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The main purpose of this work is to introduce some types of fuzzy convergence sequences of operators defined on a standard fuzzy normed space (SFN-spaces) and investigate some properties and relationships between these concepts. Firstly, the definition of weak fuzzy convergence sequence in terms of fuzzy bounded linear functional is given. Then the notions of weakly and strongly fuzzy convergence sequences of operators are introduced and essential theorems related to these concepts are proved. In particular, if ( ) is a strongly fuzzy convergent sequence with a limit where linear operator from complete standard fuzzy normed space into a standard fuzzy normed space then belongs to the set of all fuzzy bounded linear operators . Furthermore, the concept of a fuzzy compact linear operator in a standard fuzzy normed space is introduced. Also, several fundamental theorems of fuzzy compact linear operators are studied in the same space. More accurately, every fuzzy compact linear operator is proved to be fuzzy bounded where and are two standard fuzzy normed spaces
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Zadeh L. Fuzzy sets. Inf. Control. 1965; 8: 338-353.
Efe. H , Yildiz. C. Some results in fuzzy compact linear operators. JCAA. 2010; 12:251-262.
Saadati R, Vaezpour S M. Some results on fuzzy Banach spaces. J. Appl. Math. 2005; 17: 475-484.
Katsaras A. Fuzzy topological vector spaces II. Fuzzy Sets Syst. 1984; 12: 143-154.
Feblin C. Finite dimensional fuzzy normed linear spaces. Fuzzy Sets Syst .1992;48:239–48.
Shih-Chuan C, John N. Fuzzy linear operators and fuzzy normed linear spaces. International Conference on Fuzzy Theory and Technology Proceedings. Oct 14 1992; p: 193-197.
Bag T, Samanta SK. Finite dimensional fuzzy normed linear spaces. J Fuzzy Math .2003;11(3):687–705.
Sadeqi I , Salehi M . Fuzzy compact operators and topological degree theory. Fuzzy Sets Syst. 2009;160:1277-1285.
Mehmet K, Mehmet A. On Generalized Fuzzy n-Normed Spaces Including φ Function. Int J Sci Eng Res. 2013; 4(11): 2229-5518.
Font J, Galindo J, Macario S, Sanchis M. Mazur-Ulam type theorems for fuzzy normed spaces. J.Nonlinear Sci. Appl. 2017;10: 4499–4506.
Chatterjee S, Bag T, Samanta S. Some results on G-fuzzy normed linear space. Int J Pure Appl Math. 2018; 120 (5) : 1295-1320.
Tudor B, Flavius P, Sorin N. A Study of Boundedness in Fuzzy Normed Linear Spaces. J Symmetry MDPI. 2019; 11:1-13.
Sorin N, Tudor B , Flavius P. Some fixed point theorems for φ-contractive mappings in fuzzy normed linear spaces. J. Nonlinear Sci. Appl. 2017;10: 5668–5676.
Nădăban S. Fuzzy Continuous Mappings in Fuzzy Normed Linear Spaces, IJCCC. 2015;10(6):834-842.
Szabo A, Bînzar T, Nădăban S, Pater F. Some properties of fuzzy bounded sets in fuzzy normed linear space. AIP Conference Proceedings ISSN 390009. 2018.
Govindana V, Murthyb S. Solution And Hyers-Ulam Stability Of n-Dimensional Non-Quadratic Functional Equation In Fuzzy Normed Space Using Direct Method. Fuzzy Sets Syst. 2019; 16 : 384–391.
Lee K. Approximation properties in fuzzy normed spaces. Fuzzy Sets Syst. 2016; 282: 115–130.
Ju Myung K , Keun Y. Approximation Properties in Felbin Fuzzy Normed Spaces. Math J.2019; 22:1-14.
Cho Y, Rassias T, Saadati R. Fuzzy normed spaces and fuzzy metric spaces. Fuzzy Operator Theory in Mathematical Analysis.Springer, Cham. 2018; P: 11–43.
Morteza S. A comparative study of fuzzy norms of linear operators on a fuzzy normed linear
Spaces. JMM. 2015;2(2):217-234.
Rana A, Buthainah A, Fadhel F. On Completeness of Fuzzy Normed Spaces. JAM.2015;9(8):2963-2970.
Mohsenialhosseini M. Error estimates for fixed point theorems in fuzzy normed spaces. AFMI.2016;11(1):87-95.
George A, Veeramani P. On some results in fuzzy metric spaces. Fuzzy Sets Syst. 1994; 64: 395-399.
Kider J, Jameel R. Fuzzy Bounded and Continuous Linear Operators on Standard Fuzzy Normed Spaces.Eng.&Tech Journal. 2015;33(2): 178– 185.
Jameel R. On some results of analysis in a standard fuzzy normed space. M.Sc. Thesis, University of Technology, Iraq. 2014.
Kutateladze S. Fundamentals of Functional Analysis. Springer Science Business Media Dordrecht. Sobo1ev Institute of Mathematics, Novosibirsk. 1996. 276 p.