  The objective quantification of similarity between two mathematical
structures constitutes a recurrent issue in science and technology. In the
present work, we developed a principled approach that took the Kronecker's
delta function of two scalar values as the prototypical reference for
similarity quantification and then derived for more yielding indices, three of
which bound between 0 and 1. Generalizations of these indices to take into
account the sign of the scalar values were then presented and developed to
multisets, vectors, and functions in real spaces. Several important results
have been obtained, including the interpretation of the Jaccard index as a
yielding implementation of the Kronecker's delta function. When generalized to
real functions, the four described similarity indices become respective
functionals, which can then be employed to obtain associated operations of
convolution and correlation.
