Absorption Laws And Subalgebras Of The Algebras For Truth Values Of Type-2 Fuzzy Sets

This paper deals with the absorption laws and the subalgebras of algebras of truth values of type-2 fuzzy sets.First,we introduce the concepts of non-convex and convex elements of functions,and then give a necessary and sufficient condition under which the absorption laws in the algebra of truth values of type-2 fuzzy sets are true.As applications,we construct a subalgebra of the truth value algebra of type-2 fuzzy sets which is a distributive lattice.Secondly,we investigate a subalgebra of the truth value algebra of type-2 fuzzy sets,which consists of the characteristic functions of all non-empty finite subsets of the unit interval.Then we verify an equivalent description of three partial orders over the subalgebra,respectively.We also show function expressions of supremum and infimum under the three partial orders,respectively.We finally prove that the subalgebras are bounded lattices under those partial orders,respectively.