On the intuitionistic fuzzy inner product spaces

Fuzzy inner product spaces and fuzzy orthogonality

“…[11] Let (X, F, * ) be a FIP-space and u, v ∈ X. Then we say u and v are fuzzy orthogonal if F (u, v, t) = H(t), for all t ∈ R and it is denoted by u ⊥ v.…”

“…We will use the next fundamental result frequently in this paper which is taken from [11]. Theorem 2.3.…”

On some intuitionistic fuzzy hyponormal operators

“…Saadati and Park [10] introduced modulation of the intuitionistic fuzzy metric space in IFIP-space using continuous trepresentable in 2005. In 2009, Goudarzi et al [6] introduced the new definition of Intuitionistic Fuzzy Normed Spaces and also given the modified definition of Intuitionistic Fuzzy Inner Product Space (IFIP-space). Goudarzi et al [6] introduced a triplet (H, F µ,ν , T), where H is a Real vector space, T is a continuous t-representable and F µ,ν is an intuitionistic fuzzy set on H 2 × R , as an Intuitionistic Fuzzy Hilbert Space in 2009.…”

“…In 2009, Goudarzi et al [6] introduced the new definition of Intuitionistic Fuzzy Normed Spaces and also given the modified definition of Intuitionistic Fuzzy Inner Product Space (IFIP-space). Goudarzi et al [6] introduced a triplet (H, F µ,ν , T), where H is a Real vector space, T is a continuous t-representable and F µ,ν is an intuitionistic fuzzy set on H 2 × R , as an Intuitionistic Fuzzy Hilbert Space in 2009. Majumdar and Samanta [13] gave various definitions of Intuitionistic Fuzzy Inner Product space and some of their properties using (H, µ, µ * ).…”

Some Properties of Spectral Theory in Fuzzy Hilbert Spaces

“…Fuzzy Hilbert spaces is an extension to the Hilbert space. The definition of a fuzzy Hilbert space has been introduced by M. Goudarzi and S. M. Vaezpour [9] in 2009 .…”