Integration of Theoretical Foundations and Practical Implications for Neutrosophic Set Theory in Real-Time Maintenance Decision Systems (Contemporary Mathematics, 2025)
In the present era, the concepts of neutrosophic set theory are essential for handling uncertain data with three distinct components. Researchers across various fields widely use these concepts due to their significant applications. Our world is filled with unpredictability, ambiguity, and vagueness, making it crucial to replace items at the appropriate time. This research paper focuses on the importance of addressing the replacement issue to improve reliability in maintenance scheduling. Ambiguity and uncertainty were present challenges in resolving maintenance issues. For example, the group replacement model has been solved using single-valued unique hexagonal neutrosophic numbers and the enhanced score function for hexagonal neutrosophic numbers (HNN) discussed in this paper. Additionally, the removal area method is used to determine the de-eutrophication of the linear neutrosophic hexagonal number, showing significant improvement in the clarification of HNN. MATLAB code is employed for de-eutrophication and to assess the effectiveness of this method. Numerical examples are provided to validate the proposed method. Using this enhanced score function, the replacement problem has been solved in a hexagonal neutrosophic environment. A comparative study was conducted between the established and proposed methods, which will benefit researchers in the field of neutrosophic domain in the future.
Keywords: area removal method, MATLAB, replacement model, score function, single-valued unique hexagonal neutrosophic number