Research Of Fuzzy Modeling Based On The Fireworks Optimization Algorithm

Fuzzy systems could be constructed based on expert knowledge by comprehensible way and have been widely applied to various areas such as pattern recognition, data mining, due to their ability of dealing with uncertain and incomplete information. The fireworks algorithm is preformed to optimize the structure and parameters of the fuzzy model in this paper, which presents a better trade-off between interpretability and accuracy.The structure and characteristics of fuzzy system are introduced. The structure and parameters of fuzzy rule are described, and the methods of calculating the system output are introduced for the two common systems: Takagi-Sugeno fuzzy system and fuzzy classification system. The interpretability of fuzzy system is analyzed qualitatively from the aspects of input variables, fuzzy sets and fuzzy rules.First of all, the features selection is performed to decrease the dimension of model for high dimension system. The construction of fuzzy model mainly includes two parts: initial fuzzy modeling and the model optimization. The initial fuzzy model is formed by the fuzzy C-means algorithm, then, the model structure and parameters are optimized by the fireworks algorithm to improve the accuracy and interpretability of fuzzy model simultaneously. During the optimization process, the fuzzy sets and rules are simplified based on the simplification method to increase the model interpretability under the premise of accuracy requirement. The experiments on the second-order non-linear system and three classical benchmark classification problems are conducted to investigate the proposed modeling method based on fuzzy clustering and fireworks algorithm.To further enhance the performance of the model optimization, we combine the fireworks optimization algorithm with differential evolution operators, which enable the individuals to make use of the beneficial information in the swarm, improve the diversity of the swarm, enlarge the search space and avoid being trapped in local optima too early. On the basis of objective functions value, the non-dominated sorting algorithm and crowding-distance evaluation are performed to sort all the current individuals, and the individuals of high quality are selected for the next generation using the notion of Pareto dominance. The proposed fuzzy modeling approach is applied to the second-order non-linear system and three classical benchmark problems. The experimental results are compared with other existing modeling methods, the comparative results demonstrate that the proposed method leads to compact and human-comprehensible fuzzy model with remarkable accuracy.