Fermatean Fuzzy Approach to Assess Reliability within a Neutralization System

Traditional reliability evaluation frequently ignores complex system aspects, leading to data collection errors and complicating real-world collection and evaluation. To address this issue, this study presents a unique method utilizing Fermatean fuzzy sets (FFS), which is an extension of intuitionistic and Pythagorean fuzzy sets (PFS), in which the sum of the cube of belonging and nonbelonging degrees is less than or equal to 1, to evaluate the Fermatean fuzzy reliability. The study employs triangular Fermatean fuzzy numbers (TFFNs) and utilizes the failure rate parameter method to assess fuzzy reliability under the Pareto distribution and the universal generating function method. This approach is then applied to a neutralizing process system to evaluate its fuzzy reliability and conduct sensitivity tests. The findings are provided in both graphical and tabular formats to improve understanding, and they show how effective this approach is in overcoming the limitations of standard reliability evaluation techniques in complex engineering systems.