  We introduce a natural partial order in structurally natural finite subsets
the cobweb prefabs sets recently constructed by the present author. Whitney
numbers of the second kind of the corresponding subposet which constitute
Stirling-like numbers` triangular array are then calculated and the explicit
formula for them is provided. Next - in the second construction - we endow the
set sums of prefabiants with such an another partial order that their their
bell like numbers include fibonacci triad sequences introduced recently by the
present author in order to extend famous relation between binomial newton
coefficients and fibonacci numbers onto the infinity of their relatives among
which there are also the fibonacci triad sequences and binomial-like
coefficients (incidence coefficients included).
