Multi Vague Order of an Element in a Group

In this paper, we introduce the concept of Multi vagueorder of an element in a group with dimension k whichextends the classical notion of vague order. We establishvarious properties and characterizations of Multi vague groupsbased on this order.Further, we study the concepts of Multi vague-p group,Multi vague torsion. For instance, we show that GVA ={x ∈ G | tiA(x) = tiA(e) & fiA(x) = fiA(e), i = 1, 2, ...., k.}is a normal subgroup of G, and that A is a Multi vague-pInternational Journal of Applied Mathematicsgroup if and only if the quotient group GGVAis a p-group.Moreover, if A is a Multi vague group of an abelian groupG, then A is Multi vague torsion if and only if GGVAis atorsion group.