Multi-Objective Reliability–Cost Optimization of Repairable Industrial Systems under Pythagorean and Intuitionistic Fuzzy Kolmogorov Uncertainty

Abstract

This study presents a comparative optimization methodology for repairable industrial systems subject to generalized fuzzy uncertainty. We incorporate Pythagorean fuzzy sets (PFS) into dynamic Markov availability models and evaluate their behavior alongside standard intuitionistic fuzzy sets (IFS). The quadratic boundary of PFS expands non-membership supports by approximately 28% relative to the linear IFS boundary. This geometric expansion produces more conservative availability estimates, which accurately mirror epistemic ambiguity in operational failure and repair records. Three metaheuristic algorithms—multi-objective particle swarm optimization with an external repository (MOPSO), non-dominated sorting genetic algorithm II (NSGA II), and decomposition-based evolutionary optimization (MOEA/D)—are tested on two full-scale plants: a rice milling facility and a thermal power station. Both systems are modeled through Kolmogorov differential systems coupled with time-dependent Weibull failure hazards. The optimization problem simultaneously maximizes steady-state availability and minimizes lifecycle maintenance expenses while satisfying operational availability thresholds. Across five independent random seeds, MOPSO achieves superior hypervolume values (112,640 for the rice mill and 399,893 for the thermal plant) and the lowest inverted generational distance, whereas NSGA-II exhibits uniform solution spread. Transitioning from IFS to PFS shifts Pareto frontiers toward lower availability and higher maintenance expenditure. Time-dependent Weibull hazards reduce knee-point availability by 5% to 7% compared to constant-rate models. These findings emphasize the practical necessity of accounting for component aging and broader non-membership margins during system planning.