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\noindent (iii) intuitionistic fuzzy semi open (resp. intuitionistic fuzzy semi closed) [6] if there exists an intuitionistic fuzzy open (resp. intuitionistic fuzzy closed) such that U$\subseteq$A $\subseteq$ Cl(U) (resp. int(U) $\subseteq$ A $\subseteq$ U). \noindent \textbf{Definition 2.11:} An intuitionistic fuzzy set A of an intuitionistic fuzzy topological space\textbf{ }(X,\includegraphics*[width=0.14in, height=0.20in, keepaspectratio=false]{image79.eps}) }(X,$\tau $) is called \noindent (i) an intuitionistic fuzzy w-closed \textbf{[14]} if cl(A) $\subseteq$ O whenever A$\subseteq$O and O is intuitionistic fuzzy semi open. (X, \includegraphics*[width=0.14in, height=0.20in, keepaspectratio=false]{image81}) (X,$\tau $) \noindent (ii) an intuitionistic fuzzy generalized $\alpha $-closed set [8] (IFG$\alpha $CS if$\ \alpha $cl(A) $\subseteq$ O whenever A$\subseteq$O and O is IF$\alpha $OS in(X,\includegraphics*[width=0.14in, height=0.20in, keepaspectratio=false]{image83}) in(X,$\tau $) \noindent (iii) an intuitionistic fuzzy $\alpha $-generalized closed set [12] (IF$\alpha $GCS if$\ \alpha $cl(A) $\subseteq$ O whenever A$\subseteq$O and O is IFOS in(X,\includegraphics*[width=0.14in, height=0.20in, keepaspectratio=false]{image85}) in(X,$\tau $) \noindent (iv) an intuitionistic fuzzy regular closed set [4 ] (IFRCS in short) if A = cl(int(A)),

\noindent \textbf{3. INTUITIONISTIC FUZZY $\lambda$-CLOSED MAPPINGS} \noindent \textbf{Definition 3.1:} A mapping f: (X, \tau $\tau $ ) ? (Y, $\sigma $) is said to be intuitionistic fuzzy \textbf{$\lambda$-}closed map (IF \textbf{$\lambda$}-- closed map) if f(V) is $\lambda$-closed in (Y, $\sigma $) for every closed set V in (X, $\tau $). \noindent \textbf{Theorem 3.2: }Every IF closed map is an IF \textbf{$\lambda$-}closed map but not conversely.

\noindent \textbf{Example 3.4: }Let X = \{ a, b\} and Y = \{u, v\}\textbf{ }intuitionistic fuzzy sets U and V are defined as follows; U=\{$<$a,0.5,0.5.$>$,$<$b,0.2,0.8$>$\} V=\{$<$u,0.5,0.5$>$, $<$v,0.3,0.6$>$\} \noindent Let $\tau $ =\{0,1,U\} and $\sigma $ =\{0,1,V\} be Intuitionistic fuzzy topologies on X and Y respectively. Define a map f: (X, $\tau $) ? (Y,$\ \sigma (Y,$\sigma $ ) by f(a) =u and f(b) = v. \noindent Then f (U)=f(\{$<$a,0.5,0.5$>$, $<$b,0.8,0.2$>$\}) = \{$<$u,0.5,0.5$>$, $<$v,0.8,0.2 $>$\} is $\lambda$ -closed set in Y But \{$<$u,0.5,0.5$>$, $<$v,0.8,0.2$>$\} is not closed set in Y. Hence f is intuitionistic fuzz $\lambda$ - closed mapping in Y but not intuitionistic fuzzy closed in Y

\noindent \textbf{Example 3.9}: Let X = \{a,b\}\textbf{ }and Y=\{u,v\} and intuitionistic fuzzy sets U and V are defined as follows; U= \{$<$ a, 0.5,0.5$>$, $<$ b, 0.2,0.8 $>$\} and V=\{$<$u,0.5,0.5$>$, $<$v, 0.3, 0.7$>$\} \noindent Let \tau =\{0,1,U\} and $\sigma $=\{0,1,V\} be intuitionistic fuzzy topologies on X and Y respectively. Define a map f:(X, \tau ) ? (Y,$\ \sigma (Y,$\sigma $ ) by f(a) =u and f(b) = v. \noindent Then f (U)=f(\{$<$a,0.5,0.5$>$, $<$b,0.8,0.2$>$\}) = \{$<$u,0.5,0.5$>$, $<$v,0.8,0.2 $>$\} is IF $\lambda$-closed set in Y but not IF preclosed set in Y. Hence f is intuitionistic fuzzy $\lambda$ -closed map but not intuitionistic fuzzy pre closed map.

\noindent \textbf{Example 3.11}: Let X = \{a,b\} and Y=\{u,v\} and intuitionistic fuzzy sets U and V are defined as follows U = \{$<$a, 0.5, 0.5$>$, $<$b, 0.5,0.4$>$\} and V = \{$<$a, 0.5, 0.5$>$, $<$b, 0.5, 0.2$>$\}. \noindent Let \tau =\{0,1,U\} and $\sigma $ =\{0,1,V\} be intuitionistic fuzzy topologies on X and Y respectively. Define a map f:(X, \tau ) ? (Y,$\ \sigma (Y,$\sigma $ ) by f(a) =u and f(b) = v. \noindent Then f(U) =f($<$a, 0.5, 0.5$>$, $<$b, 0.4,0.5$>$\} = ($<$u, 0.5, 0.5$>$, $<$v, 0.4,0.5$>$\} is intuitionistic fuzzy IF $\lambda$-closed set but not IF w-closed set Hence f is intuitionistic fuzzy $\lambda$-closed mapping but not intuitionistic fuzzy w-closed mappings. \noindent \textbf{Example 3.12}: Let X = \{a,b\} and Y=\{u,v\} and intuitionistic fuzzy sets U and V are defined as follows. U=\{$<$a, 0.5, 0.5$>$, $<$b, 0.5,0.5 $>$\} and V = \{$<$u, 0.5, 0.5$>$, $<$v, 0.4, 0.6 $>$\}. \noindent Let \tau =\{0,1,U\} and $\sigma $ =\{0,1,V\} be intuitionistic fuzzy topologies on X and Y respectively. Define a map f:(X, \tau ) ? (Y,$\ \sigma (Y,$\sigma $ ) by f(a) =u and f(b) = v . \noindent f(U)=f\{( $<$ a,0.5,0.5$>$,$<$b, 0.5, 0.5$>$)\}= \{$<$u,0.5,0.5$>$,$<$v, 0.5, 0.5$>$ \} is IF w-closed set not IF $\lambda$-closed set. Hence f is intuitionistic fuzzy w- closed mapping but not intuitionistic fuzzy $\lambda$ - closed mappings.

\noindent \textbf{Example 3.14: }Let X = \{a, b\}, Y=\{u, v\} and intuitionistic fuzzy sets U and V are defined as follows. U=\{ $<$a,0.5,0.5$>$,$<$b,0.6,0.3\}, V=\{$<$a,0.5,0.5$>$,$<$b,0.2,0.6 \}. \noindent Let \includegraphics*[width=0.14in, height=0.20in, keepaspectratio=false]{image98}= $\tau $= \{$\mathop{0}\limits_{\sim } $,$\mathop{1}\limits_{\sim } $, U \} and $\sigma $ =\{$\mathop{0}\limits_{\sim } $ $\mathop{1}\limits_{\sim } $, V\} be intuitionistic fuzzy topologies on X and Y respectively.Define map: f: (X, \includegraphics*[width=0.14in, height=0.20in, keepaspectratio=false]{image100}) (X,$\tau $) ? (Y,\includegraphics*[width=0.16in, height=0.20in, keepaspectratio=false]{image102}) (Y,$\sigma $) by f(a)=u and f(b)=v then f\{($<$a,0.5,0.5$>$,$<$b,0.3,0.6$>$ \}= \{$<$a,0.5,0.5$>$,$<$b,0.3,0.6 \} is intuitionistic fuzzy g-closed set but not intuitionistic fuzzy --$\lambda$ closed set. Hence f is intuitionistic fuzzy g-closed mapping and not intuitionistic fuzzy $\lambda$- mapping. \noindent \textbf{Example 3.15 : }Let X X= \{a,b \} and Y=\{u, v\} and intuitionistic fuzzy sets U and V are defined as follows U=\{$<$a,0.5,0.5$>$,$<$b,0.5, 0.2 $>$\} and V=\{$<$a,0.5,0.5$>$, $<$b,0.5,0.4$>$\}. Let \includegraphics*[width=0.14in, height=0.20in, keepaspectratio=false]{image104}= $\tau $= \{ $\mathop{0}\limits_{\sim } $ $\mathop{1}\limits_{\sim } $ U\} and $\sigma $ = \{ $\mathop{0}\limits_{\sim } $ $\mathop{1}\limits_{\sim } $ ,V\} be intuitionistic fuzzy topologies on X and Y respectively. Define the map f : X (X,\includegraphics*[width=0.14in, height=0.20in, keepaspectratio=false]{image106} ) (X,$\tau $) ? (Y,\includegraphics*[width=0.16in, height=0.20in, keepaspectratio=false]{image108}) (Y,sigma $) by f(a)=u and f(b)=v. Then f\{($<$a,0.5,0.5$>$, $<$b,0.2, 0.5 $>$\} = \{$<$a,0.5,0.5$>$, $<$b,0.2, 0.5 $>$\} is intuitionistic fuzzy $\lambda$-closed set but not intuitionistic fuzzy g closed set. Hence f is intuitionistic fuzzy $\lambda$- mappings and not intuitionistic fuzzy g-closed mappings. \noindent \textbf{Remark 3.16: }The concept of intuitionistic fuzzy $\lambda$- closed mappings and intuitionistic fuzzy semi closed mappings are independent as seen from the following examples. \noindent \textbf{Example 3.17: }Let X=\{a,b\}, Y=\{u, v\} and intuitionistic fuzzy sets U and V are defined as follows: U=\{$<$a, 0. 5, 0 .5 $>$, $<$b, 0.6, 0 .4$>$\},V= \{$<$u, 0.8,0.2 $>$, $<$v, 0.1, 0 .9 $>$\}. Let \includegraphics*[width=0.14in, height=0.20in, keepaspectratio=false]{image110} $\tau $ = \{$\mathop{0}\limits_{\sim } $, $\mathop{1}\limits_{\sim } $,U\} and $\sigma $ =\{ $\mathop{0}\limits_{\sim } $, $\mathop{1}\limits_{\sim } $ ,V\} be intuitionistic fuzzy topologies on X and Y respectively. Define the map f: (X,\includegraphics*[width=0.14in, height=0.20in, keepaspectratio=false]{image112}) (X,$\tau $) ? (Y,\includegraphics*[width=0.16in, height=0.20in, keepaspectratio=false]{image114}) (Y,$\sigma $) by f(a)=u and f(b)=v then the mapping f($<$a, 0. 5, 0 .5$>$, $<$b, 0.4, 0 .6$>$)=\{$<$u, 0. 5, 0 .5 $>$, $<$v, 0.4, 0 .6$>$\} is intuitionistic fuzzy semi closed set and not intuitionistic fuzzy $\lambda$ - closed set . Hence f is intuitionistic fuzzy semi closed mapping but not intuitionistic fuzzy $\lambda$ - closed. \noindent \textbf{Example 3.18: }Let X=\{a,b\}, Y=\{u,v \} and intuitionistic fuzzy sets U and V are defined as follows: U= \{$<$a, 0.5, 0.5$>$, $<$b, 0.5, 0.2$>$\}, V= \{a, 0 .5, 0.5$>$, $<$b, 0.5, 0 .4$>$\}. \noindent Let\includegraphics*[width=0.18in, height=0.16in, keepaspectratio=false]{image116}=\{ Let $\tau $=\{ $\mathop{0}\limits_{\sim } $ $\mathop{1}\limits_{\sim } $, U\} and $\sigma $=\{ $\mathop{0}\limits_{\sim } $ $\mathop{1}\limits_{\sim } $ ,V\}be intuitionistic fuzzy topologies on \textit{X} and Y respectively. Define the map f : (X,\includegraphics*[width=0.14in, height=0.20in, keepaspectratio=false]{image118}) (X,$\tau $) ? (Y,\includegraphics*[width=0.16in, height=0.20in, keepaspectratio=false]{image120}) (Y,$\sigma $) by f(a)=x and f(b)=y then f(U) =f\{($<$a, 0.5, 0.5$>$, $<$b, 0.2, 0.5 $>$)\} =\{($<$u, 0.5, 0.5$>$, $<$v, 0.2, 0.5 $>$)\} is intuitionistic fuzzy $\lambda$- closed set but not intuitionistic fuzzy semi closed set. \noindent Hence f is intuitionistic fuzzy $\lambda$-closed mappings but not intuitionistic fuzzy semi closed mapping.

\noindent \textbf{Example 3.20: }Let X=\{a,b,\}, Y=\{u, v\} and intuitionistic fuzzy sets U and V are defined as follows: U= \{$<$a, 0.5, 0.5$>$, $<$b, 0.3, 0.5 $>$\}, V= \{u, 0 .5, 0.5$>$, $<$v, 0.5, 0 .3 $>$\}. \noindent Let =\{$\mathop{0}\limits_{\sim } $, $\mathop{1}\limits_{\sim } $ ,U \} and $\sigma $ =\{$\mathop{0}\limits_{\sim } $ $\mathop{1}\limits_{\sim } $ ,V\}be intuitionistic fuzzy topologies on X and Y respectively. Define the map f: (X, \includegraphics*[width=0.14in, height=0.20in, keepaspectratio=false]{image123}) $\tau $) ? (Y,\includegraphics*[width=0.16in, height=0.20in, keepaspectratio=false]{image125}) (Y,sigma $) by f(a)=u and f(b)=v then f($<$a, 0.5, 0.5$>$, $<$b, 0.5, 0.3 $>$\} =$<$u, 0.5, 0.5$>$, $<$v, 0.5, 0.3 $>$\} is intuitionistic fuzzy $\lambda$-closed set, but not intuitionistic fuzzy semi pre closed set. Then f is intuitionistic fuzzy $\lambda$-closed mapping, but not intuitionistic fuzzy semi pre closed mapping. \noindent \textbf{Example 3.21: }Let X=\{a, b\}, Y=\{u,v\} and intuitionistic fuzzy sets U and V are defined as follows: U= \{$<$a, 0. 5, 0 .5 $>$, $<$b, 0. 4, 0 .6$>$\} and V = \{$<$u, 0.2,0.8 $>$, $<$v, 0 .1, 0 .9$>$\}. \noindent Let \includegraphics*[width=0.14in, height=0.20in, keepaspectratio=false]{image127}=\{$\mathop{0}\limits_{\sim $\tau $=\{$\mathop{0}\limits_{\sim } $, $\mathop{1}\limits_{\sim } $, U\} and $\sigma $=\{$\mathop{0}\limits_{\sim } $ $\mathop{1}\limits_{\sim } $,V\} be intuitionistic fuzzy topologies on X and Y respectively. Define the map f: (X, \includegraphics*[width=0.14in, height=0.20in, keepaspectratio=false]{image129}) $\tau $) ? (Y, $\sigma (Y,$\sigma $) by f(a)=u and f (b)=v. \noindent Then f (\{$<$a, 0. 5, 0 .5 $>$, $<$b, 0. 4, 0 .6$>$\})=\{$<$u, 0. 5, 0 .5 $>$, $<$v, 0. 4, 0 .6$>$\} is intuitionistic fuzzy semi pre closed mapping but not intuitionistic fuzzy $\lambda$-closed mapping.

\noindent \textbf{Example 3.23:} Let X = \{a,b\} and Y=\{u,v \}and intuitionistic fuzzy sets U and V are defined as follows; U= \{$<$ a, 0.4 ,0.6 $>$, $<$ b, 0.3,0.7 $>$ \},V=\{$<$ a,0.2,0.8 $>$,$<$b, 0.3, 0.7 $>$ \} \noindent Let \includegraphics*[width=0.14in, height=0.20in, keepaspectratio=false]{image131}=\{0,1,U\} $\tau $} and $\sigma $ =\{0,1,V\} be intuitionistic fuzzy topologies on X and Y respectively. Define a map f:(X, \includegraphics*[width=0.14in, height=0.20in, keepaspectratio=false]{image133}) f:(X,$\tau $) ? (Y,$\ \sigma (Y,$\sigma $ ) by f(a) =u and f(b) = v \noindent Then f(\{$<$a,0.6,0.4$>$, $<$b,0.7,0.3$>$\}) = \{\{$<$a,0.6,0.4$>$, $<$b,0.7,0.3$>$\}) is IF G$\alpha $-closed set but not IF-closed set. Hence f is intuitionistic fuzzy $\lambda$-mapping but not intuitionistic fuzzy IF G$\alpha $-closed mapping. \noindent \textbf{Example 3.24 :} Let X = \{a,b\} and Y=\{u,v \}and intuitionistic fuzzy sets U and V are defined as follows; U= \{$<$ a, 0.1,0.9$>$, $<$ b, 0.3,0.7$>$\}.V=\{$<$ a,0.8,0.2$>$, $<$b, 08, 0.1$>$\} \noindent Let \includegraphics*[width=0.14in, height=0.20in, keepaspectratio=false]{image136}=\{0,1,U\} $\tau $=\{0,1,U\} and $\sigma $ =\{0,1,V\} be intuitionistic fuzzy topologies on X and Y respectively. Define a map f:(X, \includegraphics*[width=0.14in, height=0.20in, keepaspectratio=false]{image138}) f:(X,$\tau $) ? (Y,$\ \sigma (Y,$\sigma $) by f(a) =u and f(b) = v \noindent Then f(\{$<$a,0.9,0.1 $>$, $<$b,0.7,0.3 $>$\}) = \{$<$a,0.9,0.1 $>$, $<$b,0.7,0.3 $>$\})${\rm \ IF\ }{\rm -}{\rm closed\ set}$ in Y but is not $IF{\rm G}\alpha {\rm closed\ set}$. Hence f is intuitionistic fuzzy $\lambda$- mapping but not intuitionistic fuzzy$\ IF{\rm G}\alpha {\rm closed}$ mapping.

\noindent \textbf{Example 3.26: }Let X = \{a,b\} and Y=\{u,v \}and intuitionistic fuzzy sets U and V are defined as follows; U= \{$<$ a, 0.6,0.4 $>$, $<$ b, 0.7,0.2 $>$ \}.V=\{$<$u, 0.2, 0.6 $>$,$<$b, 0.2, 0.7 $>$ \} \noindent Let \includegraphics*[width=0.14in, height=0.20in, keepaspectratio=false]{image141}=\{0,1,U\} $\tau $=\{0,1,U\} and $\sigma $ =\{0,1,V\} be intuitionistic fuzzy topologies on X and Y respectively. Define a map f:(X, \includegraphics*[width=0.14in, height=0.20in, keepaspectratio=false]{image143}) f:(X,$\tau $) ? (Y,$\ \sigma (Y,$\sigma $ ) by f(a) =u and f(b) = v \noindent Then f (U)=f(\{$<$ a, 0.6,0.4$>$,$<$b, 0.7,0.2 $>$\}=\{$<$a,0.6,0.4$>$,$<$b,0.7,0.2 $>$\}in${\rm \ }\alpha {\rm G}{\rm \ closed\ set\ }$Y.but not $\lambda$ -closed set in Y . Hence f is intuitionistic fuzzy IF$\alpha {\rm G}$-closed mapping, but not IF$\lambda$-closed mapping. \noindent \textbf{Example 3.27: }Let X = \{a,b\} and Y=\{u,v \}and intuitionistic fuzzy sets U and V are defined as follows; U= \{$<$ a, 0.2,0.8 $>$, $<$ b, 0.3,0.7 $>$ \}.V=\{$<$u, 0.6, 0.4 $>$,$<$b, 0.7, 0.3 $>$ \} \noindent Let \includegraphics*[width=0.14in, height=0.20in, keepaspectratio=false]{image146}=\{0,1,U\} $\tau $=\{0,1,U\} and $\sigma $ =\{0,1,V\} be intuitionistic fuzzy topologies on X and Y respectively. Define a map f:(X, \includegraphics*[width=0.14in, height=0.20in, keepaspectratio=false]{image148}) f:(X,$\tau $) ? (Y,$\ \sigma (Y,$\sigma $ ) by f(a) =u and f(b) = v \noindent Then f (U)=f(\{$<$ a, 0.8,0.2$>$,$<$b, 0.7,0.3 $>$\}=\{$<$a,0.8,0.2$>$,$<$b,0.7,0.3 $>$\}is${\rm \ }$

\noindent \textbf{Proof: }(i) $\Leftrightarrow $ (ii) is obvious. \noindent \textbf{Definition 3.37:} A mapping f: (X,\includegraphics*[width=0.14in, height=0.20in, keepaspectratio=false]{image151}) (X,$\tau $) ? (Y,$\sigma $) is said to be intuitionistic fuzzy \textbf{$\lambda$}--open map (IF \textbf{$\lambda$}--open map) if f(V) is $\lambda$-open set in (Y,${\rm \ }\sigma {\rm ),for\ every\ open\ set\ in\ (Y,}\sigma {\rm ).}$ \noindent \textbf{4. CONCLUSION }In this paper we have introduced intuitionistic fuzzy $\lambda$- open\textbf{ }mappings, intuitionistic fuzzy $\lambda$-closed mappings and studied some of their properties.