A comprehensive entropy measure of probabilistic hesitant fuzzy information and its application in game decision making

In the realm of strategic decision making, particularly within interactive game-based decision contexts, the rational evaluation and prioritization of expected payoffs pose significant challenges. Decision making processes are often confronted with dual uncertainties, stemming from individual cognitive hesitancy and the inherent fuzziness of strategic options. To address these complexities, probabilistic hesitant fuzzy elements (PHFEs) serve as an effective mathematical framework. Furthermore, a comprehensive entropy measure for probabilistic hesitant fuzzy information is developed and successfully applied to game decision-making processes. Firstly, a new entropy measure method for PHFE is proposed in terms of dual-dimensional characterization of fuzziness and non-specificity. Then, a novel score function for PHFE is introduced by utilizing the proposed entropy foundation, and integrated it into a fuzzy bi-matrix game model. The model can better solve complex game decision making problems, such as ecological management. The framework demonstrates the superiority of strategy selection in complex fuzziness information.