Abstract
In this paper, we present the idea of interval valued fuzzy subgroup defined over a certain t-conorm ( \mathrm {\Gamma } -IVFSG) and prove that every IVFSG is \mathrm {\Gamma } -IVFSG. We use this ideology to define the concepts of \Gamma -IVF cosets, \mathrm {\Gamma } -IVFNSG and formulate their various important algebraic characteristics. We also propose the study of the notion of level subgroups of \mathrm {\Gamma } -IVFSG and investigate the condition under which a \mathrm {\Gamma } -IVFS is \Gamma -IVFSG. Moreover, we extend the study of this phenomenon to introduce the concept of quotient group of a group Z relative to the \Gamma -IVFNSG and acquire a correspondence between each \Gamma -IVF(N)SG of a group Z and \Gamma -IVF(N)SG of its quotient group. Furthermore, we define the index of \Gamma -IVFSG and establish the \Gamma -interval valued fuzzification of Lagrange's theorem of any \Gamma -IVFSG of a finite group Z .