In this work,we focus our study on Fuzzy hyponormal operators acting on a fuzzy Hilbert space(FH space).we have given some properties of Fuzzy hyponormal operators on a FH space.And also we introduced the definition of Fuzzy class (N) operator acting on a Fuzzy Banach space (FB-space) and some definitions, theorems are discussed in detail.

In this paper, We introduce the definition of M-fuzzy hyponormal operator and also explored about some important properties of M-Fuzzy hyponormal operator from Fuzzy hyponormal operators in fuzzy Hilbert space. For a fuzzy continuous linear operator T on a Fuzzy Hilbert space H there exists a real number M if (T − zI) * u ≤ M (T − zI) u for all u ∈ H and for all z ∈ C (field of complex numbers).We have given some definitions which are related to M-fuzzy hyponormal operator in fuzzy Hilbert space.

Using the definition of Intuitionistic Fuzzy Hyponormal (IFHN) operator, i.e. S ∈ IFB(H) is an IFHN-operator if P µ,ν (S * x, u) ≤ P µ,ν (Sx, u), ∀x ∈ H or equivalently S * S−SS * ≥ 0, we investigate certain properties of IFHN-operators on an IFH-space. The definition of intuitionistic fuzzy class (N) of operators and some spectral properties are introduced. Also, a few theorems are discussed in detail.