This paper provides an in-depth review of the optimal design of type-1 and type-2 fuzzy inference systems (FIS) using five well known computational frameworks: genetic-fuzzy systems (GFS), ...neuro-fuzzy systems (NFS), hierarchical fuzzy systems (HFS), evolving fuzzy systems (EFS), and multi-objective fuzzy systems (MFS), which is in view that some of them are linked to each other. The heuristic design of GFS uses evolutionary algorithms for optimizing both Mamdani-type and Takagi–Sugeno–Kang-type fuzzy systems. Whereas, the NFS combines the FIS with neural network learning systems to improve the approximation ability. An HFS combines two or more low-dimensional fuzzy logic units in a hierarchical design to overcome the curse of dimensionality. An EFS solves the data streaming issues by evolving the system incrementally, and an MFS solves the multi-objective trade-offs like the simultaneous maximization of both interpretability and accuracy. This paper ofers a synthesis of these dimensions and explores their potentials, challenges, and opportunities in FIS research. This review also examines the complex relations among these dimensions and the possibilities of combining one or more computational frameworks adding another dimension: deep fuzzy systems.
The problem of resilient energy-to-peak filtering for a class of uncertain continuous-time nonlinear systems is investigated in this paper. A Takagi-Sugeno fuzzy model with norm-bounded uncertainties ...is used to represent the nonlinear plant. Attention is focused on the design of an energy-to-peak filter such that the filtering error system is asymptotically stable and the prescribed energy-to-peak filtering performance is guaranteed, where the designed filter is assumed to have additive gain variations. The proposed design is aimed at all filter matrices with gain variations, which improves the existing results on resilient energy-to-peak filtering for continuous-time systems. A simulation example is provided to show the effectiveness of the proposed methods.
The identification problem incorporated in feedback control of uncertain nonlinear systems exhibiting complex behavior has been solved in different ways. Some of these solutions have used artificial ...intelligence methods like fuzzy logic and neural networks. However, their individual implementation suffers from certain drawbacks, such as the black-box nature of neural network and the problem of finding suitable membership functions for fuzzy systems. These weaknesses can be avoided by implementing a hybrid structure combining these two approaches, the so-called neuro-fuzzy system. In this paper, a neuro-fuzzy system that implements differential neural networks (DNNs) as consequences of Takagi-Sugeno (T-S) fuzzy inference rules is proposed. The DNNs substitute the local linear systems that are used in the common T-S method. In this paper, DNNs are used to provide an effective instrument for dealing with the identification of the uncertain nonlinear system, while the T-S rules are used to provide the framework of previous knowledge of the system. The main idea is to carry out an online identification process of an uncertain nonlinear system with the aim to design a closed-loop trajectory tracking controller. The methodology developed in this study that supports the identification and trajectory control designs is based on the Lyapunov formalism. The DNN implementation results in a time-varying T-S system. As a consequence, the solution of two time-varying Riccati equations was used to adjust the learning laws in the DNN as well as to adjust the gains of the controller. Two results were provided to justify the existence of positive-definite solutions for the class of Riccati equations used in the learning laws of DNNs. A complete description of the learning laws used for the set of DNN identifiers is also obtained. An autonomous underwater vehicle system is used to demonstrate the performance of the controller on tracking a desired 3-D path by this combination of the DNN and the T-S system.
This paper examines quantized stabilization for Takagi-Sugeno (T-S) fuzzy systems with a hybrid-triggered mechanism and stochastic cyber-attacks. A hybrid-triggered scheme, which is described by a ...Bernoulli variable, is adopted to mitigate the burden of the network. By taking the effect of the hybrid-triggered scheme and stochastic cyber-attacks into consideration, a mathematical model for a closed-loop control system with quantization is constructed. Theorems for main results are developed to guarantee the asymptotical stability of networked control systems by using Lyapunov stability theory and linear matrix inequality techniques. Based on the derived sufficient conditions in theorems, the controller gains are presented in an explicit form. Finally, two practical examples demonstrate the feasibility of designed algorithm.
Abstract
This paper deals with the stock portfolio selection problem involved with trapezoidal fuzzy number returns and multiple mental accounts. A fuzzy behavioral portfolio decision model is ...proposed to maximize the possibilistic mean value of portfolio return and ensure the portfolio return of each mental account exceeding the given minimum fuzzy aspiration level with a given probability. Then, some programming models are designed to solve the optimal portfolio strategy. Finally, one numerical example is given to illustrate the effectiveness of the proposed fuzzy behavioral portfolio decision approach.
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