A New Approach to Automatic and Optimal Membership Function Generation for Fuzzy System Modelling

During the last few decades, the optimization-based data-driven approach has been widely used for generating membership functions in fuzzy-based systems, where the shapes of membership functions are mostly considered either triangular or trapezoidal. However, the number of parameters that are required to be estimated for a triangular membership function is three (left vertex, center, and right vertex). For a trapezoidal membership function, it is four (left base point, left shoulder, right base point, and right shoulder). Whereas, the number of parameters required for a Gaussian membership function is two (mean and standard deviation). Therefore, a fuzzy system modelled using the Gaussian membership function can significantly reduce the number of parameters when the number of subsets for the antecedent and consequent membership functions is large. However, not much attention is given to designing fuzzy models with Gaussian-shaped membership functions; most of the existing fuzzy modelling techniques impose many restrictions on the membership functions’ parameters. As a result, the flexibility and scope of the optimization techniques are reduced. This study, therefore, suggests a novel optimization-based technique to frame fuzzy membership functions in which the membership functions are Gaussian-shaped, and very few restrictions are imposed on the parameter selection. A comparative analysis is carried out between the conventional method and the proposed method with different optimization techniques (Differential Evolution (DE), Particle Swarm Optimization (PSO), and Genetic Algorithm (GA)) to approximate four standard nonlinear functions.