Interpretability improvement of fuzzy systems: Reducing the number of unique singletons in zeroth order Takagi-Sugeno systems

This paper addresses one specific aspect of complexity reduction/interpretability improvement in fuzzy systems - how to limit the number of unique singletons in 0-th order Takagi-Sugeno (TS) systems, where the common practice is to assign an unique singleton to each rule. While abundance of free parameters makes 0-th order TS systems effective in data-driven identification, it also presents a computational load and an obstacle for interpretability and reliability of fuzzy rules. The developed reduction algorithm that utilizes singleton mapping matrix, subtractive clustering and least squares estimation algorithms, is able to bring the number of unique singletons down to the desired level without substantial accuracy loss.