Neutrosophic sets and its application to decision support have become a topic of great importance. In this paper, a new model for decision making for software quality appraisal is presented based on single valued neutrosophic number (SVN-numbers) and the fuzzy decision map method (FDM). The proposed framework is composed of four activities, framework, criteria weighting, gathering information and rating alternatives. Software alternatives are rated based on aggregation operator and the ranking of alternatives is based on scoring and accuracy functions. The FDM method is included and allows a correct weighting of different criteria involved. Additionally the common decision resolution scheme for helping decision maker to reach a reliable decision is used giving methodological support t. A case study is developed showing the applicability of the proposal for software quality appraisal. Further works will concentrate in extending the proposal for group decision making and developing a software tool.