The interpolation and approximation of a function by the neural network operator for an irregular grid of data points are frequently used in the applications of neural networks such as image and signal processing. In this paper, we prove interpolation and approximation results for a continuous function defined on a box-domain of \(\mathbb {R}^{s}\) by neural network operators for multivariate data of irregular grid points. We measure the rate of approximation in terms of the modulus of continuity of the functions being approximated. We define this neural network interpolation operator by using the linear combinations of sigmoidal functions from a new class of sigmoidal functions and by using the fractional mean values of the function instead of its sample values.