Type-2 TSK Fuzzy Logic System Research Articles

Design and application of Type-2 fuzzy logic system based on improved ant colony algorithm

In this paper, an improved ant colony optimization (IACO) with global pheromone update is proposed based on ant colony optimization (ACO), and it is used to design interval Type-2 TSK fuzzy logic system (FLS), including parameters adjustment and rules selection. The performance of the system can be improved by obtaining the optimal parameters and reducing the redundant rules. In order to verify the feasibility of the proposed method, the intelligent FLS is applied to predict the international petroleum price and the Zhongyuan environmental protection shares price. It is proved that the IACO can improve the efficiency of the original algorithm and accelerate the convergence speed. The simulations show that both IACO and ACO are feasible and have a high performance for the design of FLS. The simulation results compared with back-propagation design (BP algorithm) show that intelligent algorithms have an advantage over the classical algorithm, the simulation result compared with without rule-selection shows that reduced redundant rules can improve the performance, and the result compared with the Type-1 FLS shows that interval Type-2 TSK FLS has a better performance than the Type-1 TSK FLS.

Hybrid Learning for General Type-2 TSK Fuzzy Logic Systems

This work is focused on creating fuzzy granular classification models based on general type-2 fuzzy logic systems when consequents are represented by interval type-2 TSK linear functions. Due to the complexity of general type-2 TSK fuzzy logic systems, a hybrid learning approach is proposed, where the principle of justifiable granularity is heuristically used to define an amount of uncertainty in the system, which in turn is used to define the parameters in the interval type-2 TSK linear functions via a dual LSE algorithm. Multiple classification benchmark datasets were tested in order to assess the quality of the formed granular models; its performance is also compared against other common classification algorithms. Shown results conclude that classification performance in general is better than results obtained by other techniques, and in general, all achieved results, when averaged, have a better performance rate than compared techniques, demonstrating the stability of the proposed hybrid learning technique.

Design and Application of Interval Type-2 TSK Fuzzy Logic System Based on QPSO Algorithm

Studies on interval type-2 TSK fuzzy logic system is a hot topic in the current academic area. Parameter identification is very important for system design. Commonly used parameter identification methods are the least-square algorithm, BP algorithm, etc., few scholars use QPSO algorithm for parameter identification. In this paper, we propose a design of interval type-2 TSK fuzzy logic system based on quantum behaved particle swarm optimization (QPSO) intelligent algorithm. Firstly, by combining the A1–C1, A2–C0, A2–C1 interval type-2 TSK fuzzy logic system with neural network, the fuzzy neural network system is designed. Then, the QPSO intelligent algorithm was used to tune the fuzzy neural network system parameters, and the designed system model is applied to predict the Nasdaq Composite Index and International Gold Prices. Both QPSO algorithm and BP algorithm have been used to train the system model. By comparing QPSO algorithm and BP algorithm, the performance index and simulation results illustrated the proposed model is effective and feasible, which can achieve a better performance. Finally, compare the performance of the four fuzzy logic systems, it can be seen the effect of A2–C1 fuzzy logic system is better than that of the other three fuzzy logic systems.

Exact analytical inversion of interval type-2 TSK fuzzy logic systems with closed form inference methods

In this study, an exact analytical inversion procedure is presented for interval type-2 Takagi–Sugeno–Kang fuzzy logic systems (IT2 TSK FLSs) with closed form inference methods. In this inversion procedure, the inversion variable is needed to be defined by piecewise linear interval type-2 fuzzy sets (PWL IT2 FSs). This provides a way to define an IT2 TSK FLS in a form that is composed of several fuzzy subsystems with respect to the inversion variable. In the proposed procedure, the output definitions of fuzzy subsystems are derived in a unique parametric form in terms of the inversion variable by using parameters of linear definition of membership functions. By rearranging this definition with respect to the inversion variable; either a linear, quadratic or cubic equation is obtained depending on the types of the inference method and rule consequents of the IT2 TSK FLS. Since explicit analytical solutions are available for these types of equations, the exact inverse solution(s) of each fuzzy subsystem can easily be calculated. The inverse solution set of overall IT2 TSK FLS is obtained by composing the inverse solutions of all fuzzy subsystems. The exactness and feasibility of the proposed inversion procedure has been illustrated through simulation examples.

A hybrid learning method composed by the orthogonal least-squares and the back-propagation learning algorithms for interval A2-C1 type-1 non-singleton type-2 TSK fuzzy logic systems

The purpose of this paper is to present a hybrid learning method for interval A2-C1 type-1 non-singleton type-2 TSK fuzzy logic system that uses the recursive orthogonal least-squares algorithm to tune the type-1 consequent parameters, and the back-propagation algorithm to tune the interval type-2 antecedent parameters. Based on the combination of these two training algorithms the new hybrid learning method changes the interval type-2 fuzzy model parameters adaptively and minimizes the proposed error function as the new type-1 non-singleton input---output data pairs are processed. Its antecedent sets are interval type-2 fuzzy sets, its consequent sets are type-1 fuzzy sets, and its inputs are type-1 non-singleton fuzzy numbers with uncertain standard deviations. Comparison with the non-hybrid interval A2-C1 type-1 non-singleton type-2 Takagi---Sugeno---Kang fuzzy logic system that only uses the back-propagation algorithm for both antecedent and consequent parameter's adaptation demonstrates that the proposed hybrid algorithm is a well-performing nonlinear adaptation that enables the interval type-2 fuzzy model to optimally match the nonlinear behavior of the process. The application of the interval type-2 fuzzy logic as adaptable predictor using the proposed hybrid learning method was constructed for the modeling and prediction of the transfer bar surface temperature in an industrial hot strip mill facility. Experimental results demonstrated that this method improves the temperature prediction performance of the interval A2-C1 type-1 non-singleton type-2 Takagi---Sugeno---Kang fuzzy logic system.

On-line Adaptive Interval Type-2 Fuzzy Controller Design via Stable SPSA Learning Mechanism

This paper proposes an interval type-2 Takagi-Sugeno-Kang fuzzy neural system (IT2TFNS) to develop an on-line adaptive controller using stable simultaneous perturbation stochastic approximation (SPSA) algorithm. The proposed IT2TFNS realizes an interval type-2 TSK fuzzy logic system formed by the neural network structure. Differ from the most of interval type-2 fuzzy systems, the type-reduction of the proposed IT2TFNS is embedded in the network by using uncertainty bounds method such that the time-consuming Karnik-Mendel (KM) algorithm is replaced. The proposed stable SPSA algorithm provides the gradient free property and faster convergence. However, the stable SPSA algorithm inherently has the problem for on-line adaptive control. Hence, in order to achieve the on-line result, we utilize the sliding surface to develop a new on-line adaptive control scheme. In addition, the corresponding stable learning is derived by Lyapunov theorem which guarantees the convergence and stability of the closed-loop systems. Simulation and comparison results are shown to demonstrate the performance and effectiveness of our approach.

A robust interval Type-2 TSK Fuzzy Logic System design based on Chebyshev fitting

This paper presents two approaches for the design of an interval Type-2 TSK Fuzzy Logic System (FLS), taking into account the uncertainties about the consequent parameters. While the first approach deals with the tuning of the consequent parameters used for the system output computation, the second one, based on a linear Chebyshev fitting, shows more robustness as it considers the consequent sets instead of only the consequent crisp values. This approach deals with all parameters at the consequent level, by taking into account the upper and lower bounds of the consequent set instead of the mean value. The effectiveness of both approaches in terms of robustness to noise is evaluated through the design of IT2 TSK FLS A1-C1 forecasters for the Mackey-Glass time-series.

Type2 TSK Fuzzy Logic System and its Type1 Counterpart

An interval type-2 TSK fuzzy logic system can be obtained by considering the membership functions of its existed type-1 counterpart as primary membership functions and assigning uncertainty to cluster centers, standard deviation of Gaussian membership functions and consequence parameters. In many cases it has been difficult to determine the spread percentages for these parameters to obtain an optimal model. In order to develop robust and reliable solutions for the problems, this paper distinguishes the differences between type-2 TSK system and its counterpart, analyzes the sensibility of the outputs of a type-2 TSK fuzzy system, and discusses the approximation capacities of type-2 TSK FLS and its type-1 counterpart as well.

Interval Type-2 TSK 퍼지논리시스템 기반 다중 퍼지 예측시스템 설계

본 논문은 예측 시스템의 성능을 개선하기 위해 비선형데이터의 내재된 특성이나 불확실성을 보다 효과적으로 반영할 수 있는 Interval Type-2 TSK 퍼지논리 시스템 기반 다중 퍼지 예측시스템의 설계를 다룬다. 본 논문에 제시된 다중 예측시스템들은 데이터의 비선형적 특성들을 효과적으로 고려하기 위해 설계되며, 각각의 시스템은 Type-1 TSK 퍼지논리나 다른 방법들에 비해 데이터의 불확실성을 충분히 반영할 수 있는 Interval Type-2 TSK 퍼지논리를 기반으로 구현된다. 또한, 1차 차분변환 과정을 통해, 데이터의 원형으로부터 최적의 차분데이터를 생성하고, 이들을 각 시스템의 입력으로 사용함으로써 시스템 설계 시 보다 안정된 통계적 정보를 제공할 수 있도록 한다. 마지막으로, 두 개의 전형적인 시계열 데이터의 예측 시뮬레이션을 통해 제안된 방법의 효용성을 검증한다. This paper presents multiple fuzzy prediction systems based on an Interval type-2 TSK fuzzy Logic System so that the uncertainty and the hidden characteristics of nonlinear data can be reflected more effectively to improve prediction quality. In proposed method, multiple fuzzy systems are adopted to handle the nonlinear characteristics of data, and each of multiple system is constructed by using interval type-2 TSK fuzzy logic because it can deal with the uncertainty and the characteristics of data better than type-1 TSK fuzzy logic and other methods. For input of each system, the first-order difference transformation method are used because the difference data generated from it can provide more stable statistical information to each system than the original data. Finally, computer simulations are performed to show the effectiveness of the proposed method for two typical time series examples.