An exact inversion method for multi-input-single-output decomposable TS fuzzy systems

In this paper, a new method for fuzzy inference system optimization is presented. The proposed method performs type-1, interval type-2 and general type-2 fuzzy inference systems design using a hierarchical genetic algorithm as optimization method. This method is an improvement of a fuzzy system optimization approach presented in previous works where only the optimization of type-1 and interval type-2 fuzzy inference systems was performed using a human recognition application. The human recognition is performed using three biometric measures namely iris, ear, and voice, where the main idea is to perform the combination of responses in the modular neural networks using an optimized fuzzy inference system to improve the final results without and with noisy conditions. The main contribution of the proposed method is an optimization able to select type of fuzzy logic, granulation of each fuzzy variable and fuzzy rules selection to design optimal fuzzy inference systems applied in combining modular neural networks responses. The results obtained show the effectiveness of the proposed method to design structures of fuzzy inference systems. Statistical comparisons are performed with previous results, where better results can be observed using the proposed method. The design of optimal structures of fuzzy inference systems include among other parameters; type of fuzzy logic (type-1, interval and general type-2 fuzzy logic), type of inference model (Mamdani model or Sugeno model), and consequents of the fuzzy if–then rules.

In this study, a new fuzzy system structure that reduces the number of inputs is proposed for dynamic system identification applications. Algebraic fuzzy systems have some disadvantages due to many inputs. As the number of inputs increase, the number of parameters in the training process increase and hence the classical fuzzy system becomes more complex. In the conventional fuzzy system structure, the past information of both inputs and outputs are also regarded as inputs for dynamic systems, therefore the number of inputs may not be manageable even for “single input and single output” systems. The new dynamic fuzzy system module (DFM) proposed here has only a single input and a single output. We have carried out identification simulations to test the proposed approach and shown that the DFM can successfully identify non-linear dynamic systems and it performs better than the classical fuzzy system.

Zero-order TSK-type fuzzy system learning using a two-phase swarm intelligence algorithm

An interval type-2 fuzzy logic system (IT2FLS) can function well with uncertain data, with which a type-1 fuzzy logic system (T1FLS) is ineffective because its membership function rests upon crisp values. However, similar to T1FLSs, there are challenges associated with IT2FLSs in selecting parameters, which can significantly affect the accuracy of the classification results with their relatively high sensitivity. This paper discusses and proposes a hybrid model based on IT2FLS and particle swarm optimization (PSO) for prediction problems. The main objective of this paper is to find the optimal solution for the unknown fuzzy systems using labelled data for training the fuzzy system. The PSO technique was used to find the optimal parameters of the Gaussian membership functions which utilized for IT2FLSs. The authors tested two data sets for each of the two prediction problems, namely: burnt forest area prediction and wine quality prediction. The predictive results were compared with other predictive methods including random forest (RF), support vector machines (SVM), artificial neural network (ANN), adaptive neuro fuzzy inference system (ANFIS) and IT2FLS with parameters generated by using the fuzzy c-means algorithm (IT2FLS-FCM). Experiment results showed that the proposed method could significantly improve accuracy compared to several other predictive techniques.

This paper presents a systematic design method of a controller using the discrete fuzzy PI control and the particle swarm optimization (PSO). Unlike a conventional PI controller, the discrete fuzzy PI controller has variable gains according to its input variables. Generally, it is complicated to tune the parameters of a fuzzy controller because there are too many parameters which are strongly coupled. In the discrete-time domain, the discrete fuzzy PI controller is a superset of the conventional PI controller. And the initial parameters of the fuzzy PI controller are selected by using the inclusion relationship. And, for the sake of simplicity, only four rules are used to construct a nonlinear fuzzy control surface. The tuning parameters of the discrete fuzzy PI controller are optimized by using the PSO. To verify the effectiveness of the controller designed by using the discrete fuzzy PI control and the PSO, we applied it to a wind turbine pitch controller. As a result, the proposed controller has variable gains, unlike the PI controller, and make the pitch controller operate in boarder operating regions.

Fuzzy systems based on fuzzy if-then rules have been applied to various problems. The main application area has been fuzzy control problems. In many cases, such fuzzy systems can handle only a few input variables. This is because the number of fuzzy if-then rules exponentially increases as the number of input variables increases. In this paper, we try to design fuzzy classification systems based on fuzzy if-then rules for multidimensional pattern classification problems with many attributes. For designing such fuzzy classification systems, we compare two frameworks in the area of genetics-based machine learning: the Michigan approach and the Pittsburgh approach. The performance of fuzzy rule-based classification systems is also compared with that of various pattern classification methods. In computer simulations, we use a wine classification problem with 13 attributes, a cancer diagnosis problem with 9 attributes, and a credit approval problem with 14 attributes. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(12): 10–19, 1997

Fuzzy logic controllers are designed for spacecraft hovering flight in a binary asteroid system. The binary asteroid system is modeled as an ellipsoid-sphere system where the spherical harmonics method is adopted to represent the gravitational field of the asteroids. The method to design the fuzzy logic controllers is introduced in detail. Hovering flight about the inner collinear equilibrium point L 1 of binary asteroid Didymos is numerically presented. Detailed steps on roughly estimating the scaling gains of fuzzy logic controllers are also summarized. Numerical simulations are performed to show the effectiveness of the proposed method. Moreover, the aforementioned fuzzy logic controllers can be used for both continuous and impulsive thrusters. The fuzzy controllers with continuous thrust, the fuzzy controllers with fixed thrust, and the other two kinds of sliding-mode controllers are optimized in the same way and compared in the same simulation environment together, to show tremendous advantages of fuzzy logic controllers and continuous thrusters on both control performance and propellant consumption.

In this paper mathematical models of Mamdani type fuzzy PI or PD controllers via Center of Gravity (CoG) defuzzification are obtained. These controllers are called the simplest fuzzy PI or PD controllers as minimal number of fuzzy sets (two fuzzy sets on each of the two-input variables and three fuzzy sets on the output variable) are employed. The basic components of these models are L-type and Y-type membership functions on each input variable, trapezoidal or triangular membership functions on output variable, minimum / algebraic product t-norm, maximum OR operator, three linear fuzzy control rules, minimum / algebraic product inference and CoG defuzzification. Mathematical models of fuzzy controller via CoG defuzzification were not reported in the literature and are therefore presented for the first time in this paper.

In this paper, two knowledge based controllers are proposed to overcome the difficulties of a computed torque nonlinear controller (NC) in perfect trajectory tracking of nonholonomic wheeled mobile robots (WMRs). First, the effects of different dynamic models developed in angular andCartesian coordinate systems are fully examined on the persistent excitation condition and consequently on the trajectory tracking performance of WMRs. Using the dynamic model coordinated in theCartesian frame as the base of theNCresults in perfect compensation of large position off‐tracks and unbiased estimation of the plant's unknown parameters. However, using theWMR's dynamic model with rotation angles of driving wheels as the base of nonlinear and fuzzy controllers leads to accurate orientation tracking. Through replacing the proportional and differential terms of theNCby fuzzy functions, a fuzzy nonlinear controller (FNC) is generated. Due to the complicated dynamics of the WMR in which the center of mass does not coincide with the center of rotation, the expert knowledge of fuzzy controllers is extracted considering the rotation angles and rates of driving wheels as input variables. Fuzzy tuning of theNCresults in a superior tracking performance against measurement noises, though the control torques are decreased and smoothed significantly. Second, a complete fuzzy controller (FC) is generated to make perfect tracking of theWMR's position and orientation. The local stability analysis of fuzzy controllers is examined considering the corresponding analytical structures as nonlinear controllers. The superior performances of the proposed fuzzy controllers compared to those of theNCs are evaluated through simulations.

The use of fuzzy rule-based systems in regression problems is widely extended due to the precision of the obtained models. Moreover, the use of Mamdani models is usually referred to as a good choice in many real problems, since it provides an interpretable and precise functional relationship between the output and input variables. In this paper we present a new leaning Mamdani fuzzy system FRLC-Rgress (Fuzzy Rule Learning through Clustering for Regression Problems). This provides an accurate fuzzy system and simple Mamdani fuzzy rule bases for regression problems. FRLC-Rgress based on linguistic modifiers and fuzzy clustering achieves a low complexity of the learned models while keeping a high accuracy, by following two stages: multi- granularity, fuzzy discretization of the variables, and perceptual learning of the fuzzy rules. FRLC-Rgress is experimented using six real-world datasets. It outperforms two of the most and simple fuzzy systems (genetic fuzzy systems) in state of the art.

Interpretability improvements to find the balance interpretability-accuracy in fuzzy modeling: an overview.- Regaining comprehensibility of approximative fuzzy models via the use of linguistic hedges.- Identifying flexible structured premises for mining concise fuzzy knowledge.- A multiobjective genetic learning process for joint feature selection and granularity and contexts learning in fuzzy rule-based classification systems.- Extracting linguistic fuzzy models from numerical data-AFRELI algorithm.- Constrained optimization of fuzzy decision trees.- A new method for inducing a set of interpretable fuzzy partitions and fuzzy inference systems from data.- A Feature Ranking Algorithm for Fuzzy Modelling Problems.- Interpretability in multidimensional classification.- Interpretable semi-mechanistic fuzzy models by clustering, OLS and FIS model reduction.- Trade-off between approximation accuracy and complexity: TS controller design via HOSVD based complexity minimization.- Simplification and reduction of fuzzy rules.- Effect of rule representation in rule base reduction.- Singular value-based fuzzy reduction with relaxed normalization condition.- Interpretability, complexity, and modular structure of fuzzy systems.- Hierarchical genetic fuzzy systems: accuracy, interpretability and design autonomy.- About the trade-off between accuracy and interpretability of Takagi-Sugeno models in the context of nonlinear time series forecasting.- Accurate, transparent and compact fuzzy models by multi-objective evolutionary algorithms.- Transparent fuzzy systems in modeling and control.- Uniform fuzzy partitions with cardinal splines and wavelets: getting interpretable linguistic fuzzy models.- Relating the theory of partitions in MV-logic to the design of interpretable fuzzy systems.- A formal model of interpretability of linguistic variables.- Expressing relevance and interpretability of rule-based systems.- Conciseness of fuzzy models.- Exact trade-off between approximation accuracy and interpretability: solving the saturation problem for certain FRBSs.- Interpretability improvement of RBF-based neurofuzzy systems using regularized learning.- Extracting fuzzy classification rules from fuzzy clusters on the basis of separating hyperplanes.

This paper discusses the problem of suboptimal local piecewise H ∞ fuzzy control of quasi-linear spatiotemporal dynamic systems with control magnitude constraints. A Takagi-Sugeno fuzzy partial differential equation (PDE) model with space-varying coefficient matrices is first assumed to be derived for exactly describing nonlinear system dynamics. In the light of the fuzzy model, a local piecewise fuzzy feedback controller is then constructed to guarantee the exponential stability with a prescribed H ∞ disturbance attenuation level for the resulting closed-loop system, while the control constraints are also ensured. A sufficient condition on the existence of such fuzzy controller is developed by the Lyapunov direct method and an integral inequality and presented in terms of space algebraic linear matrix inequalities (LMIs) coupled with LMIs. By virtue of extreme value theorem, a suboptimal-constrained local piecewise H ∞ fuzzy control design in the sense of minimizing the disturbance attenuation level is formulated as a minimization optimization problem with LMI constraints. Finally, the proposed method is applied to solve the feedback control of a quasi-linear FitzHugh-Nagumo equation with space-varying coefficients, and simulation results show its effectiveness and merit.

This paper presents two new mathematical models of the simplest fuzzy PID controller which employ two fuzzy sets (negative and positive) on each of the three input variables (error, change in error and double change in error) and four fuzzy sets (-2, -1, +1, +2) on the output variable (incremental control). L-type, Γ-type and II-type membership functions are considered in fuzzification process of input and output variables. Controller modelling is done via algebraic product AND operation, maximum/bounded sum OR operation, Mamdani minimum inference method, and centre of sums (CoS) defuzzification. The new models obtained in this manner turn out to be nonlinear, and their properties are studied. Since digital controllers are implemented on the digital processors, the computational and memory requirements of the fuzzy controllers and conventional (non-fuzzy) controller are compared. Stability analysis of closed loop systems containing the fuzzy controller models is done using the small gain theorem.

Typical Takagi–Sugeno PI and PD fuzzy controllers: analytical structures and stability analysis

A fuzzy logic expert system to estimate intrinsic extinction vulnerabilities of marine fishes to fishing