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In this paper, a new switching sequence convex optimization (SSCO) algorithm is proposed for solving non-convex optimization problem with complex time-varying relaxation matrix structures that arises during output feedback design. Firstly, the introduced time-varying relaxation matrix combines the membership functions and the designed switching mechanism to adjust the positive and negative terms of the inequality constraints. As a result, relaxed controller design conditions with complex matrix structures are established. The proposed SSCO algorithm employs switching optimization variables and inner approximation strategy, which is able to compute non-convex optimization problems with complex matrix structures more flexibly and converge quickly. It is worth noting that the implementation of the SSCO algorithm requires a set of strictly feasible initial solutions. Therefore, an initialization iterative algorithm is proposed, which overcomes the difficulties of transforming the solving problem into a typical non-convex optimization problem and linearizing multiple different concave parts, by which a set of optimized feasible solutions are obtained. Finally, simulation examples are used to demonstrate the superiority of the design scheme proposed in this paper. [ABSTRACT FROM AUTHOR]

This paper proposes a variable-type hierarchical fuzzy system (VTHFS) with high accuracy and strong interpretability. An improved rear-part direct-connected structure is used in the VTHFS, which eliminates the intermediate variables of the hierarchical fuzzy system (HFS). A new feature sorting method is proposed to find suitable input variables for each layer of subsystems of VTHFS. Under the proposed topology structure, layer by layer training of VTHFS can be achieved by changing the expected output of each layer, thereby reducing residual errors layer by layer and improving the prediction accuracy of VTHFS. Three fuzzy set distribution constraints are used in parameter optimization of VTHFS to improve the interpretability, including integrity, distinguishability, and footprint of uncertainty. The type of fuzzy set is automatically adjusted according to the uncertainty characteristics of input data measured by fuzziness, which further enhances the semantic interpretability of the VTHFS and solves the problem of requiring prior knowledge to define the fuzzy set type in existing research. Finally, the proposed VTHFS is tested on the regression data sets in the real world. Experimental results demonstrate the effectiveness of the feature sorting method and the fuzzy set type adjustment method. Through a large number of quantitative indicators, it can be confirmed that VTHFS has stronger interpretability and higher prediction accuracy compared to other fuzzy systems. [ABSTRACT FROM AUTHOR]

This paper proposes a novel gradient-boosting-based ensemble system with a fuzzy regression tree (FRT) as its base component for regression tasks. FRT first initializes the rule space as a whole. In each division round, the rule space is supervised to be divided into smaller subspaces using a novel guaranteed membership division method. The consequent parameters are optimized using fuzzy weighted regularized L2 least squares. The FRT corresponding to the minimum MSE is kept as the initial model for the next division round. The above operation is repeated until the FRT reaches the maximum division rounds. Using gradient boosting to train subsequent FRTs to build hierarchical fuzzy regression tree (HFRT). The HFRT can guarantee the high accuracy while ensuring the low complexity of computation, particularly suitable for solving high-dimensional problems. HFRT performed ablation analysis experiments and compared with state-of-the-art algorithms on 28 data sets. The results confirm the effectiveness of the HFRT. [ABSTRACT FROM AUTHOR]