The polygonal fuzzy numbers are employed to define a new fuzzy arithmetic. A novel ex-tension principle is also introduced for the increasing function σ:R→R. Thus it is convenient to con-struct a fuzzy neural network model with succinct learning algorithms. Such a system possesses some universal approximation capabilities, that is, the corresponding three layer feedforward fuzzy neural networks can be universal approximators to the continuously increasing fuzzy functions. A novel ex-tension principle is also introduced for increasing function σ: R → R. It is convenient to con-struct a fuzzy neural network model with succinct learning algorithms. Such a system possesses some universal approximation capabilities, that is, the corresponding three layer feedforward fuzzy neural networks can be universal approximators to continuously increasing fuzzy functions.