Fuzzy set operations

Defuzzification

Type-2 fuzzy sets and systems

Neuro-fuzzy

Mathematics

Data mining

Fuzzy classification

Fuzzy associative matrix

Artificial intelligence

Fuzzy control system

Fuzzy number

Fuzzy rule

Computer science

Fuzzy set

Fuzzy logic

IEEE Transactions on Cybernetics

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.

Fuzzy Broad Learning System: A Novel Neuro-Fuzzy Model for Regression and Classification