In view of the complex calculation process and counter-intuitive phenomena of the existing entropy measures of hesitant fuzzy sets, a comprehensive hesitant fuzzy entropy is proposed. At the same time, the traditional TOPSIS method is improved based on the cumulative prospect theory, and a multi-attribute decision-making model with unknown attribute weights is constructed. First, a new definition of hesitation fuzzy entropy is offered based on fuzziness and uncertainty. Then, the comprehensive hesitation fuzzy entropy of the hesitation fuzzy element is provided, and it is shown that it fulfills the new axiomatic definition. Additionally, the results compared with the existing entropys demonstrate that the proposed entropy not only more accurately captures the fuzziness of hesitant fuzzy elements, but also resolves the paradoxical phenomena. Finally, the comprehensive entropy measure is applied and analyzed using the improved TOPSIS method. The case study serves as evidence for the success of the proposed approach. In addition, when compared to the existing entropies, the comprehensive hesitant fuzzy entropy offers the benefits of straightforward calculation and simple comprehension, at the same time, the improved TOPSIS method can take into account the psychological preferences of decision makers, and the effect is more reasonable than traditional methods.