Fuzzy Modeling of High-Dimensional Systems: Complexity Reduction and Interpretability Improvement

Abstract—Fuzzy modeling of high-dimensional systems is a challenging topic. This paper proposes an effective approach to data-based fuzzy modeling of high-dimensional systems. An initial fuzzy rule system is generated based on the conclusion that optimal fuzzy rules cover extrema [8]. Redundant rules are removed based on a fuzzy similarity measure. Then, the structure and parameters of the fuzzy system are optimized using a genetic algorithm and the gradient method. During optimization, rules that have a very low firing strength are deleted. Finally, interpretability of the fuzzy system is improved by fine training the fuzzy rules with regularization. The resulting fuzzy system generated by this method has the following distinct features: 1) the fuzzy system is quite simplified; 2) the fuzzy system is interpretable; and 3) the dependencies between the inputs and the output are clearly shown. This method has successfully been applied to a system that has 11 inputs and one output with 20 000 training data and 80 000 test data. Index Terms—Complexity reduction, fuzzy modeling, interpretability, optimization, regularization. I