Neutrosophic Refined Power Mean Operator and Its Application to MADM Problems Based on Cross-Entropy Measures

In real-world decision-making, constructing mathematical models is often difficult because the data are incomplete, uncertain, or even contradictory. The neutrosophic refined set provides a robust and flexible approach for effectively handling and representing these types of uncertainties. Various studies have highlighted its significant applications in decision making. In this study, a power mean operator is introduced to aggregate multiple Neutrosophic Refined Sets (NRSs) into a Single-Valued Neutrosophic Set (SVNs). The core mathematical properties of the newly introduced neutrosophic refined power mean operator are established. Moreover, two categories of neutrosophic refined cross-entropy measures are presented: one adapted from the SVNs-cross-entropy measure, and the other specifically formulated for neutrosophic refined sets. By employing the defined measures, an innovative decision making strategy is developed under the neutrosophic refined set environment. To demonstrate the effectiveness and practical relevance of the grounded strategy a numerical example based on the selection of an educational stream is solved.