  In this work, we study the Kantorovich variant of max-min neural network
operators, in which the operator kernel is defined in terms of sigmoidal
functions. Our main aim is to demonstrate the $L^{p}$-convergence of these
nonlinear operators for $1\leq p<\infty$, which makes it possible to obtain
approximation results for functions that are not necessarily continuous. In
addition, we will derive quantitative estimates for the rate of approximation
in the $L^{p}$-norm. We will provide some explicit examples, studying the
approximation of discontinuous functions with the max-min operator, and varying
additionally the underlying sigmoidal function of the kernel. Further, we
numerically compare the $L^{p}$-approximation error with the respective error
of the Kantorovich variants of other popular neural network operators. As a
final application, we show that the Kantorovich variant has advantages compared
to the sampling variant of the max-min operator and Kantorovich variant of the
max-product operator when it comes to approximate noisy functions as for
instance biomedical ECG signals.
