An inverse prospect theory-based algorithm in extended incomplete additive probabilistic linguistic preference relation environment and its application in financial products selection

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.