Abstract: In recent years vague set theory has received more and more attention, because many of the real life problems are information in the form of vague values. In this paper an attempt is made to study on triangular vague sets from various perspectives of algebraic properties, graphical representations and practical applications. Operators, namely triangular vague ordered weighted averaging (TVOWA) operator and the triangular vague hybrid aggregation (TVHA) operator are defined for multiple attribute group decision making (MAGDM) problems. Based on the triangular vague weighted arithmetic averaging (TVWAA) operator, the TVHA operator and the Hamming distance function for triangular vague sets, a model is developed to solve the Multiple Attribute Group Decision Making (MAGDM) problems. This proposed model is explained with an illustration.