RETRACTED ARTICLE: Tensor based stacked fuzzy neural network for efficient data regression

Random vector functional link and extreme learning machine have been extended by the type-2 fuzzy sets with vector stacked methods, this extension leads to a new way to use tensor to construct learning structure for the type-2 fuzzy sets-based learning framework. In this paper, type-2 fuzzy sets-based random vector functional link, type-2 fuzzy sets-based extreme learning machine and Tikhonov-regularized extreme learning machine are fused into one network, a tensor way of stacking data is used to incorporate the nonlinear mappings when using type-2 fuzzy sets. In this way, the network could learn the sub-structure by three sub-structures’ algorithms, which are merged into one tensor structure via the type-2 fuzzy mapping results. To the stacked single fuzzy neural network, the consequent part parameters learning is implemented by unfolding tensor-based matrix regression. The newly proposed stacked single fuzzy neural network shows a new way to design the hybrid fuzzy neural network with the higher order fuzzy sets and higher order data structure. The effective of the proposed stacked single fuzzy neural network are verified by the classical testing benchmarks and several statistical testing methods. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s00500-022-07402-3.