Probabilistic hesitant fuzzy TOPSIS emergency decision-making method based on the cumulative prospect theory

In order to fully consider the decision-maker's limited rationality and attitude to risk, this paper constructs the probabilistic hesitant fuzzy TOPSIS emergency decision-making model based on the cumulative prospect theory under the probabilistic hesitant fuzzy environment. Aiming at the problem of missing probabilistic information in the probabilistic hesitant fuzzy element, a new complement scheme is proposed. In this scheme, the weighted average result of the original data information is used to complement, and the original data information is retained to a large extent. Then this paper proposes several probabilistic hesitant fuzzy distance measures based on Lance distance. The decision reference point is constructed by the probabilistic hesitant fuzzy Lance distance, which overcomes the influence of the extreme value on the decision-making result, and defines the value function based on the probabilistic hesitant fuzzy Lance distance. In view of the fact that the attribute weights are completely unknown, the probabilistic hesitant fuzzy exponential entropy is constructed by using the actual data, and the attribute weights of different prospect states are obtained. Aiming at the problem that attribute weights of different prospect states have different effects on the cumulative prospect value, the expression of the cumulative prospect value is improved. The improved closeness coefficient of the TOPSIS method is used to order the emergency schemes. Finally, the new method is applied to the emergency decision-making case of a sudden outbreak of epidemic respiratory disease. The results show that the contrast of the new method is obvious, which is conducive to distinguish different schemes. The new method is more suitable for the complex and changeable emergency decision-making field.