The concept of an n-equidistant polygonal fuzzy number is introduced to avoid the complexity of the operations between fuzzy numbers. Firstly, the properties of linear operations and the convergence of n-equidistant polygonal fuzzy numbers are discussed, the method how to change a fuzzy number into an n-equidistant polygonal fuzzy number is shown. Next, for given a µ-integrable polygonal fuzzy valued function, an n-equidistant polygonal fuzzy valued function is constructed. By introducing the definition of K-quasi-additive integral and Kintegral norm, the universal approximation of polygonal fuzzy neural network are studied. The final result indicates that the polygonal fuzzy neural network still possess universal approximation to an integrable system.