A novel neuro-fuzzy model named fuzzy broad learning system (BLS) is proposed by merging the Takagi–Sugeno (TS) fuzzy system into BLS. The fuzzy BLS replaces the feature nodes of BLS with a group of TS fuzzy subsystems, and the input data are processed by each of them. Instead of aggregating the outputs of fuzzy rules produced by every fuzzy subsystem into one value immediately, all of them are sent to the enhancement layer for further nonlinear transformation to preserve the characteristic of inputs. The defuzzification outputs of all fuzzy subsystem and the outputs of enhancement layer are combined together to obtain the model output. The ${k}$ -means method is employed to determine the centers of Gaussian membership functions in antecedent part and the number of fuzzy rules. The parameters that need to be calculated in a fuzzy BLS are the weights connecting the outputs of enhancement layer to model output and the randomly initialized coefficients of polynomials in consequent part in fuzzy subsystems, which can be calculated analytically. Therefore, fuzzy BLS retains the fast computational nature of BLS. The proposed fuzzy BLS is evaluated by some popular benchmarks for regression and classification, and compared with some state-of-the-art nonfuzzy and neuro-fuzzy approaches. The results indicate that fuzzy BLS outperforms other models involved. Moreover, fuzzy BLS shows advantages over neuro-fuzzy models regarding to the number of fuzzy rules and training time, which can ease the problem of rule explosion to some extent.

中文翻译：

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模糊广义学习系统：一种用于分类和回归的新型神经模糊模型

通过将Takagi-Sugeno（TS）模糊系统合并到BLS中，提出了一种称为模糊广义学习系统（BLS）的新型神经模糊模型。模糊BLS用一组TS模糊子系统替换BLS的特征节点，并且输入数据由每个子系统处理。与其将每个模糊子系统产生的模糊规则的输出立即汇总为一个值，不如将它们全部发送到增强层以进行进一步的非线性变换，以保留输入的特性。将所有模糊子系统的去模糊化输出和增强层的输出组合在一起，以获得模型输出。采用$ {k} $ -means方法确定前部分的高斯隶属函数的中心以及模糊规则的数量。在模糊BLS中需要计算的参数是将增强层的输出连接到模型输出的权重，以及随后在模糊子系统中多项式的随机初始化的多项式的系数，这些可以通过解析来计算。因此，模糊BLS保留了BLS的快速计算特性。所提出的模糊BLS已通过一些流行的基准进行了回归和分类评估，并与一些最新的非模糊和神经模糊方法进行了比较。结果表明，模糊BLS优于其他模型。此外，就模糊规则的数量和训练时间而言，模糊BLS在神经模糊模型方面显示出优势，可以在一定程度上缓解规则爆炸的问题。