We obtain the general solution of the following functional equation \begin{multline*} f(kx_1+x_2+\cdots+x_k)+f(x_1+kx_2+\cdots+x_k)+\cdots+f(x_1+x_2+\cdots+kx_k) +f(x_1)+f(x_2)+\cdots+f(x_k)=2kf(x_1+x_2+\cdots+x_k),~k\geq2. \end{multline*} We establish the Hyers--Ulam--Rassias stability of the above functional equation in the fuzzy normed spaces. More precisely, we show under suitable conditions that a fuzzy $q$-almost affine mapping can be approximated by an affine mapping. Further, we determine the stability of same functional equation by using fixed point alternative method in fuzzy normed spaces.