In this paper, we introduce intuitionistic smooth bitopological spaces and the notions of intuitionistic fuzzy semiinterior and semiclosure. Based on these concepts, the characterizations for the intuitionistic fuzzy pairwise semicontinuous mappings are obtained. Chang [1] introduced the notion of fuzzy topology. Chang’s fuzzy topology is a crisp subfamily of fuzzy sets. However, in his study, Chang did not consider the notion of openness of a fuzzy set, which seems to be a drawback in the process of fuzzification of topological spaces. To overcome this drawback, Šostak [2 , 3] , based on the idea of degree of openness, introduced a new definition of fuzzy topology as an extension of Chang’s fuzzy topology. This generalization of fuzzy topological spaces was later rephrased as smooth topology by Ramadan [4] . Çoker and his colleague [5 , 6] introduced intuitionistic fuzzy topological spaces using intuitionistic fuzzy sets which were introduced by Atanassov [7] . Mondal and Samanta [8] introduced the concept of an intuitionistic gradation of openness as a generalization of a smooth topology. On the other hand, Kandil [9] introduced the concept of fuzzy bitopological spaces as a natural generalization of Chang’s fuzzy topological spaces. Lee and his colleagues [10 , 11] introduced the notion of smooth bitopological spaces as a generalization of smooth topological spaces and Kandil’s fuzzy bitopological spaces. Lim et al. [12] defined the term “intuitionistic smooth topology,” which is a slight modification of the intuitionistic gradation of openness of Mondal and Samanta, therefore, it is different from ours. In this paper, we introduce intuitionistic smooth bitopological spaces and the notions of intuitionistic fuzzy ( , )-( r, s )-semiinterior and semiclosure. Based on these concepts, the characterizations for the intuitionistic fuzzy pairwise ( r, s )-semicontinuous mappings are obtained. I denotes the unit interval [0, 1] of the real line and I ₀ = (0, 1]. A member μ ; of I ^X is called a fuzzy set in X. For any μ ∈ I ^X , μ ^c denotes the complement 1- μ . By and we denote constant mappings on X with value of 0 and 1, respectively. Let X be a nonempty set. An intuitionistic fuzzy set A is an ordered pair where the functions μ _A : X → I and γ _A : X → I denote the degree of membership and the degree of nonmembership, respectively, and μ _A + γ _A ≤ 1. Obviously, every fuzzy set μ in X is an intuitionistic fuzzy set of the form ( μ , - μ ). I(X) denotes a family of all intuitionistic fuzzy sets in X and “IF” stands for intuitionistic fuzzy. Definition 1.1. ( [4] ) A smooth topology on X is a mapping T : I^X → I which satisfies the following properties: The pair (X, T) is called a smooth topological space. Definition 1.2. ( [11] ) A system ( X , T ₁ , T ₂ ) consisting of a set X with two smooth topologies T ₁ and T ₂ on X is called a smooth bitopological space. Definition 1.3. ( [5] ) An intuitionistic fuzzy topology on X is a family T of intuitionistic fuzzy sets in X which satisfies the following properties: The pair ( X, T ) is called an intuitionistic fuzzy topological space . Now, we define the notions of intuitionistic smooth topological spaces and intuitionistic smooth bitopological spaces. Definition 2.1. An intuitionistic smooth topology on X is a mapping : I(X) → I which satisfies the following properties: The pair ( X, T ) is called an intuitionistic smooth topological space . Let ( X, T ) be an intuitionistic smooth topological space. For each , an r -cut is an intuitionistic fuzzy topology on X . Let ( X, T ) be an intuitionistic fuzzy topological space and Then the mapping T ^r : I(X) → I defined by becomes an intuitionistic smooth topology on X . Definition 2.2. Let A be an intuitionistic fuzzy set in intuitionistic smooth topological space (X, T ) and Then A is said to be Definition 2.3. Let (X, T ) be an intuitionistic smooth topological space. For and for each A ∈ I(X) , the IF -r-interior is defined by and the IF - r-closure is defined by Theorem 2.4. Let A be an intuitionistic fuzzy set in an intuitionistic smooth topological space (X, T ) and Then Proof. It follows from Lemma 2.5 in [13] . Definition 2.5. A system ( X , , ) consisting of a set X with two intuitionistic smooth topologies and on X is called a intuitionistic smooth bitopological space (ISBTS for short). Throughout this paper the indices i, j take the value in {1, 2} and i ≠ j . Definition 2.6. Let A be an intuitionistic fuzzy set in an ISBTS ( X , , ) and r, s ∈ I ₀ . Then A is said to be Theorem 2.7. Let A be an intuitionistic fuzzy set in an ISBTS ( X , , ) and r, s ∈ I ₀ . Then the following statements are equivalent: Proof. (1) ⇒ (2) Let A be an ( , )-( r, s )-semiopen set. Then there is an IF - r -open set B in X such that B ⊆ A ⊆ -cl( B, s ). Thus -int( B^c, s ) ⊆ A^c ⊆ B^c . Since B^c is IF - r -closed in X , A^c is a IF ( , ) -( r, s )-semiclosed set in X. (2) ⇒ (1) Let A^c be an IF ( , )-( r, s )-semiclosed set. Then there is an IF - r -closed set B in X such that -int( B, s ) ⊆ A^c ⊆ B . Hence B^c ⊆ A ⊆ -cl( B^c, s ). Because B^c is IF - r -open in X , A is an IF ( , )-( r, s )-semiopen set in X . (1) ⇒ (3) Let A be an IF , )-( r, s )-semiopen set in X . Then there exist an IF - r -open set B in X such that B ⊆ A ⊆ -cl( B, s ). Since B is IF - r -open, we have B = -int( B, r ) ⊆ -int( A, r ). Thus (3) ⇒ (1) Let -cl( -int( A, r ), s ) ⊇ A and take B = -int( A, r ). Then B is an IF - r -open set and Hence A is an IF ( , )-( r, s )-semiopen set. (3) ⇔ (4) It follows from Theorem 2.4. Theorem 2.8. Let A be an intuitionistic fuzzy set in an ISBTS ( X , , ) and r, s ∈ I ₀ . Then Proof. (1) Let A be an IF - r -open set in ( X , ). Then A = -int( A, r ). Thus we have Hence A is IF ( , )-( r, s )-semiopen in ( X , , ). (2) Similar to (1). The following example shows that the converses of the above theorem need not be true. Example 2.9. Let X = { x, y } and let A ₁ , A ₂ , A ₃ , and A ₄ be intuitionistic fuzzy sets in X defined as and Define : I ( X ) → I and : I ( X ) → I by and Then ( , ) is an ISBT on X . Note that and Hence A ₃ is IF ( , )-( , )-semiopen and A ₄ is IF ( , )-( , )-semiopen in ( X , , ). But A ₃ is not an IF - -open set in ( X , ) and A ₄ is not an IF - -open set in ( X , ). Theorem 2.10. Let ( X , , ) be an ISBTS and r, s ∈ I ₀ . Then the following statements are true: (1) If { A_k } is a family of IF ( , )-( r, s )-semiopen sets in X , then A_k is IF ( , )-( r, s )-semiopen. (2) If { A_k } is a family of IF ( , )-( r, s )-semiclosed sets in X , then A_k is IF ( , )-( r, s )-semiclosed. Proof. (1) Let { A_k } be a collection of IF ( , )-( r, s )-semiopen sets in X . Then for each k , So we have Thus A_k is IF ( , )-( r, s )-semiopen. (2) It follows from (1) using Theorem 2.7 . Definition 2.11. Let ( X ; , ) be an ISBTS and r, s I ₀ . For each A I ( X ), the IF ( , )-( r, s )-s emiinterior is defined by and the IF (( , )-( r, s )- semiclosure is defined by Obviously, ( , )-scl( A, r, s ) is the smallest IF ( , )-( r, s )-semiclosed set which contains A and ( , )-scl( A, r, s )is the greatest IF ( , )-( r, s )-semiopen set which is contained in A. Also, ( , )-scl( A, r; s ) = A for any IF ( , )-( r, s )- semiclosed set A and ( , )-scl( A, r, s )= A for any IF ( , )-( r, s )-semiopen set A . Moreover, we have Also, we have the following results: (1) ( , )-scl( , ,r, s ) = , ( , )-scl(