Measures of type-2 fuzzy numbers: Balancing fast and slow thinking in decision analysis

Inspired by dual-process theory (DPT), type-2 fuzzy numbers (T2FNs) are introduced to model human judgment. Specifically, the judgment is functioned simultaneously by two systems: the intuitive System 1 referred to as fast thinking, and the analytical System 2 referred to as slow thinking. As a novel modeling tool for decision making, T2FNs have a wide range of potential applications in artificial intelligence, decision analysis, and related domains. To facilitate their extensive application, we adhere to DPT's thinking mechanism, in which the processes of fast and slow thinkings are relatively autonomous while also being capable of mutual cooperation, and then develop some measures for T2FNs, including fuzzy entropy, distance measure, similarity measure, and correlation coefficient. In contrast to the existing fuzzy measures, the proposed ones allow for the quantification of mechanism between fast and slow thinkings. As such, they offer a solid theoretical interpretation for decision analysis. Finally, a numerical example is given to show that the proposed measures are capable of capturing the balanced interplay between fast thinking and slow thinking in human decision making.