On The Type-2 Fuzzy System Modelling And Its Optimization

Type-2 fuzzy logic introduced new formalisms capable of overcoming the inherent uncertainties of approximating real-world processes by computational models.Type-2fuzzy logic system which is designed based on type-2 fuzzy logic can effectively restrain uncertainties,it has been proved to be an efficient tool for modelling real life systems.Type-2 fuzzy logic system establishes the fuzzy model by the utilization of process data,has been widely used in many areas,such as modelling,monitoring and control,it has emerged as a promising data-driven technique.The main issues of type-2 fuzzy logic system modelling are the selection design method of membership functions and its optimization method based on the process data.In this dissertation,based on the basic tools,such as type-2 fuzzy sets and type-reduction method,the type-2 fuzzy modelling problem is solved by heuristic algorithm,uniform design method and tensor regression method.To the fuzzy modelling problem,it is hard to get good generalization with noisy data,an interval type-2 neuro-fuzzy modelling method is proposed based on quantum-inspired bacterial foraging algorithm.In order to unearth more information of the system with few fuzzy rules and decrease the parameters' number of the type-2 fuzzy system,uniform design method is used for interval type-2 neuro-fuzzy modelling.To simplify the structure of the model and improve the inference speed of the fuzzy system,the fuzzy model is trained by regularized extreme learning structure,and the learning structure is designed based on triangular type-2 fuzzy sets.A step further,tensor structure and generalized M-P inverse of the tensor are used for fuzzy modelling,randomized weight initialization method and single layer structure of the extreme learning are adopted,the type-2 fuzzy system modelling problem is converted into solving a tensor equation problem.Finally,from the point view of fuzzy modelling,extended type-reduction method of concave type-2 fuzzy sets is studied.The main work of this dissertation can be summarized as follows:1.The self-constructing generation approach of interval type-2 fuzzy rules is proposed at first,the fuzzy rules are generated by clustering the input-output training patterns,and the initial rule base is obtained at the structural identification stage.A hybrid evolving learning algorithm which is designed based on quantum-inspired bacterial foraging algorithm and recursive least squares method is adopted to optimize model parameters.The constructed interval type-2 neuro-fuzzy logic model presents better noisy reduction property and robustness.Furthermore,to generate few rules which can represent as much information as possible the system has,a uniform design based rule generation approach is proposed,in which the mean of Gaussian membership functions are generated by uniform design and only standard deviations are adjusted by input-output training patterns.To the consequent learning,two optimization methods are involved,one is the recursive singular value decomposition,and the other is the weighted least squares estimator.BMM method is used for defuzzification.The uniform distribution of the fuzzy membership functions is guaranteed by the uniform design method,the impact of the training sequence for the fuzzy rules is reduced.Owing to the absence of antecedent parameters' optimization,the running time of the algorithm is saved greatly.2.In order to simplify the model structure,to reduce the number of parameters for the type-2 fuzzy system,extreme learning mechanism is adopted for system modelling.An efficient type-reduction method of triangular type-2 fuzzy set is used for fuzzy model,it is also used to solve gain matrix of the regression problem,parameters of the model can be obtained by solving the regularized optimization problem.The proposed triangular type-2 fuzzy model can improve the system's ability of tackling the uncertainties,and it presents the potential ability in fuzzy system modelling.Furthermore,a tensor based type-2 extreme learning method is proposed.In contrast to the work on extreme learning machine,regularized extreme learning machine,weighted regularized extreme learning machine and least squares support vector machine,which are the most often used learning algorithm in regression problems,triangular type-2 fuzzy set is adopted to formulate the uncertainty,the tensor structure is used to construct the extreme learning method,only type-2 fuzzy membership functions are needed,extreme learning results are solved by tensor based regression problem in which classical M-P inverse of matrix is replaced by M-P inverse of tensor.The type-reduction of type-2 fuzzy set is avoided,hence the type-2fuzzy structure can be seamlessly incorporated into the extreme learning scheme.3.For a class of concave type-2 fuzzy sets whose secondary membership function consists of triangular membership functions and spikes,a type-reduction method called concave analytical type-reduction method with spikes is proposed.The type-reduction method is free of the steps,such as discourse partition and discourse refinement for primary membership,thus its calculation complexity is reduced.Moreover,the proposed method is extended to type-2 fuzzy set whose secondary membership function consists of trapezoid membership functions and spikes with a trapezoidal fuzzy number approximation operator.The proposed type-reduction methods can address a more general class of type-2 fuzzy sets,and it is more convenient for type-2 fuzzy modelling and inference.