On the Intuitionistic fuzzy topological (metric and normed) spaces

In this paper, we define precompact set in intuitionistic fuzzy metric spaces and prove that any subset of an intuitionistic fuzzy metric space is compact if and only if it is precompact and complete. Also we define topologically complete intuitionistic fuzzy metrizable spaces and prove that any $G_{\delta }$ set in a complete intuitionistic fuzzy metric spaces is a topologically complete intuitionistic fuzzy metrizable space and vice versa. Finally, we define intuitionistic fuzzy normed spaces and fuzzy boundedness for linear operators and so we prove that every finite dimensional intuitionistic fuzzy normed space is complete.Comment: 16 page

New notions of triple ideal convergent on intuitionistic fuzzy normed spaces

In this paper, we introduce and study the notions of MI3(µ,v)(T), MI03(µ,v)(T), MI3(µ,v)(T, F) and MI03(µ,v)(T, F) for triple sequences in intuitionistic fuzzy normed space for the sequence. Furthermore, some topological properties are established on these spaces.Publisher's Versio

A FIXED POINT APPROACH TO THE STABILITY OF GENERAL QUADRATIC EULER-LAGRANGE FUNCTIONAL EQUATIONS IN INTUITIONISTIC FUZZY SPACES

In this paper, we prove the generalized Hyers-Ulam stability of a general k-quadratic Euler-Lagrange functional equation:for any fixed positive integer in intuitionistic fuzzy normed spaces using a fixed point method

ON GENERALIZED STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES VIA IDEALS IN INTUITIONISTIC FUZZY NORMED SPACES

In this paper, we introduce the concept of I₂-lacunary statistical convergence and strongly I₂-lacunary convergence with respect to the intuitionistic fuzzy norm (μ,v), investigate their relationship, and make some observations about these classes. We mainly examine the relation between these two new methods and the relation between I₂-statistical convergence in the corresponding intuitionistic fuzzy normed space

Sezgisel fuzzy normlu uzaylarda ℐ-lacunary istatiksel yakınsaklık

In this study, first, we investigate the notions of ℐ-lacunary statistical convergence and strongly ℐlacunary convergence with regards to the intuitionistic fuzzy norm (IFN for short) (μ,ν). Then, we investigate relationships among this new concepts and make important observations about them. Futhermore, we examine the relations among ℐ-lacunary statistical convergence and ℐ-statistical convergence in terms of IFN (μ,ν) in the corresponding intuitionistic fuzzy normed space.Bu çalışmada, ilk olarak (μ,ν) sezgisel normuna göre ℐ-lacunary istatistiksel yakınsaklık ve kuvvetli ℐlacunary yakınsaklık kavramları tanımlandı. Daha sonra bu kavramlar arasındaki ilişkiler incelendi ve bu kavramlar üzerine önemli gözlemler yapıldı. Bununla birlikte, ilgili sezgisel fuzzy normlu uzayda (μ,ν) sezgisel normuna göre ℐ-lacunary istatistiksel yakınsaklık ile ℐ-istatistiksel yakınsaklık arasındaki ilişkiler incelendi