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.

In this paper we introduce the gradation of separation axioms ST 0 , RT 0 in an intuitionistic fuzzy topological space in the sense of Mondal and Samanta [7]. Using these concepts we have introduced and studied α-and α *-RT 0 intuitionistic fuzzy topological spaces.

We introduce the notion of (r,s)-connected sets in intuitionistic fuzzy topological spaces and investigate some properties of them. In particular, we show that every (r,s)-component in an intuitionistic fuzzy topological space is (r,s)-component in the stratification of it.

Based on previous results that study the completion of fuzzy metric spaces, we show that every intuitionistic fuzzy quasi-metric space, using the notion of fuzzy metric space in the sense of Kramosil and Michalek to obtain a generalization to the quasi-metric setting, has a bicompletion which is unique up to isometry.

Due to importance of the concepts of θ-closure and δ-closure, it is natural to try for their extensions to fuzzy topological spaces. So, Ganguly and Saha introduced and investigated the concept of fuzzy δ-closure by using the concept of quasicoincidence in fuzzy topological spaces. In this paper, we will introduce the concept of δ-closure in intuitionistic fuzzy topological spaces, which is a g...

We prove some properties of several types of connectedness defined in intuitionistic fuzzy special topological spaces.

in this paper, we prove the generalized hyers-ulam stability of the quadratic functionalequation$$f(x+y)+f(x-y)=2f(x)+2f(y)$$in non-archimedean $mathcal{l}$-fuzzy normed spaces.

This paper aims to present a short survey on two numerical functions determined by a hypergroupoid, called the fuzzy grade and the intuitionistic fuzzy grade of a hypergroupoid. It starts with the main construction of the sequences of join spaces and (intuitionistic) fuzzy sets associated with a hypergroupoid. After some computations of the above grades, we discuss some similarities and differe...

The purpose of this paper is to construct the concept of semi$theta$-compactness in intuitionistic fuzzy topological spaces. We give some characterizationsof semi $theta$-compactness and locally semi -compactness. Also, wecompare these concepts with some other types of compactness in intuitionisticfuzzy topological spaces.

In this paper we determine the sequences of join spaces and Atanassov's intuitionistic fuzzy sets associated with all i.p.s. hypergroups of order less than or equal to 6, focusing on the calculation of their lengths.