Vol.09 Issue-02, (July - December, 2017) ISSN: 2394-9309 (E) / 0975-7139 (P) Aryabhatta Journal of Mathematics and Informatics (Impact Factor- 5.856) Double-Blind Peer Reviewed Refereed Open Access International e-Journal - Included in the International Serial Directories Aryabhatta Journal of Mathematics and Informatics http://www.ijmr.net.in email id- irjmss@gmail.com Page 1 On N-Generated Q-Fuzzy Normal Subgroups Dr. M. Mary JansiRani 1 , N. Kalpana 2 , P. Priya 3 1. Head & Assistant Professor, PG & Research Department of Mathemetics, Thanthi Hans Roever College of Arts and Science, Perambalur. 2 & 3. Research scholar, PG & Research Department of Mathemetics, Thanthi Hans Roever College of Arts and Science, Perambalur. Abstract In this paper, we introduce the concept of n-generated Q-fuzzy normal group and n- generated Q-fuzzy left and right cosets and discussed some of its properties Keywords Fuzzy set, fuzzy subgroup, Q-fuzzy subgroup , n  generated Q- fuzzy subgroups , Q- fuzzy normal subgroup, Q-fuzzy normalizer , n  generated Q- fuzzy normal subgroups, n  generated Q- fuzzy normalizer subgroups, n  generated Q- fuzzy left and right cosets 1.INTRODUCTION After the introduction of the concept of fuzzy sets by L.A.Zadeh [1], researchers were conducted the generalizations of the notion of fuzzy sets, A. Rosenfeld [2] introduced the concept of fuzzy group and the idea of “Intuitionistic Fuzzy Set” was first published by K.T. Atanassov [3]. S. sabu sebastian and T.V Ramakrishnan [4,5] introduced the concept of Multi-fuzzy sets and Multi-fuzzy subgroups. Also R.Muthuraj and S.Balamurugan [6] produced some results in Multi-fuzzy groups and its lower level subgroups. A.solairaju, S.rethinakumar, M Maria Arockia Raj introduce the concept of n  generated fuzzy sets and its subgroups. A.Solairaju and R. Nagarajan [7] introduce and define a new algebraic structure of Q-fuzzy normal subgroups and Q-fuzzy left and right cosets. In this paper we introduce n- generated Q-fuzzy normal subgroups and n-generated Q-fuzzy left and right cosets 2. PRELIMINARIES 2.1. Definition Let X be a non- empty universal set and let A be an Fuzzy Multi set on X . The n-generated Fuzzy set on X is constructed from the Fuzzy Multi set and is defined as     1 , () () ....... () : 1 2 n n n x x x x x X A A A k k        