Document Type : Research Paper

Author

• K. Cunderlkova

Mathematical Institute, Slovak Academy of Sciences, Stefanikova 49, 814 73 Bratislava, Slovakia

Abstract

The classical ergodic theory has
been built on σ-algebras. Later the Individual ergodic
theorem was studied on more general structures like MV-algebras
and quantum structures. The aim of this paper is to formulate the
Individual ergodic theorem for intuitionistic fuzzy observables
using  m-almost everywhere convergence, where  m is an
intuitionistic fuzzy state. We show the Kolmogorov construction
for 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