The classical ergodic theory has been built on -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.

First, we introduce the concept of Intuitionistic Fuzzy group congruence and we obtain the characterizations of Intuitionistic Fuzzy group congruences on an inverse semigroup and a T* -pure semigroup, respectively. Also, we study some properties of Intuitionistic Fuzzy group congruence. Next, we introduce the notion of Intuitionistic Fuzzy sernilattiee congruence and we give the characterization of Intuitionistic Fuzzy semilattice congruence on a T* -pure semigroup. Finally, we introduce the concept of Intuitionistic Fuzzy normal congruence and we prove that (IFNC (Es), n, V) is a complete lattice. And we find the greatest Intuitionistic Fuzzy normal congruence containing an Intuitionistic Fuzzy congruence on E8.

This study introduces the idea of Intuitionistic Fuzzy soft hyperalgebra. First, Intuitionistic Fuzzy soft hyperalgebra is defined and this definition is supported with an example. A level soft set is formed over a hyperalgebra of an Intuitionistic Fuzzy soft set. The relation between soft hyperalgebras and intuitionistic Fuzzy soft hyperalgebras is given. Finally, Intuitionistic Fuzzy soft hyperalgebra homomorphism is established and demonstrated if the image and inverse image of an Intuitionistic Fuzzy soft hyperalgebra are both Intuitionistic Fuzzy soft hyperalgebras under homomorphism.

The object of this paper is to introduce the notion of Intuitionistic Fuzzy continuous mappings and Intuitionistic Fuzzy bounded linear operators from one Intuitionistic Fuzzy n-normed linear space to another. Relation between Intuitionistic Fuzzy continuity and Intuitionistic Fuzzy bounded linear operators are studied and some interesting results are obtained.

In the current paper, consider the Fuzzy normed linear space (X, N) which is defined by Bag and Samanta. First, we construct a new Fuzzy topology on this space and show that these spaces are Hausdorff locally convex Fuzzy topological vector space. Some necessary and sufficient conditions are established to illustrate that the presented Fuzzy topology is equivalent to two previously studied Fuzzy topologies.