Assessment of industrial fault diagnosis using rough approximations of fuzzy hypersoft sets.

Reliable and timely fault diagnosis is critical for the safe and efficient operation of industrial systems. However, conventional diagnostic methods often struggle to handle uncertainties, vague data, and interdependent multi-criteria parameters, which can lead to incomplete or inaccurate results. Existing techniques are limited in their ability to manage hierarchical decision structures and overlapping information under real-world conditions. To address these limitations, this paper proposes a novel diagnostic framework based on Hypersoft Fuzzy Rough Set (HSFRS) theory.This hybrid approach integrates the flexibility of hypersoft sets for modeling multi-parameter relationships, the strength of fuzzy logic in handling vagueness, and the approximation capabilities of rough set theory to manage data uncertainty. Using a pseudo fuzzy binary relation, we define lower and upper approximation operators for fuzzy subsets within the parameter space. An enhanced Bingzhen and Weimin model-based decision-making algorithm is developed to support intelligent diagnosis. A case study involving a conveyor belt system is presented, evaluating eight fault states using five primary parameters and twenty sub-parameters. The results confirm the robustness, interpretability, and effectiveness of the proposed model in complex industrial scenarios by ranking the states based on fuzzy hypersoft closeness degrees.