INTUITIONISTIC FUZZY SEMI δ-PRE IRRESOLUTE MAPPINGS

unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract. This paper introduces the concept of intuitionistic fuzzy semi δ -pre irresolute mappings in intuitionistic fuzzy topological spaces. We investigate some of their properties and obtain several preservation properties and characterizations.


INTRODUCTION
The concept of fuzzy sets was introduced by Zadeh in his classis paper [11]. Using the concept of fuzzy set Chang [2] introduced the fuzzy topological spaces. Atanassov [1] introduced the notion of intuitionistic fuzzy sets. Coker [4] defined the intuitionistic fuzzy topological spaces. This approach provided a wide field for investigation in the area of fuzzy topology and its applications. In the recent past many researchers such as Coker [5], Joen [6] and Lupianez [8] studied various topological concepts in intuitionistic fuzzy topology. Recently Thakur, Rathor and Bajpai [9] introduced the concepts of Intuitionistic fuzzy semi δ -preopen sets and Intuitionistic fuzzy semi δ -precontinuity in Intuitionistic fuzzy topology. The present paper introduces the concept of Intuitionistic fuzzy semi δ -pre irresolute mappings and studied some of their properties in Intuitionistic fuzzy topological spaces.

PRELIMINARIES
Let X be a nonempty fixed set and I the closed interval [0, 1]. An intuitionistic fuzzy set A is an object having the form A = {< x, µ A (x), ν A (x) >: x ∈ X} where the functions µ A : X → I and ν A : X → I denote the degree of membership namely µ A (x) and the degree of nonmembership (namely ν A (x)) of each element x ∈ X to the set A, respectively, and 0 ≤ µ A (x) + ν A (x) ≤ 1 for each x ∈ X. For the basic properties of Intuitionistic fuzzy sets and Intuitionistic fuzzy points, the researchers should refer ( [1,8]. An intuitionistic fuzzy topology on a nonempty set X is a family τ of intuitionistic fuzzy sets in X, which contains0 and1 and closed with respect to any union and finite intersection. Intuitionistic fuzzy closed) but the converse may not be true [3].
Let (X, τ) be an Intuitionistic fuzzy topological space and A be an intuitionistic fuzzy set of X. Then the intuitionistic fuzzy semi δ -preinterior (denoted by sδ pint) and intuitionistic fuzzy semi δ -preclosure (denoted by sδ pcl) of A respectively defined as follows: Definition 2.4. [9] Let A be an intuitionistic fuzzy set A of an intuitionistic fuzzy topological space (X, τ) and x (α,β ) be an intuitionistic fuzzy point of X. A is called:

INTUITIONISTIC FUZZY SEMI δ -PRE IRRESOLUTE MAPPINGS
In this section, we introduce the concept of intuitionistic fuzzy semi δ -pre irresolute mappings and study some of their properties in intuitionistic fuzzy topological spaces.
Definition 3.1. A mapping f from an intuitionistic fuzzy topological space (X, τ) to another in- Remark 3.1. Every intuitionistic fuzzy semi δ -pre irresolute mappings is intuitionistic fuzzy semi δ -pre continuous but the converse may not be true.    (e). for every intuitionistic fuzzy point x (α,β ) of X and every intuitionistic fuzzy semi δ -pre neighborhood A of f (x (α,β ) ), there is an intuitionistic fuzzy semi δ -pre neighborhood U of (f). for every intuitionistic fuzzy point x (α,β ) of X and every intuitionistic fuzzy set A ∈ IFSδ PO(Y ) such that f (x (α,β ) ) q A, there is an intuitionistic fuzzy set O ∈ IFSδ PO(X) such that x (α,β )q O and f (O) ⊆ A.
(d) ⇒ (e) Let x (α,β ) be an intuitionistic fuzzy point of X and A be a semi δ -pre neighborhood of f (x (α,β ) ). Then U = f −1 (A) is an intuitionistic fuzzy semi δ -pre neighborhood of Then f (x c (α,β ) ) q A and so by ( f ), there exists an intuitionistic fuzzy set O ∈ IFSδ PO(X), such that (f) ⇒ (g) Let x (α,β ) be an intuitionistic fuzzy point of X and A be semi δ -Q-neighborhood of f (x (α,β ) ). Then there is an intuitionistic fuzzy open set (g) ⇒ (h) Let x (α,β ) be an intuitionistic fuzzy point of X and A be a semi δ -pre-Q-neighborhood Then A is intuitionistic fuzzy semi δ -pre-Q-neighborhood of f (x (α,β ) ). So there is an intuitionistic fuzzy semi δ -pre Q-neighborhood U of x (α,β ) such that f (U) ⊆ A. Now U being an intuitionistic fuzzy semi δ -pre Q-neighborhood of x (α,β ) . Then there exists an intuitionistic ). Now sδ pcl( f (A)) ∈ IFSδ PC(Y ) and hence f −1 (sδ pcl( f (A))) ∈ IFSδ PC(X).
Hence go f is intuitionistic fuzzy semi δ -precontinuous.

CONCLUSION
In this paper, a new class of mappings called Intuitionistic fuzzy semi δ -pre irresolute mappings have been introduced, it is shown by examples that the concepts of Intuitionistic fuzzy semi δ -pre irresolute mappings is stronger than the Intuitionistic fuzzy semi δ -pre continuous mappings and independent to the Intuitionistic fuzzy continuous mappings. Several characterizations and properties of these class of Intuitionistic fuzzy mappings have been studied.