ISSN: 2319-8753 International Journal of Innovative Research in Science, Engineering and Technology (An ISO 3297: 2007 Certified Organization) Vol. 3, Issue 5, May 2014 Copyright to IJIRSET www.ijirset.com 12309 The Zhang and Fu’s Similarity Measure on Intuitionistic Fuzzy Multi Sets *P. Rajarajeswari, **N. Uma * Asst. Professor, Department of Mathematics, Chikkanna Arts College, Tirupur, Tamil Nadu, India ** Asst. Professor, Department of Mathematics, SNR Sons College, Coimbatore, Tamil Nadu, India ABSTRACT: In this paper we introduce a novel Similarity measure for Iintuitionistic fuzzy multi sets (IFMS) based on Zhang and Fu’s measure, as Similarity Measure is an important topic in fuzzy set theory. The unique feature of this method is that it considers multi membership, non membership and hesitancy degree for the same element. Since the proposed measure of IFMS is mathematically valid and demonstrates the superiority of the existing methods, we apply this measure to medical diagnosis and, pattern recognition problems. KEYWORDS: Intuitionistic fuzzy set, Fuzzy Multi sets, Intuitionistic Fuzzy Multi sets, Similarity measure. I. INTRODUCTION The Intuitionistic Fuzzy sets (IFS) proposed by Krasssimir T. Atanassov [1], [ 2] was the generalisation of the Fuzzy set (FS) introduced by Lofti A. Zadeh [3]. The object, partially belong to a set with a membership degree ( ) between 0 and 1 are represented by the FS whereas the IFS represent the uncertainty with respect to both membership (∈ [0,1]) and non membership (∈ [0,1]) such that  +  ≤ 1 . Here, the number  =1 −− is called the hesitation degree or intuitionistic index. The study of distance and similarity measure of IFSs gives lots of measures, each representing specific properties and behaviour in real-life decision making and pattern recognition works. For measuring the degree of similarity between vague sets, Chen and Tan [4] proposed two similarity measures. The Hamming, Euclidean distance and similarity measures were introduced by Szmidt and Kacprzyk [5], [6], [7], [8]. The Geometric distance and similarity measures were given by Xu [9]. Most of the similarity measures reflect the degree of membership and non membership; Li et al [10] made a comparative study for similarity measures between IFSs and found the inadequate conditions for similarity measures. Therefore the hesitation degree was introduced for similarity measure. Zhang and Fu [11] proposed a new similarity measure for IFSs by considering the hesitation degree also. Later some modifications were made by Binyamin et al [12] on Zhang and Fu’s method for better results. The Multi set [13] allows the repeated occurrences of any element and hence the Fuzzy Multi set ( FMS) can occur more than once with the possibly of the same or the different membership values was introduced by R. R. Yager [14]. Recently, the new concept Intuitionistic Fuzzy Multi sets ( IFMS) was proposed by T.K Shinoj and Sunil Jacob John [15] which allows the repeated occurrences of different membership and non membership functions . As various distance and similarity methods of IFS are extended for IFMS distance and similarity measures [16], [17], [18], [19] and [20]. And in this paper we extend the Zhang and Fu’s measure of IFSs to IFMSs. The numerical results of the examples show that the developed similarity measures are well suited to use any linguistic variables. The organization of this paper is as follows: In section 2, the Fuzzy Multi sets, Intuitionistic Fuzzy Multi sets and similarity measures of IFMS are presented. The section 3 deals with the proposed Zhang and Fu’s measure for the IFMS. The