In this paper, we introduce the notion of single and set-valued maps satisfying OWC property in IFMS using implicit relation. Also, we obtain common fixed point theorems for single and set-valued maps satisfying OWC properties in IFMS using implicit relation. Several authors [1 – 5] studied and developed the various concepts in different direction and proved some fixed point in fuzzy metric space. Also, Jungck [6] introduced the concept of compatible maps, and Vijayaraju and Sajath [7] obtained some common fixed point theorems in fuzzy metric space. Recently, Park et.a.. [8] introduced the intuitionistic fuzzy metric space (IFMS), Park [12 , 13] studied the compatible and weakly compatible maps in IFMS, and proved common fixed point theorem in IFMS. Also, Park [9] proved some properties for several types compatible maps, and Park [10] defined occasionally weakly semi-compatible map and obtained some fixed point using this maps in IFMS. In this paper, we introduce the notion of single and set-valued maps satisfying occasionally weakly compatible (OWC) property in IFMS using implicit relation. Also, we obtain common fixed point theorems for single and set-valued maps satisfying OWC property in IFMS using implicit relation. In this part, we recall some definitions, properties and known results in the IFMS as follows : Let us recall ( [11] ) that a continuous t −norm is an operation ∗ : [0, 1] × [0, 1] → [0, 1] which satisfies the following conditions: (a)∗ is commutative and associative, (b)∗ is continuous, (c) a ∗ 1 = a for all a ∈ [0, 1], (d) a ∗ b ≤ c ∗ d whenever a ≤ c and b ≤ d ( a , b , c , d ∈ [0, 1]). Also, a continuous t −conorm is an operation ⋄ : [0, 1] × [0, 1] → [0, 1] which satisfies the following conditions: (a)⋄ is commutative and associative, (b)⋄ is continuous, (c) a ⋄ 0 = a for all a ∈ [0, 1], (d) a ⋄ b ≥ c ⋄ d whenever a ≤ c and b ≤ d ( a , b , c , d ∈ [0, 1]). Definition 2.1 . ( [8] ) The 5−tuple ( X , M , N , ∗, ⋄) is said to be an intuitionistic fuzzy metric space (IFMS) if X is an arbitrary set, ∗ is a continuous t −norm, ⋄ is a continuous t −conorm and M , N are fuzzy sets on X ² × (0, ∞) satisfying the following conditions; for all x , y , z in X and all s , t ∈ (0, ∞), Note that ( M , N ) is called an IFM on X . The functions M ( x , y , t ) and N ( x , y , t ) denote the degree of nearness and the degree of non-nearness between x and y with respect to t , respectively Through out this paper, X will represent the IFMS and CB ( X ), the set of all non-empty closed and bounded subsets of X . For A , B ∈ CB ( X ) and for every t > 0, denote If A consists of a single point a , we write δ _M ( A , B , t ) = δ _M ( a , B , t ), δ ^N ( A , B , t ) = δ ^N ( a , B , t ). Furthermore, if B consists of a single point b , we write δ _M ( A , B , t ) = M ( a , b , t ), δ ^N ( A , B , t ) = N ( a , b , t ). It follows immediately from definition that Also, δ _M ( A , B , t ) = 1 and δ ^N ( A , B , t ) = 0 if and only if A = B = { a } for al A , B ∈ CB ( X ). Definition 2.2 . Let X be an IFMS, A : X → X and B : X → CB ( X ). (a) A point x ∈ X is called a coincidence point of hybrid maps A and B if x = Ax ∈ Bx . (b) Hybrid maps A and B are said to be compatible if ABx ∈ CB ( X ) for all x ∈ X and whenever { x _n } is a sequence in X such that Bx _n → D ∈ CB ( X ) and Ax _n → x ∈ D . (c) Hybrid maps A and B are said to be weakly compatible if ABx = BAx whenever Ax ∈ Bx . (d) Hybrid maps A and B are said to be occasionally weakly compatible (OWC) if there exists some points x ∈ X such that Ax ∈ Bx and ABx ⊆ BAx . Example 2.3 . Let X = [0, ∞) with a ∗ b = min{ a , b }, a ⋄ b = max{ a , b } for all a , b ∈ [0, 1] and for all t > 0, Define the maps A : X → X and B : X → CB ( X ) by Here 1 is a coincidence point of A and B , but A and B are not weakly compatible as BA (1) = [1, 5] ≠ AB (1) = [2, 5]. Also, A and B are OWC hybrid maps as A and B are weakly compatible at x = 0 as A (0) ∈ B (0) and 0 = AB (0) ⊆ BA (0) = {0}. Hence weakly compatible hybrid maps are OWC, but the converse is not true in general. Theorem 3.1 . Let X be an IFMS with t ∗ t = t and t ⋄ t = t for all t ∈ [0, 1]. Also, let A , B : X → X and S , T : X → CB ( X ) be single and set-valued mappings such that the hybrid pairs ( A , S ) and ( B , T ) are OWC satisfying for every x , y ∈ X , t > 0. Also, let implicit relation Φ = { ϕ , ψ } such that ϕ : [0, 1] ⁵ → [0, 1] and ψ : [0, 1] ⁵ → [0, 1] continuous functions satisfying (a) ϕ ( t ₁ , t ₂ , t ₃ , t ₄ , t ₅ ) is non-increasing in t ₂ and t ₅ for all t > 0. ψ ( t ₁ , t ₂ , t ₃ , t ₄ , t ₅ ) is non-decreasing in t ₂ and t ₅ for all t > 0. (b) ϕ ( t , t , 1, 1, t ) ≥ 0 implies that t = 1, and ψ ( t , t , 0, 0, t ) ≤ 1 implies that t = 0 for all t > 0. Then A , B , S and T have a unique common fixed point in X . Proof Since the hybrid pairs ( A , S ) and ( B , T ) are OWC maps, there exist two elements u , v ∈ X such that Au ∈ Su , ASu ⊆ SAu and Bv ∈ Tv , BTv ⊆ TBv . First, we prove that Au = Bv . As Au ∈ Su and Bv ∈ Tv , so, If Au ≠ Bv , then δ _M ( Su , Tv , t ) < 1 and δ ^N ( Su , Tv , t ) > 0. Using (1) for x = u and y = v , we have That is, Also, ϕ , ψ satisfies (b), so This is a contradiction which gives Au = Bv Now, we prove that A ² u = Au . Suppose that A ² u ≠ Au , then δ _M ( SAu , Tv , t ) ＜ 1 and δ ^N ( SAu , Tvt ) ＞ 0. Also, using (1) for x = Au and y = v , we get Also, Au ∈ Su and ASu ∈ SAu , so AAu ∈ ASu ⊆ SAu , Bv ∈ Tv and BTv ⊆ TBv , hence Therefore But ϕ , ψ satisfies (b), so, a contradiction and hence A ² u = Au = Bv . Similarly, we can show that B ² v = Bv . Let Au = Bv = z , then Az = z = Bz , z ∈ Sz and z ∈ Tz . Therefore z is a fixed point of A , B , S and T . Finally, we prove the uniqueness of the fixed point. Let z ≠ z ₀ be another fixed point of A , B , S and T , then by (1), we have, From (b), we get This is a contradiction. Hence z = z ₀ . Therefore z is unique common fixed point of A , B , S and T . Example 3.2 . Let X be an IFMS in which X = R ⁺ , a ∗ b = min{ a , b } and a ⋄ b = max{ a , b } for all a , b ∈ [0, 1] such that for all t > 0, Define the maps A , B , S and T on X by Define ϕ : [0, 1] → [0, 1], ψ : [0, 1] → [0, 1] as Here the pairs ( A , S ) and ( B , T ) are OWC and the contractive condition is satisfied. Hence 1 is a unique common fixed point of A , B , S and T . Corollary 3.3 . Let X be an IFMS, t ∗ t = t and t ⋄ t = t for all t ∈ [0, 1] and let A : X → X and S , T : X → CB ( X ) be single and set-valued mappings such that the hybrid pair ( A , S ) and ( A , T ) are OWC satisfying for every x , y ∈ X , t ＞ 0 and ϕ , ψ are satisfies (a) and (b), respectively in Theorem 3.1. Then A , S and T have a unique common fixed point in X . Proof Suppose that A = B in Eq. (1) of Theorem 3.1, then we get this corollary. Corollary 3.4 . Let X be an IFMS, t ∗ t = t and t ⋄ t = t for all t ∈ [0, 1] and let A : X → X and S : X → CB ( X ) be single and set-valued mappings such that the hybrid pair ( A , S ) is OWC satisfying for every x , y ∈ X , t ＞ 0 and ϕ , ψ are functions satisfying (a) and (b), respectively in Theorem 3.1. Then A and S have a unique common fixed point in X . Proof Suppose that A = B and S = T in Eq. (1) of Theorem 3.1, then we get this corollary. Park et.al. [8] introduced the IFMS, and proved common fixed point theorem in IFMS. Also, Park [9] proved some properties for several types compatible maps, and Park [10] defined occasionally weakly semi-compatible map and obtained some fixed point using this maps in IFMS. In this paper, we introduce the notion of single and set-valued maps satisfying OWC property in IFMS using implicit relation. Also, we obtain common fixed point theorems for single and set-valued maps satisfying OWC property in IFMS using implicit relation. Conflict of Interest No potential conflict of interest relevant to this article was reported. Jong Seo Park received the B.S., M.S. and Ph.D. degrees in mathematics from Dong-A University, Busan, Korea, in 1983, 1985 and 1995, respectively. He is currently Professor in Chinju National University of Education, Jinju, Korea. His research interests include fuzzy mathematics, fuzzy fixed point theory and fuzzy differential equation, etc. E-mail: parkjs@cue.ac.kr