Annals of Fuzzy Mathematics and Informatics Volume 3, No. 2, (April 2012), pp. 255- 266 ISSN 2093–9310 http://www.afmi.or.kr @FMI c  Kyung Moon Sa Co. http://www.kyungmoon.com Anti fuzzy ideals of Γ-near-rings T. Srinivas, T. Nagaiah, P. Narasimha Swamy Received 7 June 2011; Revised 6 August 2011; Accepted 12 August 2011 Abstract. In this paper we introduce the notion of an anti fuzzy ideals of a Γ-near-ring, anti fuzzy ideals of a Γ-residue class near-ring, anti level subset of fuzzy set and complement of anti fuzzy ideals. Further, we discuss the relation between anti fuzzy ideals of Γ-near-rings and anti level subset of a fuzzy sets. Also we prove that if μ is an anti fuzzy ideal of a Γ-near-ring M then Mμ = {x ∈ M : μ(x)= μ(0)} is an ideal of M. 2010 AMS Classification: 16Y30, 03E72 Keywords: Γ-near-ring, Anti fuzzy ideal, Anti level subset, Complement of anti fuzzy ideal and f -invariant anti fuzzy ideal. Corresponding Author: T. Srinivas (thotasrinivas.srinivas@gmail.com) 1. Introduction After the introduction of fuzzy set by Zadeh [14] in 1965, the researchers in mathematics were trying to introduce and study the concept of fuzzyness in different mathematical systems under study. Γ-near-rings were defined by Bh. Satyanarayana [11]. The ideal theory in Γ-near-rings was studied by Bh. Satynarayana [11] and G. L. Booth [2]. Fuzzy ideals of rings were introduced by W. Liu [9] and it has been studied by several authors [4, 5, 7, 10, 13]. R. Biswas [1] introduced the concept of anti fuzzy subgroups and K. H. Kim and Y. B. Jun studied the notion of anti fuzzy ideals in near-rings in [8]. In [3] S. K. Datta introduced the concept of anti fuzzy bi-ideals in rings. T. S. Ravisankar and U. S. Shukla in [12], Y. B. Jun, M. Sapanci and M. A. Ozturk in [6] studied the structure of Γ-near-rings. Anti fuzzy ideals of Γ-rings were studied by Min Zhou, D. Xiang and J. Zhan in [15]. In this paper we introduce the concept of anti fuzzy ideals of Γ-near-ring, f -invariant anti fuzzy ideals and anti level subset of a fuzzy set. We examine some related properties and study the relation between anti fuzzy ideal of a Γ-near-ring and anti level subset of a fuzzy set. The proofs are almost similar to anti fuzzy ideals in near-rings [8] and anti fuzzy ideals of Γ-rings [15].