On Complete Sublattices of the Algebra of Truth Values of Type-2 Fuzzy Sets

The algebra of truth values of type-2 fuzzy sets contains isomorphic copies of the algebra of truth values of type-1 fuzzy sets and the algebra of truth values of interval-valued fuzzy sets. The algebra of truth values of type-2 fuzzy sets is not a lattice, but these subalgebras are lattices, and in fact, are complete lattices. There are many other subalgebras that are lattices, for example, the subalgebra of convex normal elements. This paper examines several subalgebras which are lattices, with the goal of determining whether or not they are complete.