The structure and realization of a polygonal fuzzy neural network

Abstract

As a generalization of ladder fuzzy numbers, the polygonal fuzzy numbers can be approximately represented by a group of ordered real numbers, it not only keeps the closeness of arithmetic operations, and also inherits some excellent properties of ladder fuzzy numbers. To modify defects of the definition of the original polygonal fuzzy numbers, the method of an equidistant subdivision is firstly introduced, and the specific algorithm of general fuzzy numbers into the polygonal fuzzy numbers by two examples is explained in detail. Secondly, using the extension operations of polygonal fuzzy numbers, a polygonal fuzzy neural network is constructed by mathematical methods, and the coefficients transform formulas of the new network are obtained. In addition, it is also proved that the new network still possesses approximation with respect to a continuous polygonal fuzzy valued function. Finally, the approximation algorithm and realization process of the polygonal fuzzy neural networks to a two-polygonal fuzzy valued function are given by means of an example.