K. Cunderlkova - Mathematical Institute, Slovak Academy of Sciences, Stefanikova ۴۹, ۸۱۴ ۷۳ Bratislava, Slovakia

The classical ergodic theory hasbeen built on σ-algebras. Later the Individual ergodictheorem was studied on more general structures like MV-algebrasand quantum structures. The aim of this paper is to formulate theIndividual ergodic theorem for intuitionistic fuzzy observablesusing  m-almost everywhere convergence, where  m is anintuitionistic fuzzy state. We show the Kolmogorov constructionfor intuitionistic fuzzy observables, too.

The intuitionistic fuzzy event, the intuitionistic fuzzy observable, the intuitionistic fuzzy state, the product, the upper limit, the lower limit, the m-almost everywhere convergence, the m-preserving transformation, the Individual ergodic theorem, the Kolmogorov construction