The Technique of Ordering Preference by Similarity to Ideal Solution (TOPSIS) method is one of the basic decision-making (DM) methods used in multi-criteria decision-making (MCDM) problems. In this study, various variants of the TOPSIS method are comparatively analyzed from algorithmic perspectives. The TOPSIS-based methods adapted to various application areas in the last years, especially in the last decade are discussed. As can be seen from literature studies, TOPSIS approaches with fuzzy information are widely used. Triangular, trapezoidal and sometimes Gaussian fuzzy numbers are used in processing fuzzy information. Details of various TOPSIS approaches are discussed and comparative analysis is made from these and similar perspectives.