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