Selecting financial products is one of the most fundamental investment activities to both individuals and companies, and therefore it is very important to establish an efficient and practical method for financial products selection. To address the challenge of the complicated decision-making environment and decision makers’ expression habits for the selection of financial products, this paper develops the incomplete additive probabilistic linguistic preference relation to depict decision makers’ preferences. Considering that, when decision makers express their opinions using probabilistic linguistic preference relation, it is possible that the sum of the value of the probability information is more than 1, this paper also extends the concepts of probabilistic linguistic term set, additive probabilistic linguistic preference relation and incomplete additive probabilistic linguistic preference relation to improve and ensure their practicability. Moreover, an “inverse prospect theory-based” algorithm is proposed to choose proper financial products. The algorithm processes the original incomplete additive probabilistic linguistic preference relation by using the inverse functions of the prospect theory at first. Then, a priority weights deriving model is established based on the extended concepts. Finally, the numerical case and analysis is presented as the evidences to the conclusion that the proposed algorithm is practical and robust.

选择金融产品是个人和公司最基本的投资活动之一，因此，建立一种高效实用的金融产品选择方法非常重要。为解决复杂的决策环境和决策者的表达习惯对金融产品选择的挑战，本文建立了不完全的加性概率语言偏好关系来描述决策者的偏好。考虑到当决策者使用概率语言偏好关系表达意见时，概率信息的值之和可能大于1，因此本文还扩展了概率语言术语集的概念，通过加性概率语言偏好关系和不完全性加性语言偏好关系来改善并确保其实用性。此外，提出了一种基于“逆向前景理论”的算法来选择合适的金融产品。该算法首先通过使用前景理论的逆函数来处理原始的不完全加性概率语言偏好关系。然后，基于扩展概念建立了优先权重推导模型。最后，通过数值算例和分析，证明了所提算法的实用性和鲁棒性。提出了一种基于“逆向前景理论”的算法来选择合适的金融产品。该算法首先通过使用前景理论的逆函数来处理原始的不完全加性概率语言偏好关系。然后，基于扩展概念建立了优先权重推导模型。最后，通过数值算例和分析，证明了所提算法的实用性和鲁棒性。提出了一种基于“逆向前景理论”的算法来选择合适的金融产品。该算法首先通过使用前景理论的逆函数来处理原始的不完全加性概率语言偏好关系。然后，基于扩展概念建立了优先权重推导模型。最后，通过数值算例和分析，证明了所提算法的实用性和鲁棒性。