S.K. Samanta

Fuzzy bounded linear operators

In this paper, a notion of boundedness of a linear operator from a fuzzy normed linear space to another fuzzy normed linear space is introduced and two types (strong and weak) of fuzzy bounded linear operators are defined. Relation between fuzzy continuity and fuzzy boundedness is studied. Definitions of fuzzy bounded linear functionals are given and the notions of fuzzy dual spaces are developed. The Hahn-Banach theorem, the Open mapping theorem, the Closed graph theorem and the Uniform boundedness principle theorem are established.

Gradation of openness: fuzzy topology

Abstract In an earlier paper, we have given a new definition of fuzzy topology by introducing a concept of gradation of openness of fuzzy subsets. In order to make the concept more appropriate, in this paper we modify the definition of gradation function and then study subspace of fuzzy topological spaces, gradation preserving maps and category of fuzzy topological spaces and gradation preserving maps.

On intuitionistic gradation of openness

In this paper, we introduce a concept of intuitionistic gradation of openness on fuzzy subsets of a nonempty set X and define an intuitionistic fuzzy topological space. We prove that the category of intuitionistic fuzzy topological spaces and gradation preserving mappings is a topological category. We study compactness of intuitionistic fuzzy topological spaces and prove an analogue of Tychonoffs theorem.

Fuzzy topology: fuzzy closure operator, fuzzy compactness and fuzzy connectedness

Abstract In this paper definitions of fuzzy closure operator, fuzzy compactness and fuzzy connectedness are given in a redefined fuzzy topological space and then some characteristic properties of fuzzy closure operator, product theorems of fuzzy compactness, invariance of fuzzy compactness and fuzzy connectedness under gradation preserving maps and invariance of fuzzy connectedness under the fuzzy closure operator are studied.

Topology of interval-valued intuitionistic fuzzy sets

In this paper topology of interval-valued intuitionistic fuzzy sets is defined and some of its properties are studied. It is shown that the category of topological spaces of interval-valued intuitionistic fuzzy sets and continuous functions forms a topological category.

Fuzzy topology redefined

Abstract In this paper we give a new definition of fuzzy topology by introducing a concept of gradation of openness of fuzzy subsets, and then study fuzzy continuity.

A comparative study of fuzzy norms on a linear space

In this paper, a comparative study among several types of fuzzy norms on a linear space defined by various authors has been made and it is shown that, broadly, they may be classified into two types, one of which is Katsarass type and the other is Felbins type.

Fuzzy bounded linear operators in Felbin's type fuzzy normed linear spaces

In this paper, definitions of strongly fuzzy bounded linear operator and weakly fuzzy bounded linear operators are given and the idea of their fuzzy norms are introduced. The concept of fuzzy dual spaces are introduced and the Hahn-Banach theorem is established in fuzzy setting.

Fuzzy proximities and fuzzy uniformities

Abstract A new definition of fuzzy proximity is given and some of its properties are studied. We also give a definition of fuzzy uniformity whose underlying fuzzy proximity is a fuzzy proximity in our sense.

Fuzzy proximities structures and fuzzy grills

Abstract In this paper definitions of basic proximities of fuzzy sets and basic fuzzy proximities are given and a classification scheme for proximities of fuzzy sets as well as fuzzy proximities are introduced.