arXiv subjects
Publications and source records attributed to T. K. Samanta.
In this paper, first we have established two sets of sufficient conditions for a mapping to have unique fixed point in a intuitionistic fuzzy metric space and then we have redefined the contraction mapping in a intuitionistic fuzzy metric space and thereafter we proved the Banach Fixed Point theorem.
In this paper, generalised intuitionistic fuzzy soft sets and relations on generalised intuitionistic fuzzy soft sets are defined and a few of their properties are studied. An application of generalised intuitionistic fuzzy soft sets in decision making with respect to degree of preference is investigated.
In this paper we have studied the relation between the fuzzy left (respectively right) ideals of $Γ-$semiring and that of operator semiring. Thereafter, we have established that the Lattices of all fuzzy left (respectively right) ideal of $Γ-$semiring is equivalent to that of Left operator semiring. Also we have established few properties relating the $k-$ideals and $h-$ideals of $Γ-$semiring with that of operator semiring.
Intuitionistic fuzzy Banach algebra is introduced and a few properties of it is studied. The properties of invertible elements and relation among invertible elements, open set, closed set are emphasized. Topological divisors of zero is defined and its relation with closed set are studied.
In this paper, we introduce cone normed linear space, study the cone convergence with respect to cone norm. Finally, we prove the completeness of a finite dimensional cone normed linear space.
Intuitionistic Fuzzy derivative, Intuitionistic Fuzzy Gateaux derivative, Intuitionistic Fuzzy Fréchet derivative are defined and a few of their properties are studied. The relation between Intuitionistic Fuzzy Gateaux derivative and Intuitionistic Fuzzy Fréchet derivative are emphasized.
The notion of Intuitionistic fuzzy hypervector space has been generalized and a few basic properties on this concept are studied. It has been shown that the intersection and union of an arbitrary family of Intuitionistic fuzzy hypervector spaces are also Intuitionistic fuzzy hypervector space. Lastly, the notion of a linear transformation on a hypervector space is introduced and established an important theorem relative to Intuitionistic fuzzy hypervector spaces.
In respect of the definition of intuitionistic fuzzy n-norm \cite{Vijayabalaji}, the definition of generalised intuitionistic fuzzy $ψ$ norm (\, in short GIF$ψ$N \,) is introduced over a linear space and there after a few results on generalized intuitionistic fuzzy $ψ$ normed linear space and finite dimensional generalized intuitionistic fuzzy $ψ$ normed linear space have been developed. Lastly, we have introduced the definitions of generalised intuitionistic fuzzy $ψ$ continuity , sequentially intuitionistic fuzzy $ψ$ continuity and it is proved that they are equivalent.
Various types of fuzzy anti-continuity and fuzzy anti-boundedness are defined. A few properties of them are established. The intra and inter relation among various types of fuzzy anti-continuity and fuzzy anti-boundedness are studied.
A few of the algebraic and topological properties of int. fuzzy continuity and int. fuzzy uniform continuity are investigated. Also, the concept of int. fuzzy uniform convergence is introduced thereafter a few result on int. fuzzy uniform convergence are studied.
Using the concept of fuzzy field, we have considered the fuzzy field of real and complex numbers and thereafter we have established a few standard results of real and complex numbers with respect to a membership function.