Two prospect theory-based decision-making models using data envelopment analysis with hesitant fuzzy linguistic information

Abstract The ultimate goal of the optimal alternative selection decision-making is to achieve higher returns with as few risks as possible. However, the existing multi-attribute decision-making (MADM) methods rarely measure their returns and risks simultaneously. In addition, these methods have no clear explanation for how to improve the non-optimal alternatives. Considering this, this paper constructs the returns and risks of alternatives in an identical measurement system by extending DEA model, thereby selecting the optimal alternative more comprehensively and improving the non-optimal alternatives. First, considering the bounded rationality of experts, the prospect theory is introduced into the information evaluation using hesitant fuzzy linguistic term sets to fully characterize the experts' psychological behavior under uncertainty. Then, by constructing the return-risk ratio as the efficiency evaluation index, two prospect theory-based hesitant fuzzy linguistic superefficiency models, namely the risk-oriented (RIHFLS) and return-oriented (REHFLS) models, are proposed to fully rank the alternatives. Furthermore, these two models are extended to RIHFLPS and REHFLPS models considering different importance of attributes. By adjusting the returns and risks to the target values, the non-optimal alternatives can be enhanced to efficient state. Finally, the feasibility and superiority of the proposed methods are verified by an application example.