Interval type-2 fuzzy logic systems: theory and design

TLDR

The study develops the theory and design framework for interval type‑2 fuzzy logic systems, including efficient inference and parameter‑tuning methods. The authors introduce a simplified inference algorithm based on a general formula, define upper and lower membership functions, illustrate it with Gaussian primary MFs, and propose a parameter‑tuning approach for interval type‑2 FLSs. Applying the proposed system to noisy, non‑stationary time‑series forecasting, the authors demonstrate that interval type‑2 FLSs outperform type‑1 FLSs under uncertain signal‑to‑noise ratios.

Abstract

We present the theory and design of interval type-2 fuzzy logic systems (FLSs). We propose an efficient and simplified method to compute the input and antecedent operations for interval type-2 FLSs: one that is based on a general inference formula for them. We introduce the concept of upper and lower membership functions (MFs) and illustrate our efficient inference method for the case of Gaussian primary MFs. We also propose a method for designing an interval type-2 FLS in which we tune its parameters. Finally, we design type-2 FLSs to perform time-series forecasting when a nonstationary time-series is corrupted by additive noise where SNR is uncertain and demonstrate an improved performance over type-1 FLSs.