“d score” for type-2 fuzzy number incorporating the interaction between fast thinking and slow thinking

Modeling human thinking process is essential in decision making. According to dual-process theory, fast thinking and slow thinking in our brains shape our judgments and decisions. Type-2 fuzzy number (T2FN) models the shaping process with these two thinking patterns. However, how to model the interaction between them is a mystery, which can be referred as interactive thinking. In this paper, we propose a d score of T2FN to reveal their interaction mechanism, where an interaction coefficient θ is used to measure the interaction. This score describes fast and slow thinking patterns and the transformation process between them, and how the interaction helps decision makers make better decisions. We propose two optimization models to solve for the coefficient θ. With the collected data based on questionnaires, we find a dominant role of interactive thinking in practice. In particular, it is most common that fast thinking and slow thinking play equally important roles in forming our judgments. Moreover, our results suggest that fast thinking tends to correspond with questions that contain complex information, while slow thinking tends to correspond with simple information.