The Properties Of Operations Of Type-2 Fuzzy Sets With Lattice Values As Truth Values

This paper deals with type-2 fuzzy sets whose truth values are in a complete distributive lattice.First,it generalizes type-2 fuzzy sets from [0,1] to a complete distributive lattice.Then it discusses the operations and properties of type-2 fuzzy sets with lattice values as truth values,for instance,commutativity,associativity,distributivity and idempotent.Next,it discusses the operations and properties of type-2 fuzzy sets with lattice values as truth values which are monotone increasing,for instance,commutativity,associativity,distributivity,idempotent and absorptivity.Finally,the conditions that the last type-2 fuzzy sets form a lattice are given.