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Fuzzy classification is the process of grouping elements into a fuzzy set whose membership function is defined by the truth value of a fuzzy propositional function.
A fuzzy class ~C = { i | ~Π } is defined as a fuzzy set ~C of individuals i satisfying a fuzzy classification predicate ~Π which is a fuzzy propositional function. The domain of the fuzzy class operator ~{.|.} is the set of variables V and the set of fuzzy propositional functions ~PF, and the range is the fuzzy powerset of this universe, ~P:
~{.|.}:V × ~PF ⟶ ~P
A fuzzy propositional function is, analogous to, an expression containing one or more variables, such that, when values are assigned to these variables, the expression becomes a fuzzy proposition in the sense of.