  The present work reports a comparative performance of artificial neurons
obtained in terms of the real-valued Jaccard and coincidence similarity indices
and respectively derived functionals. The interiority index and classic
cross-correlation are also included for comparison purposes. After presenting
the basic concepts related to real-valued multisets and the adopted similarity
metrics, including the generalization of the real-valued Jaccard and
coincidence indices to higher orders, we proceed to studying the response of a
single neuron, not taking into account the output non-linearity (e.g.~sigmoid),
respectively to the detection of gaussian two-dimensional stimulus in presence
of displacement, magnification, intensity variation, noise and interference
from additional patterns. It is shown that the real-valued Jaccard and
coincidence approaches are substantially more robust and effective than the
interiority index and the classic cross-correlation. The coincidence-based
neurons are shown to have the best overall performance respectively to the
considered type of data and perturbations. The potential of the multiset
neurons is further illustrated with respect to the challenging problem of image
segmentation, leading to impressive cost/benefit performance. The reported
concepts, methods, and results, have substantial implications not only for
pattern recognition and machine learning, but also regarding neurobiology and
neuroscience.
