In this chapter we study the rate of pointwise convergence in the q-mean to the Fuzzy-Random unit operator of very precise univariate Fuzzy-Random neural network operators of Cardaliaguet. Euvrard and “Squashing” types. These Fuzzy-Random operators arise in a natural and common way among Fuzzy-Random neural networks. These rates are given through Probabilistic-Jackson type inequalities involving the Fuzzy-Random modulus of continuity of the engaged Fuzzy-Random function or its Fuzzy derivatives. Also several interesting results in Fuzzy-Random Analysis are given of independent merit, which are used then in the proofs of the main results of the chapter. This chapter follows [17].