A class of extended fuzzy system

In the space w₂¹[a,b] and w, which stands for a space with a reproducing kernel in a dot product space, two classes of extended fuzzy systems are proposed respectively, by the reproducing kernels in a revised sense The new fuzzy systems are in fact the best interpolation operators in w₂¹[a,b] or w, respectively, which are employed readily just like the existing fuzzy systems but have better approximating characters.