Individual ergodic theorem for intuitionistic fuzzy observables using intuitionistic fuzzy state

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.

Keywords:

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