ANALYSIS OF THE UNCERTAINTY MODELING PROPERTY OF A PARALLELOGRAM MEMBERSHIP FUNCTION IN TYPE-2 FUZZY LOGIC SYSTEMS AS APPLIED TO NONLINEAR SYSTEMS

In fuzzy systems, the membership function (MF) is crucial. The best MF for a specific fuzzy system is highly dependent on the nature of the problem that the fuzzy system is supposed to solve. As a result, proper MF selection is needed to improve the fuzzy system¿s efficiency. This study aims to evaluate the applicability of a novel parallelogram MF in nonlinear system modelling and control. The proposed type-2 MF has a crisp membership degree at the endpoints of the footprint of uncertainty (FOU) and uncertain values in-between. When dealing with data whose membership degree is certain at the boundary but uncertain in the in-between, the proposed MF having its highest uncertainty at the midpoint of the MF width is advantageous. Tuning the parameters of the proposed MF will provide a variety of triangular and quadrilateral FOU shapes that better capture the uncertainties in the training data. The gradient descent learning algorithm was used to tune the consequent parameters of the evaluated interval type-2 fuzzy system. The performance results demonstrated the parallelogram MF based fuzzy system¿s capability in modelling and control tasks. A comparison of our suggested MF¿s performance with Gaussian, elliptical, and triangular MF reveals the regions where it excels. © 2025, Scibulcom Ltd.. All rights reserved.