TYPE-4 FUZZY LOGIC SYSTEMS FOR HIERARCHICAL UNCERTAINTY: THEORY, ALGORITHMS, AND APPLICATIONS IN DECISION SUPPORT

Abstract

Higher-order fuzzy systems such as Type-2 and Type-3 models enhance robustness by representing uncertainty at multiple levels, yet they remain limited when uncertainty extends to the distribution of meta-membership functions themselves. This paper proposes a Type-4 Fuzzy Logic System (T4-FLS) as a generalized framework for hierarchical uncertainty modeling. A formal definition of Type-4 fuzzy sets is presented, together with a hierarchical type-reduction algorithm that progressively collapses Type-4 → Type-3 → Type-2 → Type-1 representations via nested α-cuts and centroid computations. Theoretical properties, reduction consistency, and computational complexity are analyzed. The practical utility of T4-FLS is demonstrated in two case studies: (i) chaotic time-series forecasting and (ii) clinical risk stratification for sepsis patients. Across both tasks, T4-FLS outperformed Type-1, Type-2, and Type-3 systems in AUROC, calibration error, and robustness to noise, while maintaining interpretability and computational efficiency. These results highlight the potential of Type-4 fuzzy systems as a next-generation decision-support tool in high-uncertainty domains such as healthcare and nonlinear dynamics.