Research On Novel Membership Function And Optimization Strategy For Interval Type-2 Fuzzy Systems

The most extensively used application of fuzzy logic is in identification and control,which is acknowledged to be a well-accepted methodology for creating systems that can give sufficient performance in the face of uncertainty and imprecision.Furthermore,the fuzzy logic theory provides a technique for lessskilled employees to quickly design useful algorithms in a user-friendly manner that is similar to human thinking and perception.The majority of industrial systems are nonlinear and susceptible to various sources of uncertainty.As a result,data collected by these systems for the development of their models may contain noise and outliers,affecting the approximation accuracy of their models.Hence,robust techniques,such as fuzzy systems,are required for modeling and control of such systems.The type-2 fuzzy system has a footprint of uncertainty(FOU),which makes it significantly better at dealing with imprecision in non-linear systems than its type-1 equivalent.The design of a fuzzy system involves structural design and parameter optimization.Structural design includes;selection of the type of fuzzifier,type of membership function,number of membership functions,type of rules(Mamdani or TSK),type of inference engine,and method of type reduction/defuzzification.While parameter optimization entails employing optimization techniques to arrive at the best antecedent and consequent parameters,experts can also design the parameters.The main content of this dissertation includes the following aspects.1)A novel parallelogram membership function is proposed.Our proposed interval type-2 MF has a certain membership degree at the FOU’s extremities and a range of uncertain values in between.The proposed MF has its maximum uncertain width at the midpoint of the MF width,which is an advantage when dealing with data whose membership degree is certain at the boundary and uncertain in-between.Tuning the parameters of the suggested MF would turn it into various triangular and quadrilateral FOU shapes,which will better capture the training data’s uncertainty.2)We analyzed the novel membership function based on: 1)The impact of FOU size on IT2 FS performance was examined.Results reveal that the best FOU size for a particular fuzzy system is heavily dependent on the nature of the problem that the fuzzy system is supposed to solve.As a result,proper FOU size selection through optimization or using expert knowledge is required to improve the fuzzy systems’ performance.2)A performance comparison between IT2 FS using the novel parallelogram MF and IT2 FS that use Gaussian,elliptical,and triangular MF was conducted.The simulation results of chaotic Mackey-Glass time series prediction showed the suitability of the novel MF-based IT2 FS over the other MFs.The 3-PRS parallel robot control problem also reveals the novel MF’s superiority over the triangular and elliptical MFs.3)An investigation into the effect of increasing the number of MF on the performance of IT2 FS was also conducted.The number of MF defines the number of classes in which the input space is being classified.Results reveal that when the MF parameters are not part of the parameters to be optimized,increasing the number of MF reduces the chances of the optimizer arriving at optimum consequent parameters,which significantly reduces the IT2 FS accuracy.Because of the increased MF parameters,an increase in the number of MF greatly increases the computing time.3)As already observed in our research,increasing the number of MF in a fuzzy system without optimizing the MF parameters is disadvantageous,and optimizing the MF parameters significantly increases the computational cost.We modified an Extended Kalman filter algorithm for the optimization of IT2 FS parameters to optimize the MF parameters without including the MF parameters as input to the optimizer.The Kalman gain and error covariance generated during consequent parameter optimization is regulated to optimize the MF parameters.A robot hand path identification and chaotic Mackey-Glass series prediction problems were used to demonstrate the advantage of the proposed strategy.Our modified strategy,without an increase in computation cost,outperformed the unmodified strategy.This dissertation mainly proposes a new parallelogram membership function,and analyzes its characteristics from the perspectives of the footprint of uncertainty size,membership function shape comparison,and number of membership functions.The advantage of the novel membership function was demonstrated.The modified extended Kalman filter strategy can reduce the complexity of fuzzy system parameter optimization without significantly increasing the computational cost.The theoretical results of this dissertation not only help designers to understand the influence of the operators on fuzzy systems,but also provide theoretical guidance for designers to reasonably select and optimize system parameters according to the expected system design objectives.