The Simplified Fuzzy System Based On The Variable Universe Approach And Its Application

With the continuous perfection and deepening in the study of fuzzy system theory,fuzzy system has been applied successfully in various areas such as classification,control,signal processing,decision support,and so on.The goal of utilizing fuzzy system as a new means of tackling practical problems is not to intensify fuzzy concepts,but to make fuzzy concepts more distinguishable,thus simplifying the practical problems.Fuzzy system has proven to be a universal approximator.Therefore,as long as fuzzy system is complex enough,its performance is usually satisfactory.However,excessively complex design of fuzzy system can be harmful to the practical applications.There is no doubt that interpretability is the prominent feature of fuzzy system.This unique advantage enables fuzzy system to simulate human thinking more easily,thus making it more effective to tackle complex problems,in distinction from other intelligent systems such as the neural network.But in the practical application of fuzzy system,people usually just pursue the improvement of its performance according to the numerical value index solely from the viewpoint of mathematics,which causes the interpretability of fuzzy system to become worse and worse,or even totally lost.No doubt this scenario is inconsistent with the founding background of fuzzy system.Meanwhile,with the deterioration of interpretability,the application superiority of fuzzy system will be weakened.Also,this shortcoming can greatly complicate the designing process of fuzzy system.At the same time,there are always many problems during the actual designing and application process of fuzzy system,such as many subjective considerations involved during the designing process,the comparatively poor ability of fine tuning,the insufficient systematic designing methods,and so on.Trial and error adjustments or optimization techniques combined with other algorithms are commonly used to solve the issues raised above.However,these methods have the disadvantages of lower designing efficiency,lack of enough theoretical support,higher computation complexity,etc.These problems will aggravate the challenge of designing the fuzzy system.Therefore,in order to better improve the application advantage of fuzzy system in distinction from other systems,this dissertation has studied many designing key factors of fuzzy system,such as selecting the design of the membership functions,fuzzy partitions of discourse domain and the fuzzy rules extraction,and has put forward the design approach of the simplified fuzzy system.Moreover,in order to further enhance the performance of fuzzy system,the simplified fuzzy system is combined with variable universe approach,forming the systematic design strategy of the simplified fuzzy system based on variable universe.Subsequently the simplified fuzzy system based on variable universe is used in several different fields to validate its effectiveness,such as control and optimization.Its universal adaptability is also illustrated at the same time.The approach proposed in this dissertation simplifies the design of fuzzy system,highlights the interpretability of fuzzy system,and further broadens the actual application range of fuzzy system.The main researches are as follows:1.Aiming at the issues such as the lacking of reasonable methods for choosing membership functions and the poor interpretability of fuzzy system,the design method of simplified fuzzy system is proposed.In order to provide some theoretical support to membership function design,the choice of input and output membership functions which affect fuzzy system performance is studied.Moreover,the triangular membership function,which has notably simple form,is the focus of this research to further simplify the design of fuzzy system.The research expounds the good properties of triangular membership function with 1/2 overlapping degree.To ensure the interpretability of fuzzy system,the universal method of "three-partition" of discourse domain is brought forward.This method can on one hand go even further to simply the design of fuzzy system,on the other hand improve the interpretability of fuzzy system.In addition,the approximation of fuzzy system based on triangular membership function is studied.In accordance with the aforementioned research results,the main facts are given which can affect the performance of fuzzy system.In view of the facts,the simplified fuzzy system is combined with variable universe approach for the forming of systematic design method of fuzzy system.This approach emphasizes the simplicity and interpretability of the fuzzy system design,and the performance of fuzzy system can be guaranteed.2.The simplified fuzzy system based on variable universe approach is used in ensuring the stability of the inverted pendulum system.Based on the phase plane,by analyzing the motion states of inverted pendulum,the simple,core and complete fuzzy rules are extracted objectively.Double-input single-output fuzzy system with triangular membership functions which posses with 1/2 overlapping degree used for the discourse course partition is designed.On the basis of Lyapunov stability theory,the stability of simplified fuzzy system based on variable universe is proven.Simulation results show the validity of simplified fuzzy system based on variable universe.3.The simplified fuzzy system based on variable universe approach is used in optimization field,improving the simulated annealing algorithm.Focusing on the different states of objective function during the process of optimization,the meaningful and interpretable single-input single-output simplified fuzzy system is designed to adaptively adjust the key parameter of the simulated annealing algorithm--annealing temperature.Unlike the method of monotonously decreasing the annealing temperature used in traditional simulated annealing algorithm,warming-up and fast cooling strategies are creatively introduced.The new strategies significantly reduce the number of optimization calculations and the optimized efficiency of simulated annealing algorithm is greatly improved.Two examples of image reconstruction and traveller salesman problem are used to evaluate the improvement effect of simulated annealing algorithm.The application validity of the simplified fuzzy system based on variable universe is proven.4.Kalman filter is improved by using the simplified fuzzy system based on variable universe approach,through which the prediction precision of system state variables has been increased.Based on the innovation maximum likelihood estimation approach,by applying the principle of variance matching technology,the single-input single-output simplified fuzzy system with good interpretability is designed to tackle the problem of prediction precision deterioration due to the uncertainty of measurement noise.To ensure the performance of Kalman filter,the measurement noise covariance matrix is adjusted in real time by utilizing the feedback technology.Thus,the consistency between the actual value and the theoretical value of the innovation variance can be guaranteed.Simulation results of ship location show the application validity of the simplified fuzzy system based on variable universe.