Generalized FLEXible Fuzzy Inference Systems

In this paper, we propose a new variant for incremental, evolving fuzzy systems extraction from data data streams, termed as GEN-FLEXFIS (short for GENeralized FLEXible Fuzzy Inference Systems). It builds upon the FLEXFIS methodology (published by the authors before) and extends it for generalized Takagi-Sugeno (TS) fuzzy systems, which implement generalized rotated rules in arbitrary position, employing a high-dimensional kernel rather than a connection of one-dimensional components (fuzzy sets) with t-norms. The extension includes the development of the evolving clustering learning engine, termed as eVQ-A, to extract ellipsoidal clusters in arbitrary position. Furthermore, a new merging concept based on a combined adjacency-homogenuity relation between two clusters (rules) is proposed in order to prune unnecessary rules and to keep the complexity of the generalized TS fuzzy systems low. Equipped with a new projection concept for high-dimensional kernels onto one-dimensional fuzzy sets, the new approach also provides equivalent conventional TS fuzzy systems, thus maintaining interpretability when inferring new query samples. GEN-FLEXFIS will be evaluated based on high-dimensional real-world data (streaming) sets in terms of accuracy versus final model complexity, compared with conventional FLEXFIS and other well-known (evolving) fuzzy systems approaches.