Neutrosophic soft set is one of the generalizations of classical set theory with parameters. We have introduced weighted similarity measure using the normalized orthogonal distance between two single valued neutrosophic soft sets and their characteristics. Further, a decision-making framework is proposed through an algorithm for multi attribute decision making neutrosophic soft scenario. We also apply the proposed weighted similarity measure to the clinical application; identify the best type of radiotherapy treatment for tumor of moving organs such as lungs or chest walls by evaluating certain medical parameters and computation of mathematical ranking model, which are then compared with other existing similarity measures to illustrate the feasibility of the same.