This paper aims to develop a new method based on the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) to solve Multiple Attribute Decision Making(MADM) problems for Interval Vague Sets(IVSs). A TOPSIS algorithm is constructed on the basis of the concepts of the relative-closeness coefficient computed from the correlation coefficient of IVSs. This novel method also identifiesthe positive and negative ideal solutions using the correlation coefficient of IVSs. A numerical illustration explains the proposed algorithms and comparisons are made with various existing methods.