  This paper aims to present objective methods for constructing new fuzzy sets
from known fuzzy or classical sets, defined over the elements of a finite
universe's superstructure. The paper proposes rules for assigning membership
functions to these new fuzzy sets, leading to two important findings. Firstly,
the property concerning the cardinality of a power set in classical theory has
been extended to the fuzzy setting, whereby the scalar cardinality of a fuzzy
set $\tilde B$ defined on the power set of a finite universe of a fuzzy set
$\tilde A$ satisfies $\text{card}(\tilde B)=2^{\text{card}(\tilde A)}$.
Secondly, the novel algorithms allow for an arbitrary membership value to be
objectively achieved and represented by a specific binary sequence.
