A decision-making framework based on prospect theory with probabilistic linguistic term sets

Abstract

In real-world decisions, we often encounter situations when decision-makers’ (DMs’) preferences can only be expressed as uncertain linguistic terms instead of crisp values. Similarly, when decisions involving several risky prospects with linguistic outcome information, it is a challenge to properly calculate the corresponding prospect values. To address this issue, this paper proposes a decision-making framework based on prospect theory where the outcomes are characterized by probabilistic linguistic term sets (PLTSs). The key contributions of this research are twofold: Firstly, it allows DMs to express their assessment of outcomes in terms of linguistic terms with interval probabilities. Secondly, it furnishes a paradigm to extend prospect theory to accommodate other forms of fuzzy and linguistic input. To begin with, this paper first presents different types of PLTSs. Then, gains and losses are calculated based on the positive and negative reference points and the operation rules of PLTSs. In accordance with the value and probability weight functions, the weighted prospect values are determined. Finally, we apply the decision-making framework to a practical case to illustrate its feasibility under linguistic environment.

Keywords:

• Prospect theory
• probabilistic linguistic term sets
• interval probability
• multi-criteria decision-making

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 Certainty Effect implies that DMs under-weigh outcomes that are merely probable in comparison with outcomes that are obtained with certainty.

2 Isolation Effect demonstrates that DMs generally discard components that are shared by all prospects under consideration.

3 Reflection Effect indicates that risk aversion in the positive domain is accompanied by risk seeking in the negative domain.

Additional information

Funding

The work was supported in part by the China National Natural Science Foundation (Nos. 71401116, 71771155, 71571123) and funded by Sichuan University.