A prospect-regret theory-based three-way decision model with intuitionistic fuzzy numbers under incomplete multi-scale decision information systems

As a new data representation in the big data era, a multi-scale decision information system (MSDIS) realizes “multi-level, multi-angle and multi-view” evaluations in various problems. However, most of existing multi-scale data analysis models are built for complete information systems (CISs), whereas the research on incomplete multi-scale decision information systems (I-MSDISs) is not perfect. Additionally, the irrational behavior of one decision-maker (DM) often has an impact on decision outcomes. On this basis, this paper develops a prospect-regret theory-based three-way decision (3WD) model with intuitionistic fuzzy numbers (IFNs) under an I-MSDIS, which is abbreviated as PR-3WD-I-MSDIS. Specifically, we first select the optimal scale combination of I-MSDISs by the matrix theory to complete the information extraction of incomplete optimal sub-systems. Then, we further propose an attribute weight evaluation strategy under the incomplete optimal subsystem, which fully considers the neighborhood information of each object. Subsequently, the concept and calculation method of aggregated weighted fuzzy conditional probabilities are constructed from the perspective of intuitionistic fuzzy sets. Furthermore, a prospect-regret theory-based relative profit function is proposed, which sufficiently takes into account the loss and utility in decision-making processes. Finally, a novel three-way classification and ranking method is developed for solving incomplete multi-scale problems. The experimental results on real-world datasets demonstrate that the PR-3WD-I-MSDIS model achieves excellent performance.