LL-intuitionistic fuzzy σσ-algebras

The main purpose of this paper is to generalize the concept of (L,M)(L,M)-fuzzy σσ-algebras defined by Shi [F.G. Shi, (L,M)(L,M)-fuzzy σσ-algebras, International Journal of Mathematics and Mathematical Sciences. doi:10.1155/2010/356581] from LL-fuzzy sets to intuitionistic fuzzy sets; the notions of LL-intuitionistic fuzzy σσ-algebras and LL-intuitionistic fuzzy measurable functions are introduced; the relationships among LL-intuitionistic fuzzy σσ-algebras, (I,I)(I,I)-fuzzy σσ-algebras and II-fuzzifying σσ-algebras are studied. Then we give the definition of the product of LL-intuitionistic fuzzy σσ-algebras; some of their elementary properties are discussed. By use of the concept of II-fuzzifying σσ-algebras, the notion of generated LL-intuitionistic fuzzy σσ-algebras is proposed. Finally, the properties of the generated functor IζIζ from the category of II-fuzzifying σσ-algebras and II-fuzzifying measurable functions to the category of LL-intuitionistic fuzzy σσ-algebras and LL-intuitionistic fuzzy measurable functions are proved.