Hindawi Publishing Corporation International Journal of Mathematics and Mathematical Sciences Volume 2010, Article ID 949143, 25 pages doi:10.1155/2010/949143 Research Article A Theoretical Development of Distance Measure for Intuitionistic Fuzzy Numbers Debashree Guha and Debjani Chakraborty Department of Mathematics, IIT-Kharagpur, Kharagpur 721302, India Correspondence should be addressed to Debjani Chakraborty, drdebjanic@yahoo.co.in Received 4 August 2009; Revised 14 January 2010; Accepted 18 February 2010 Academic Editor: Andrzej Skowron Copyright q 2010 D. Guha and D. Chakraborty. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The objective of this paper is to introduce a distance measure for intuitionistic fuzzy numbers. Firstly the existing distance measures for intuitionistic fuzzy sets are analyzed and compared with the help of some examples. Then the new distance measure for intuitionistic fuzzy numbers is proposed based on interval difference. Also in particular the type of distance measure for triangle intuitionistic fuzzy numbers is described. The metric properties of the proposed measure are also studied. Some numerical examples are considered for applying the proposed measure and finally the result is compared with the existing ones. 1. Introduction The theory of fuzzy set introduced by Zadeh 1 in 1965 has achieved successful applications in various fields. This is because this theory is an extraordinary tool for representing human knowledge, perception, and so forth. Nevertheless, Zadeh himself established in 1973 knowledge which is better represented by means of some generalizations of fuzzy sets. The so-called extensions of fuzzy set theory arise in this way. Two years after the concept of fuzzy set was proposed, it was generalized by Gogeun and L-fuzzy set 2 was developed. There are also some other extensions of fuzzy sets. Out of several higher-order fuzzy sets, the concept of intuitionistic fuzzy sets IFSs proposed by Atanassov 3 in 1986 is found to be highly useful to deal with vagueness. The major advantage of IFS over fuzzy set is that IFSs separate the degree of membership belongingness and the degree of nonmembership nonbelongingness of an element in the set. Then in 1993, Gau and Buehrer 4 introduced the concept of vague sets, which is another generalization of fuzzy sets. Bustince and Burillo 5 pointed out that the notion of vague set is the same as that of IFSs. Another well-known generalization of ordinary fuzzy sets is the