Optimally Evolving Irregular-Shaped Membership Functions for Fuzzy Systems

Membership functions (MFs) are the most crucial components of a fuzzy system; hence improving their design is a much worthy endeavor. This paper presents a novel genetic-based approach for generating a highly generic type of MF called irregular-shaped membership function (ISMF). Defined with unevenly spaced sampling points, ISMFs are more flexible than common MF types. They can model any other shape to best match the problem domain. A GA using specifically designed coding and decoding schemes is selected as the most suitable learning mechanism, which efficiently evolves accurate ISMFs while enhancing their interpretability. Generated ISMFs are benchmarked against common MF types and are shown to consistently yield better system performance.