Recently, decision making problems has prompted extensive awareness, especially multi-attribute decision-making problem in single valued neutrosophic sets. Given the inherent characteristics of this case, a multi-attribute decision-making problem with a single valued neutrosophic sets(SVN-sets) is explored with both weights and attribute ratings expressed by single valued neutrosophic information. Firstly, some basic concepts concerning SVN-sets are reviewed for the subsequent analysis. Secondly, a linear optimization method of SVN-sets are developed to describe the sensitivity analysis of attribute weights which give changing intervals of attribute weights in which the ranking order of the alternatives is required to remain unchanging. Finally, we presented an illustrative example to show its applicability and effectiveness. Publisher's Version