A Stackelberg game-based collaborative decision optimization method for digital-intelligent industrial chains under probabilistic hesitant fuzzy information

Collaborative decision-making in the digital-intelligent industrial chain is often affected by fuzzy judgment, hesitation and probabilistic uncertainty. Traditional deterministic game models are unable to incorporate the detailed preferences mentioned above. Therefore, this paper proposes a collaborative decision-making optimisation method that combines Stackelberg game theory and probabilistic hesitant fuzzy information. An enhanced probabilistic hesitant fuzzy element, IPHFE, has been introduced by taking into account information confidence and decision risk, and a weighted geometric-arithmetic aggregation operator has been developed for fusing uncertain preferences. Based on the above, a two-tier Stackelberg game model has been built for core enterprises and node enterprises, and data sharing, revenue transfer and collaborative investment are set as the main strategic variables. A hybrid IPHF-ADE algorithm combining backward induction and adaptive differential evolution is then designed to solve the fuzzy game equilibrium. A Validation for the electronic manufacturing industrial chain is employed. The increased total industrial chain utility of the proposed method compared to Fuzzy-SG is 6.6%, and compared to Crisp-SG is 11.1%. The cooperative efficiency index is 0.812 and the fairness Gini coefficient is 0.219. Robustness tests show that the equilibrium deviation is still less than 10% after a 20% noise disturbance. Therefore, it can be expected that the new way of working will be stable in the face of multiple risks.