A new decision analysis framework for multi-attribute decision-making under interval uncertainty

In decision-making analysis, the description on decision makers' risk attitude under uncertainty is a focus topic. This paper presents a novel decision analysis framework that considers uncertainty and risk using the cumulative prospect theory. The proposed approach describes uncertain preference information using interval-valued fuzzy sets, maintaining this representation without converting intervals into crisp numbers throughout the entire process. To quantify the distance between interval-valued fuzzy sets, we introduce a comprehensive interval-valued distance model that accounts for multiple situations determined based on the relative positions between intervals. Afterwards, some related theorems about the proposed interval-valued distance model are explored mathematically. Then, with the aid of different reference points and interval-valued distance model, the overall interval-valued prospect value of each alternative is investigated. Finally, an Enhanced Minimax Regret-based (EMR) approach is developed to compare and rank the obtained overall interval-valued prospect values. An illustrative example, accompanied by detailed discussions, is provided to demonstrate the flexibility and superiority of the proposed decision analysis framework.