INTUITIONISTIC FUZZY SOFT CONTRA GENERALIZED B- CONTINUOUS FUNCTIONS

The main focus of this paper is to introduce the concept of intuitionistic fuzzy soft contra generalized b-continuous functions and intuitionistic fuzzy soft almost generalized b-continuous functions in intuitionistic fuzzy soft topological space. We further studied and established the properties of intuitionistic fuzzy soft contra gbcontinuous functions and intuitionistic fuzzy soft almost generalized b-continuous functions in intuitionistic fuzzy soft topological space.


INTRODUCTION
In this paper we de ine intuitionistic fuzzy soft generalized contra b-continuous functions and intuitionistic fuzzy soft almost generalized b-continuous functions and the properties are discussed.
A number of theories such as the theory of fuzzy sets, theory of intuitionistic fuzzy sets and theory of vague sets have been proposed for dealing with uncertainties in an ef icient way and all these have their own dif iculties. In 1999 Molodtsov Molodtsov (1999) introduce the concept of soft set theory for vagueness. Later in 2001, MAji. P. K., R. Biswas and A. R. Roy Maji et al. (2001) introduced the intuitionistic fuzzy soft sets. Moreover, Li and Cui Li et al. (2013) introduced the fundamental concepts of intuitionistic fuzzy soft topology in 2012. Also, the concept of intuitionistic fuzzy soft b-closed sets is introduced by Shuker Mahmood Khalil Khalil (2015) in 2014. Ahmed Al Omari and Mohd. Salmi Md. Noorani Al-Omari et al. (2009) studied the class of generalized b-closed sets. Dontchev Dontchev (1996) introduced the notion of contra-continuity and obtained some results compactness etc.
1. ϕ e and I e belong to τ 2. The union of any number of IF soft sets inτ belongs toτ 3. The intersection of any two IF soft sets inτ belongs to τ τ is called an IF soft topology over U and the triplet (U, τ, E) is called a IF soft topological space over U.
The members of τ are said to be IF soft open sets in U.

DEFINITION:1.6 Osmanoglu and Tokat (2013)An(F, A) ∈ IF S(U, E) is called IF soft point if for the element e ∈
The family of all IF soft gb-open sets in (U, τ , E) is denoted by IFSgbO .
De inition:1.10 Osmanoglu and Tokat (2013)Let IFS(U E ) and IFS(V k ) be two intuitionistic fuzzy soft classes, and let ω : U → V and ψ : E → K be mappings. Then a mappingω ψ: for all e ∈ ψ −1 (B)and

IF SOFT CONTRA GB-CONTINUOUS FUNCTION
De inition 3.1: Let (U, τ, E)and(V, τ ′ , K) be any two IF soft topological spaces over U and V respectively. An IF soft function ωψ : (U, τ, E) → (V, τ ′ , K) is said to be an Converse the above theorem need not be true.
τ , E) Theorem 3.6: Let(U, τ, E)and(V, τ ′ , K) be any two IF soft topological spaces over U and V respectively. Letω ψ : (U, τ, E) → (V, τ ′ , K) be an IF soft mapping andIF SgbO(U, τ, E) is closed under arbitrary union. Then the following are equivalent 1. ω ψ is an IF soft contra gb-continuous mapping Let ω ψ is an IF soft contra gb-continuous mapping and (G, K) be any IF soft closed set in (V, τ ′ , K). Then (G, K) c is an IF soft open set in (V, τ ′ , K). Therefore, by assump- Hence ω ψ is an IF soft contra gb-continuous mapping.
(ii) → (iii) Let e F be an IF soft point of (U, τ, E) and (G, K) be an IF soft closed set in Let (G, K) be an IF soft closed set in (V, τ ′ , K) and e F ∈ (ω ψ ) −1 (G, K) . Therefore ω ψ (e F ) ∈(G, K) and by assumption, there exists an IF soft gb-open set (Fe F , E) of Hence ω ψ is an IF soft contra continuous function.
Hence ω ψ is an IF soft contra b-continuous function.   (iii) If (V, τ ′ , K) is an IF soft semi-gb space, then ω ψ is IF soft gb-irresolute function.
(ii) Let (G, K) be any IF soft closed set in (V, τ ′ , K) and (V, τ ′ , K)be an IF soft semiregular space. So, by assumption (G, K) is an IF soft regular closed set in (V, τ ′ , K) and hence(ω ψ ) −1 (G, K) is IF soft gb-closed in (U, τ, E) . Therefore ω ψ is IF soft gbcontinuous function.
(iii) Let (G, K) be any IF soft gb-closed set in an IF soft semi-gb space(V, τ ′ , K) So, by assumption (G, K) is an IF soft regular closed set in(V, τ ′ , K) and hence(ω ψ ) −1 (G, K) is IF soft gb-closed in(U, τ, E) Therefore ω ψ is IF soft gbirresolute function. Conversely Let ω ψ is an IF soft almost gb-continuous mapping and (G, K) be any IF soft regular open set in(V, τ ′ , K) . Then (G, K) c is an IF soft regular closed set in (V, τ ′ , K). Therefore, by assumption, (ω ψ ) −1 (G, K) c is an IF soft gb-closed set in (U, τ, E) . That is ((ω ψ ) −1 (G, K)) c is IF soft gb-closed set in (U, τ, E) . Hence (ω ψ ) −1 (G, K) is an IF soft gb-open set in(U, τ, E) .
Theorem 4.6: Every IF soft R-map is IF soft almost gb-continuous. Proof: Let (U, τ, E)and(V, τ ′ , K)be any two IF soft topological spaces over U and V respectively. Let ω ψ : (U, τ, E) → (V, τ ′ , K) be an IF soft R-function and (G, K) be any IF soft regular closed set in (V, τ ′ , K) . Therefore, by assumption (ω ψ ) −1 (G, K) is IF soft regular closed set in (U, τ, E) . But every IF soft regular closed set is IF soft gb-closed, (ω ψ ) −1 (G, K) is IF soft gb-closed in (U, τ, E) and hence ω ψ is IF soft almost gb-continuous. (iii) For each IF soft point e F in (U, τ, E) and for each IF soft neigborhood (G, K)of ω ψ (e F ) there exists an IF soft gb-neighborhood (F, E) of e F such that ω ψ (F, E) ⊂int( cl(G, K)).

CONCLUSION
The purpose of this paper is to introduce intuitionistic fuzzy soft contra gbcontinuous function in intuitionistic fuzzy soft topological space and obtain several basic properties. Also, intuitionistic fuzzy soft almost generalized b-continuous function in intuitionistic fuzzy soft topological spaces are introduced and some of their properties are investigated.

ACKNOWLEDGMENT
We thank to referees for their valuable comments and suggestions