A Distributionally Robust Bi-Level Multi-Objective Decision Making Method Under Hybrid Uncertainty

This paper introduces a novel bi-level multi-objective optimization framework designed for decision-making under hybrid uncertainty, where system constraints account for both intuitionistic fuzzy sets and stochastic uncertainties. By combining interval programming and chance-constrained optimization, the proposed method relaxes the commonly adopted assumption of Gaussian distributions for stochastic uncertainties, thereby making it applicable to a wider range of distributional forms, including non-Gaussian scenarios. To effectively handle the interplay between fuzziness and stochasticity, we propose an acceptability index that quantifies uncertainty propagation, ensuring robust solutions that balance both sources of uncertainty. The approach provides a computationally efficient and theoretically sound decision-support tool for complex bi-level optimization problems. Numerical case studies demonstrate its ability to generate high-confidence solutions while offering flexibility in preference modeling.