 Consider a first order language for algebraic structures with a monadic predicate symbol S. Then a "fuzzy subalgebra" is a fuzzy model of a theory containing, for any "n"-ary operation h, the axioms

formula_1

and, for any constant c, S(c).The first axiom expresses the closure of S with respect to the operation h, and the second expresses the fact that c is an element in S. As an example, assume that the valuation structure is defined in [0,1] and denote by formula_2 the operation in [0,1] used to interpret the conjunction.Then a fuzzy subalgebra of an algebraic structure whose domain is D is defined by a fuzzy subset of D such that, for every d1...,dn in D, if h is the interpretation of the n-ary operation symbol h, then


Moreover, if c is the interpretation of a constant c such that s(c) = 1.