is closest to the positive ideal solution and farthest from the negative ideal solution. In this decision-making method, we present an algorithm that uses concepts such as neutrosophic soft rough matrices, neutrosophic soft rough numbers, and the cumulative geometric operator of neutrosophic soft rough numbers along with a separation measure. Finally, we provide a numerical example on medical diagnosis, illustrated by a hypothetical case study applying the proposed decision-making methods. Additionally, we compare the results obtained from these methods.</p>