The paper aims at solving the shortcomings of existing entropy measures of probabilistic hesitant fuzzy elements (PHFEs), which are either too complex in structure or too weak in discriminating ability, and proposes some hybrid entropy measures of PHFEs. The hybrid entropy measures of PHFEs can comprehensively reflect their individual and collective uncertainties, and possess some advantages of simple structure, clear physical meaning and strong discriminating ability. Based on normalized PHFEs, some hybrid cross-entropy measures of PHFEs are designed with the construction method of hybrid entropy measures, which can overcome the design flaws of existing cross-entropy measures, comprehensively reflect the individual and collective discrimination degrees between PHFEs, and possess natural symmetry. Based on proposed entropy and cross-entropy measures, a multi-attribute decision-making(MADM) method with PHFEs is further developed and applied to evaluate the combat effectiveness of UAV clusters. Numerical and theoretical results show that hybrid entropy and cross-entropy measures of PHFEs, which can be designed in pairs and supportive to each other, have a wide range of applications.