Intuitionistic fuzzy I-convergent double sequence spaces defined by compact operator and modulus function

Article type: Research Article

Authors: Khan, Vakeel A.^{a; *} | Yasmeen, ^a | Esi, Ayhan^b | Fatima, Hira^a

Affiliations: [a] Department of Mathematics, Aligarh Muslim University, Aligarh, India | [b] Department of Mathematics, Adiyaman Universiaty, Adiyaman, Turkey

Correspondence: [*] Corresponding author. Vakeel A. Khan, Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India. E-mail: [email protected].

Abstract:  In recent years, the Fuzzy theory has emerged as the most active area of research in many branches of mathematics and engineering. This new theory was introduced by L.A. Zadeh in 1965 and since then large number of research papers have been appeared by using the concept of Fuzzy set/numbers and fuzzification of many classical theories has also been made. The object of this paper is to define the intuitionistic Fuzzy I-convergent double sequence spaces  2S(μ,ν)I(T,f) and  2S(μ,ν)0I(T,f) defined by Compact Operator and Modulus Function. We study some topological and algebraic properties of these spaces and discuss the Fuzzy topology on them.

Keywords: Ideal, filter, I-convergence and I₂-convergence in intuitionistic fuzzy normed spaces, bounded linear operator, compact linear operator, modulus function

DOI: 10.3233/JIFS-17741

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 6, pp. 3905-3911, 2017