Many statistical estimators are expressible in the form S_n = Σⁿ_{k = 1} a_nkX_nk where {a_nk} are constants and {X_nk} are fuzzy random variables. Then, the convergence in probability or with probability one for S_n is of interest in determining consistency of the estimators. In statistical problems the linear form S_n involves possibly random weights and possibly dependent fuzzy random variables which are generated from independent, identically distributed fuzzy random variables. Thus, we assume the sequence of fuzzy random variables {X_nk : k 1} to be permutation invariant with respect to distributions instead of assuming independence. In particular, we look at the stochastic convergence of the form (1/A_n)Σⁿ_{k = 1} a_nX_nk, which is slightly different from the initial form S_n.