In this paper, the gradual real numbers are considered and the notion of the gradual normed linear space is given. Also some topological properties of such spaces are studied, and it is shown that the gradual normed linear space is a locally convex space, in classical sense. So the results in locally convex spaces can be translated in gradual normed linear spaces. Finally, we give an examp...

In this paper we consider general t-norm in the definition of fuzzy normed linear space which is introduced by the authors in an earlier paper. It is proved that if t-norm is chosen other than ”min” then decomposition theorem of a fuzzy norm into a family of crisp norms may not hold. We study some basic results on finite dimensional fuzzy normed linear spaces in general t-norm setting. 2010 AMS...

and Applied Analysis 3 is Cauchy. If each Cauchy sequence is convergent, then the fuzzy norm is said to be complete, and the fuzzy normed space is called a fuzzy Banach space. Let X,N be a fuzzy normed space and Y,N ′ a fuzzy Banach space. For a given mapping f : X → Y , we use the abbreviation Df ( x, y ) : f ( 2x y ) f ( 2x − y 2f x − fx y − fx − y − 2f 2x , 2.1 for all x, y ∈ X. Recall Df ≡ ...

The object of this paper is to introduce the notion of intuitionistic fuzzy continuous mappings and intuitionistic fuzzy bounded linear operators from one intuitionistic fuzzy n-normed linear space to another. Relation between intuitionistic fuzzy continuity and intuitionistic fuzzy bounded linear operators are studied and some interesting results are obtained.

Fuzzy set theory has entered into a large variety of disciplines of sciences,technology and humanities having established itself as an extremely versatileinterdisciplinary research area. Accordingly different notions of fuzzystructure have been developed such as fuzzy normed linear space, fuzzytopological vector space, fuzzy sequence space etc. While reviewing theliterature in fuzzy sequence sp...

The aim of this paper is to study the generalization of the intuitionistic fuzzy normed spaces such as intuitionistic fuzzy 2-normed space. In this structure, we have discussed the intuitionistic fuzzy 2continuity and intuitionistic fuzzy 2-boundedness. Also, we have introduced the intuitionistic fuzzy ψ-2-normed space which is a generalization of intuitionistic fuzzy 2-normed space. We have di...

Wewill define a notion for a quasi fuzzy p-normed space, then we use the fixed point alternative theorem to establish Hyers–Ulam– Rassias stability of the quartic functional equation where functions map a linear space into a complete quasi fuzzy p-normed space. Later, we will show that there exists a close relationship between the fuzzy continuity behavior of a fuzzy almost quartic function, co...

In this paper, a class of generalised best approximation problems is formulated in a fuzzy normed linear space.

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.