Projection and bidirectional projection measures of single-valued neutrosophic sets and their decision-making method for mechanical design schemes

Projection measure is one of important tools for handling decision-making problems. First, the paper proposes projection and bidirectional projection measures between single-valued neutrosophic sets, and then the comparison of numerical examples shows that the bidirectional projection measure is superior to the general projection measure in measuring closeness degree between two vectors. Next, we develop their decision-making method for selecting mechanical design schemes under a single-valued neutrosophic environment. Through the projection measure or bidirectional projection measure between each alternative and the ideal alternative with single-valued neutrosophic information, all the alternatives can be ranked and the best one can be selected as well. Finally, the proposed decision-making method is applied to the selection of design schemes of punching machine and its effectiveness and advantages are demonstrated by comparison with relative methods.