The concept of intuitionistic fuzzy β-almost compactness and intuitionistic fuzzy β-nearly compactness in intuitionistic fuzzy topological spaces is introduced and studied. Besides giving characterizations of these spaces, we study some of their properties. Also, we investigate the behavior of intuitionistic fuzzy β-compactness, intuitionistic fuzzy β-almost compactness, and intuitionistic fuzz...

In this paper, the authors investigate the generalized Ulam-Hyers stability of a Leibniz type additive and quadratic functional equation ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − − + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − + + − + − + − 3 2 3 3 = ) ( ) ( ) ( z y x f t z y x f t z f t y f t x f ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + − − + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − + − + 3 2 3 2 z y x f z y x f in the setting of intuitionistic fuzzy normed spaces using direct and fixed point methods.

let $(x, n)$ be a fuzzy normed space and $a$ be a fuzzy boundedsubset of $x$.  we define fuzzy $ell^infty$-sums and fuzzy $c_0$-sums offuzzy normed spaces. then we will show that in these spaces, all  fuzzyuniquely remotal sets are singletons.

in this paper, we introduce intuitionistic fuzzy contraction mappingand prove a fixed point theorem in intuitionistic fuzzy metric spaces.

in the present paper, we study some properties of fuzzy norm of linear operators. at first the bounded inverse theorem on fuzzy normed linear spaces is investigated. then, we prove hahn banach theorem, uniform boundedness theorem and closed graph theorem on fuzzy normed linear spaces. finally the set of all compact operators on these spaces is studied.

The purpose of this paper is to introduce and discuss the concept of orthogonality in the fuzzy metric spaces. At last we introduce and discuss the concept of orthogonality in the fuzzy normed spaces, and obtain some results on orthogonality in fuzzy normed spaces similar to orthogonality in normed spaces.

In this paper, we define and study Cheng-Mordeson L-fuzzy normed spaces. Further, we consider the finite dimensional Cheng-Mordeson L-fuzzy normed spaces and prove some theorems about completeness, compactness and weak convergence in these spaces. As application, we get a stability result in the setting of Cheng-Mordeson L-fuzzy normed spaces.

This paper investigates the fractals generated by the dynamical system of intuitionistic fuzzy contractions in the intuitionistic fuzzy metric spaces by generalizing the Hutchinson-Barnsley theory. We prove some existence and uniqueness theorems of fractals in the standard intuitionistic fuzzy metric spaces by using the intuitionistic fuzzy Banach contraction theorem. In addition to that, we an...

The aim of this paper is to present the new and interesting notionof ascending family of  $alpha $−n-norms corresponding to an intuitionistic fuzzy nnormedlinear space. The notion of best aproximation sets in an  $alpha $−n-normedspace corresponding to an intuitionistic fuzzy n-normed linear space is alsodefined and several related results are obtained.

The main purpose of this paper is to study the existence of a fixed points in fuzzy n-normed spaces. we proved our main results, a fixed point theorem for a self mapping and a common fixed point theorem for a pair of weakly compatible mappings on fuzzy n-normed spaces. Also we gave some remarks on fuzzy n-normed spaces.