Abstract—The notion of fuzzy subsets was introduced to model imprecision, ambiguity and uncertainty. Further it was generalized to intuitionistic fuzzy subsets and interval valued intuitionistic fuzzy subsets for their usefulness and applicability. In recent years, several ranking approaches based on dominance relations have been developed, in which a dominance degree and an entire dominance degree are employed in information system. Even though the theory of fuzzy sets paved a way to decision making from qualitative information, it can not be used to apply in problem with a qualitative information with lack of knowledge. So in this paper an intuitionistic fuzzy interval information system (IFIIS) is introduced and an approach of ranking from IFIIS based on the dominance degree is introduced and studied by illustrating an example. Index Terms—Interval valued intuitionistic fuzzy sets, information system, new novel accuracy score, dominance degree. I. INTRODUCTION Zadeh introduced the concept of fuzzy sets, which has been a mathematical model to solve with imprecision, ambiguity and uncertainty [1]. Theory of fuzzy sets has also developed its own measures of qualitative information, which finds application in areas such as management, medicine and meteorology. Even though the theory of fuzzy sets paved a way to model qualitative information, it can not be used to apply in problem with a qualitative information with lack of knowledge. So it was generalized to intuitionistic fuzzy subsets by Atanassov and further generalized to interval valued intuitionistic fuzzy sets by Atanassov and Gargov [2] - [4]. In last decades, rough set theory introduced by Pawlak has an important role in the field of decision making analysis [5] - [6]. In decision making analysis, interval data is an important class of data, and generalized form of single-valued data. Qian et al. proposed a ranking approach for all objects based on dominance classes and the entire dominance degree [7]. In fuzzy information system, objects are evaluated by a set of values in the unit interval or linguistic terms [8] - [9]. Even though the theory of fuzzy sets paved a way to decision making from qualitative information, it can not be used to apply in problem with a qualitative information with lack of Manuscript received March 9, 2012; revised May 11, 2012. Geetha Sivaraman is with the PI (WOS-A), DST India, Department of Mathematics, National Institute of Technology, Tiruchirappalli, Tamil Nadu, India (e-mail: geedhasivaraman@ yahoo.com). V. Lakshmana Gomathi Nayagam is with the Department of Mathematics, National Institute of Technology, Tiruchirappalli, Tamil Nadu, India (e-mail: velulakshmanan@nitt.edu). R. Ponalagusamy is with the Department of Mathematics, National Institute of Technology, Tiruchirappalli, Tamil Nadu, India (e-mail: rpalagu@nitt.edu). knowledge [8] - [9]. In information system, comparison of data plays a main role to define a dominance degree. A new novel accuracy score is defined to rank intuitionistic interval values which rank completely for comparable intuitionistic fuzzy intervals in [10]. So in this paper, an intuitionistic fuzzy interval information system is defined and a ranking algorithm based the dominance degree using this new novel accuracy score is given. This paper is organized as follows. Section 2 briefly reviews the definition of interval valued intuitionistic fuzzy sets and interval information system. In Section 3, an intuitionistic fuzzy interval information system and fuzzy dominance degree are defined and some of its properties are studied. In section 4, an algorithm for ranking of objects in interval valued intuitionistic fuzzy information system is given and it is illustrated in an example. Finally the conclusions are drawn in section 5. II. PRELIMINARIES Here we give a brief review of preliminaries. Definition 2.1 [4]: Let ] 1 , 0 [ D be the set of all closed subintervals of the interval ] 1 , 0 [ . Let     X be a given set. An interval valued intuitionistic fuzzy set in X is an expression given by   X x x x x A A A  : ) ( ), ( , =   , where ] 1 , 0 [ : , ] 1 , 0 [ : D X D X A A     with the condition. Conveniently, an interval valued intuitionistic fuzzy set in X is given by 1 ) ( ) ( < 0   x sup x sup A x A x   , } | )] ( , ) ( [ , )] ( , ) ( [ , { = X x x x x x x A U A L A U A L A      with , 1 ) ( ) ( < 0   x x U A U A   . 0 ) ( 0, ) (   x x L A L A   For each element x we can compute the unknown degree (hesitancy degree) of belongingness of X x  in A as follows , ) ( ) ( 1 [ = ) ( x x x U A U A A      )] ( ) ( 1 x x L A L A     . We will denote the set of all the IVIFSs in X by IVIFS(X). An IVIFS value is denoted by ]) , [ ], , ([ = d c b a A for convenince. Definition 2.2 [4]: Let A,B  IVIFS(X). A subset relation is defined by ) ( ) ( x x B A L B L A      , ) ( ) ( x x U B U A    and ) ( ) ( x x L B L A    , ) ( ) ( x x U B U A    , for every X x  . Intuitionistic Fuzzy Interval Information System Geetha Sivaraman, V. Lakshmana Gomathi Nayagam, and R. Ponalagusamy International Journal of Computer Theory and Engineering, Vol. 4, No. 3, June 2012 459