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In this study, a design methodology based on fuzzy sets inference and polynomial neural network(PNN) for hierarchically reorganized self-organizing network architecture is introduced to cope with over-fitting as well as multi-collinearity problems which generally appear in a conventional fuzzy neural network. The design method of the proposed self-organizing network structure provides an efficient solution to construct the hierarchically reorganized multi-layer fuzzy neural networks (HRmFNN) architecture through a synergy of multi-techniques such as L<sub>2</sub>-norm regularization, probability theory, and multi-optimization. The overall network structure is realized with the aid of parallel network structure with newly added inputs as well as effective neuron selection method through the exponential-based roulette selection technique for each layer in HRmFNN, and the least square error estimation (LSE)-based learning method with L2-norm regularization is used for constructing the stabilized network architecture, and their ensuring design methodologies result in alleviating the overfitting phenomenon and also enhancing the generalization ability. For the performance enhancement of HRmFNN directly affected by some parameters such as the number of input variables, collocation of the specific subset of input variables, the number of membership functions per each variable, and the order of polynomial in the consequent parts of the fuzzy rules, multi-particle swarm optimization (MPSO) is exploited for the effectively structural as well as parametric optimization of the proposed network. That is, the multi-optimization helps achieve a compromise between the better generation performance and the alleviated over-fitting leading to the stabilization of the proposed multi-layered self-organizing network structure with the aid of synergistic multi-techniques such as a) L<sub>2</sub>-norm regularization-based LSE learning, b) probability theory for effective neuron selection, and c) novel parallel network structure including newly added inputs and neuron selection method. The performance of the proposed network structure is quantified by comprehensive experiments and comparative analysis. It is also demonstrated through the application to cement compressive strength.

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Hierarchically Reorganized Multi-Layer Fuzzy Neural Networks Architecture Driven With the Aid of Node Selection Strategies and Structural Network Optimization