International Journal of Algebra, Vol. 5, 2011, no. 1, 37 - 47 Intuitionistic Fuzzy Rings Mohammad F. Marashdeh 1 and Abdul Razak Salleh School of Mathematical Sciences, Faculty of Science and Technology Universiti Kebangsaan Malaysia 43600 UKM Bangi, Selangor Darul Ehsan, Malaysia 1 alhafs@gmail.com Abstract In this paper we present a new formulation of intuitionistic fuzzy rings based on the notion of intuitionistic fuzzy space. A relation be- tween intuitionistic fuzzy ring based on intuitionistic fuzzy space and ordinary rings is obtained in terms of induction and correspondence. Mathematics Subject Classification: 08A72, 20N25, 03F55 Keywords: Intuitionistic fuzzy set, intuitionistic fuzzy space, intuitionis- tic fuzzy ring, intuitionistic fuzzy ideal 1 Introduction In 1982 W. J. Liu [8] introduced the concept of fuzzy ring and fuzzy ideal. In 1985 Ren [10] studied the notions of fuzzy ideal and fuzzy quotient ring. Fuzzy rings and fuzzy ideal in the sense of Liu and Ren were actually a rational extension of Rosenfield’s fuzzy group by starting with an ordinary ring and then define a fuzzy subring based on the ordinary operations of the given ring. Based on the notion of fuzzy space which play the role of universal set in ordinary algebra and using fuzzy binary operation K. A. Dib [3] obtained a new formulation for fuzzy rings and fuzzy ideals. In the case of intuitionistic fuzzy sets there were several attempts to define intuitionistic fuzzy rings [9, 7] by generalizing the approach used by Liu to define fuzzy ring. In this paper we generalize Dib’s notion for fuzzy rings based on the notion of fuzzy space to the case of intuitionistic fuzzy set relying on the notion of intuitionistic fuzzy space and intuitionistic fuzzy function defined by Fathi and Abdul Razak [4, 5, 6] which will serve as a universal set in the classical case.