Some Studies Of Symmetric Difference Operators And Negation Operations On Type-2 Fuzzy Sets

In this paper,we investigated symmetric difference operator and negation operations on type-2 fuzzy sets.First,we extended symmetric difference operators to type-2 fuzzy sets by Zadeh-extension principle,and then discussed some properties of extended symmetric difference operators.We also proved that the extended symmetric difference operator on type-2 fuzzy sets is a s-norms on type-2 fuzzy truth value algebra,and showed that the negation operations related to the symmetric difference operators are strong negation operations when extended to the type-2 fuzzy sets.Secondly,we presented some properties of negation operations of type-2 fuzzy sets on bounded lattices,and proved that the algebra of truth values for type-2 fuzzy sets on a chain is a De Morgan Birkhoff system and the negation operation of a subalgebra of truth value algebra for type-2 fuzzy sets is strong over a bounded distributive lattice.