Analysis of the Footprint of Uncertainty of a Parallelogram Membership Function
Ahmed Ibrahim, Hai Bo ZHOU, Chao Long ZHANG, Ji An DUAN · International Journal of Artificial Intelligence & Mathematical Sciences · 2022
The general effectiveness of fuzzy representation depends heavily on the membership functions. The bestfootprint of uncertainty for a specific fuzzy system is highly dependent on the nature of the problem that the fuzzysystem is supposed to solve. As a result, a proper footprint of uncertainty size selection is needed to improve the fuzzysystem’s efficiency. This research intends to investigate the impact of a unique linear parallelogram membershipfunction’s footprint of uncertainty on nonlinear system modeling and control. The proposed type-2 membershipfunction has a crisp membership degree at the end points of the footprint of uncertainty and uncertain values inbetween. When dealing with data whose membership degree is certain at the boundary but uncertain in-between, theproposed membership function having its highest uncertainty at the midpoint of the membership function width isadvantageous. Tuning the parameters of the proposed MF will provide a variety of triangular and quadrilateralfootprints of uncertainty shapes that will better capture the training data’s uncertainties. The gradient descent learningalgorithm was used to tune the consequent parameters of the evaluated interval type-2 fuzzy system. The performanceresults demonstrated the effect of the footprint of uncertainty on linear parallelogram membership function-based fuzzysystem’s capability in prediction, identification, and control tasks.