Enhanced optimization using q-rung picture fuzzy numbers and dynamic programming

Abstract Q-Rung Picture Fuzzy Numbers (q-RPFNs) have recently gained attention as a powerful framework for modelling uncertainty in complex decision-making environments. Unlike conventional fuzzy set theories q-RPFNs offer enhanced expressive capability by simultaneously capturing degrees of membership, non-membership, and hesitation with greater flexibility. This makes them particularly suitable for real-world problems where information is incomplete, ambiguous or inconsistent. In this research work a novel methodology is developed to solve Linear Programming Problems (LPPs) in uncertain settings by incorporating q-RPFNs. The proposed model integrates q-rung picture fuzzy arithmetic with fuzzy dynamic programming enabling a structured and systematic approach to handle multi-stage decision processes under uncertainty. This hybridization allows the model to effectively manage vagueness while maintaining computational tractability. The key significance of this study lies in its ability to bridge the gap between advanced fuzzy representation and optimization techniques. By embedding q-RPFNs into the dynamic programming framework the proposed approach enhances the robustness and adaptability of the solution process. It provides decision-makers with more reliable and realistic outcomes particularly in environments characterized by fluctuating and imprecise data. The novelty of the research stems from the seamless integration of q-rung picture fuzzy theory with dynamic programming for LPPs which has not been extensively explored in existing literature. This combined framework not only improves the accuracy of solutions but also offers a flexible mechanism to model higher degrees of uncertainty compared to traditional and other fuzzy extensions. Overall, the findings confirm that the proposed approach is both practical and efficient yielding superior solution quality and improved decision support for optimization problems in uncertain and fuzzy contexts.