Three-Way Decision Method Within Prospect Theory Via Intuitionistic Fuzzy Numbers in Multi-Scale Decision Information Systems

The integration of granular computing within human-inspired computational intelligence is crucial for addressing the complexities and uncertainties inherent in information. By offering a robust framework, granular computing empowers the field to effectively navigate and manage such challenging information, thereby facilitating human- like reasoning and decision-making capabilities. Additionally, granular computing promotes a holistic and interdisciplinary approach to the development of intelligent systems. Within this context, a multi-scale information system (MSIS) serves as a complex Big Data system with inherent fuzziness. It allows for the comprehensive description of problems at different granularities and levels, presenting an opportunity to extract valuable knowledge for decision-making research. However, achieving effective collaboration between humans and machines during the decision-making process remains a significant task that warrants attention. Consequently, the paper introduces a novel method known as PT-IF-G3WD, which is based on prospect theory and utilizes intuitionistic fuzzy numbers (IFNs). By focusing on the challenges of decision risks and bounded rationality in uncertain multi-scale decision information systems (MSDISs), the primary objective of this method is to address the needs of MSDISs within a generalized three-way decision (G3WD) framework. In particular, this paper introduces a matrix theory-based $q$ -consistent sub-system extraction mechanism as the initial design, which enables rapid attainment of optimal information acquisition. Second, the data information from multiple optimal sub-systems is fused using a group decision-making (GDM) perspective, incorporating binary relationships among the objects to accomplish the global evaluation of the objects. Lastly, novel rules for three-way classification and ranking are developed, taking into account the perspective of IFNs. The experimental results on real-world datasets demonstrate the effectiveness and stability of the PT-IF-G3WD method.