Fuzzy subalgebra

Fuzzy subalgebras theory is a chapter of fuzzy set theory. It is obtained from an interpretation in a multi-valued logic of axioms usually expressing the notion of subalgebra of a given algebraic structure. Fuzzy subalgebras theory is a chapter of fuzzy set theory. It is obtained from an interpretation in a multi-valued logic of axioms usually expressing the notion of subalgebra of a given algebraic structure. 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 ∀ x 1 , . . . , ∀ x n ( S ( x 1 ) ∧ . . . . . ∧ S ( x n ) → S ( h ( x 1 , . . . , x n ) ) {displaystyle forall x_{1},...,forall x_{n}(S(x_{1})land .....land S(x_{n}) ightarrow S(h(x_{1},...,x_{n}))}