Univariate fuzzy-random neural network approximation operators

In this article, we study the rate of pointwise convergence in the q-mean to thefuzzy-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 new results in fuzzy-random analysis are given of independent merit, which are used then in the proofs of the main results of the paper. © 2004 Elsevier Ltd. All rights reserved