The Intuitionistic Fuzzy Normed Space of Coefficients

Abstract

Intuitionistic fuzzy normed space is defined using concepts of t-norm and t-conorm. The concepts of fuzzy completeness, fuzzy minimality, fuzzy biorthogonality, fuzzy basicity, and fuzzy space of coefficients are introduced. Strong completeness of fuzzy space of coefficients with regard to fuzzy norm and strong basicity of canonical system in this space are proved. Strong basicity criterion in fuzzy Banach space is presented in terms of coefficient operator.

The Space of Coefficients in a Linear Topological Space

“…Every nondegenerate system (to be defined later) in a Banach space generates the corresponding Banach space of coefficients with canonical basis (see, e.g., Bilalov & Najafov, 2011;Dremin, Ivanov, & Nechitailo, 2001). Similar results are obtained in fuzzy structures (Bilalov, Farahani, & Guliyeva, 2012) which have recently gained a great scientific interest. Therefore, space of coefficients plays an important role in the study of approximative properties of systems.…”

Bounded Linear Transformations in G-Fuzzy Normed Linear Space

“…Depending on the concepts of Q-fuzzy metric and G-norm, the space of Gfuzzy normed is presented in [9]. The fuzzy functional analysis is improved and a wide variety of domains the concept of the fuzzy norm has been used, for examples one can see [10][11][12][13][14][15][16][17][18]. different types of linear bounded transformation by distinct authors introduced for more details [20][21][22][23][24].…”