Automorphisms of the algebra of fuzzy truth values

This paper is an investigation of the automorphisms of the algebra of truth values of type-2 fuzzy sets. This algebra contains isomorphic copies of the truth value algebras of type-1 and of iriterval-valued fuzzy sets. It is shown that these subalgebras are characteristic; that is, are carried onto themselves by automorphisms of the containing algebra of truth values of fuzzy sets. Some other relevant subalgebras are proved characteristic, including the subalgebra of convex normal functions. The principal tool in this study is the determination of various irreducible elements.