The energy of multi-valued neutrosophic matrix and neutrosophic hesitant matrix and relationship between them in multi-criteria decision-making

The concept of energy in graphs and matrices is frequently used in all application fields. The energy of a matrix is an extended version of the energy of a graph. The neutrosophic matrix energy concept needs to be more noticeable in multi-criteria decision-making environments. This study presents the concept of the energy of a multi-valued neutrosophic matrix. The upper and lower bounds of the proposed energy were determined. The connection between the neutrosophic hesitant matrix and the multi-valued neutrosophic matrix is provided. Since the parameters of the two matrices differ in truth, indeterminacy, and false entries, the matrix is converted into a single-valued form, and then the energy was calculated. The MCDM problem was addressed with the proposed energy, which is solved by a novel decision-making method. The task is to select a machine from a group of repaired machines in a particular industry that is in good condition. The final ranking values are calculated by the ranking energy formula that decides which is preferred. Then the comparative results were given to demonstrate the accuracy of the proposed energy outcomes.