Type-2 fuzzy logic systems

TLDR

Type‑reduction methods extend type‑1 defuzzification, capturing more rule‑uncertainty information but are computationally intensive except for interval type‑2 sets, for which we provide a simple procedure. The study introduces a type‑2 fuzzy logic system that handles rule uncertainties. The type‑2 FLS is implemented via fuzzification, inference, and output processing, focusing on type‑reduction and defuzzification, with a simple computation procedure for interval type‑2 sets. Applied to time‑varying channel equalization, the type‑2 FLS outperforms a type‑1 FLS and a nearest‑neighbor classifier.

Abstract

We introduce a type-2 fuzzy logic system (FLS), which can handle rule uncertainties. The implementation of this type-2 FLS involves the operations of fuzzification, inference, and output processing. We focus on "output processing," which consists of type reduction and defuzzification. Type-reduction methods are extended versions of type-1 defuzzification methods. Type reduction captures more information about rule uncertainties than does the defuzzified value (a crisp number), however, it is computationally intensive, except for interval type-2 fuzzy sets for which we provide a simple type-reduction computation procedure. We also apply a type-2 FLS to time-varying channel equalization and demonstrate that it provides better performance than a type-1 FLS and nearest neighbor classifier.