On Modelling of Data-Driven Monotone Zero-Order TSK Fuzzy Inference Systems using a System Identification Framework

Abstract

A system identification-based framework is used to develop monotone fuzzy If-Then rules for formulating monotone zero-order Takagi-Sugeno-Kang (TSK) fuzzy inference systems (FISs) in this paper. Convex and normal trapezoidal and triangular fuzzy sets, together with a strong fuzzy partition strategy (either fixed or adaptive), is adopted. By coupling the strong fuzzy partition with a set of complete and monotone fuzzy If-Then rules, a monotone TSK FIS model can be guaranteed. We show that when a clean multiattribute monotone dataset is used, a system identification-based framework does not guarantee the production of monotone fuzzy If-Then rules, which leads to nonmonotone TSK FIS models. This is a new learning phenomenon that needs to be scrutinized when we design data-based monotone TSK FIS models. Two solutions are proposed: 1) a new monotone fuzzy rule relabeling-based method and 2) a constrained derivative-based optimization method. A new modeling framework with an adaptive fuzzy partition is evaluated. The results indicate that TSK FIS models with better accuracy (a lower sum square error) and a good degree of monotonicity (measured with a monotonicity test) are achieved. In short, the main contributions of this study are validation of the new learning phenomenon and introduction of useful methods for developing data-based monotone TSK FIS models.