Structural Analysis And Learning Algorithms Of Polygonal Fuzzy Neural Network

A polygonal fuzzy neural network is a new type mixable intelligent system combination of an artificial network and polygonal fuzzy numbers, by determining limited points of polygonal fuzzy numbers to complete fuzzy information processing, as a result, its approximation and study ability is more capable than the regular fuzzy neural network which is based on Zadeh extension principle. This paper mainly analyze the basic properties of polygonal fuzzy neural networks, and then, the learning algorithms of two polygonal fuzzy neural networks are redesigned and improved. The main contents are the followiing.In the first chapter, it introduces the background, the present research situation of fuzzy neural networks at home and abroad and the preliminaries.In the second chapter, according to gradient descent method to improve the classic conjugate gradient algorithm. At first, in the iterative process of conjugate gradient algorithm, the optimal constants of the algorithm are obtained through the one-dimensional inexactitude A-G linear search method, and then, a polygonal fuzzy conjugate gradient algorithm is designed under environment of polygonal fuzzy neural networks. Finally, utilizing a simulation example, the some good char-acteristics of this algorithm are illustrated, for example, fast convergence to the global minimum point of error function, the convergent rate is faster than traditional fuzzy BP algorithm and so on.In the third chapter, as one kind of new networks, a multi-input and single-output polygonal fuzzy neural network is presented, and then, research the network internal structure, basic per-formance and the representative element on multidimensional polygonal fuzzy numbers space is proved to be monotonicity and uniform continuity whenever the transfer functions are nonnegative increasing functions. Further, if this network is a universal approxhnator to the class of multivariate fuzzy functions, we discuss the composite form and common properties of this function.In the forth chapter, in order to avoid the process of complex calculation of partial derivatives of error functions corresponding to the connection weights and threshold values of polygonal fuzzy neural network with multi-input and single-output, by means of Hebb rules as well as elementary particle swarm algorithm to obtain two kind of optimal learning algorithms respectively. Finally, by simulating example to analyze the two class of algorithms, the results show that their stability and convergent speed are better than the traditional partial derivative algorithms, this laid the foundation for the further research and application of polygonal fuzzy neural network.