A novel multi-granularity variable precision neutrosophic rough set and group decision-making application with three strategies

This paper proposes a novel neutrosophic rough set model to solve group decision-making problems. First, we proposed a novel multi-granularity variable-precision neutrosophic rough set model, which included three basic models: optimistic, pessimistic, and compromise. Second, the properties of the upper and lower approximations of the multi-granularity variable-precision neutrosophic rough set were investigated by means of the residual implications of triangular norms, and their favorable algebraic properties were proved. Finally, the effectiveness, stability, and sensitivity of the three proposed models were verified through a multi-attribute group decision-making example in a single universe, and the experimental results showed that this method could accurately rank the targets. In summary, our method provided multiple strategies and fault tolerance.