The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is a multi-criteria decision analysis method, which was originally developed by Ching-Lai Hwang and Yoon in 1981[1] with further developments by Yoon in 1987,[2] and Hwang, Lai and Liu in 1993.
[3] TOPSIS is based on the concept that the chosen alternative should have the shortest geometric distance from the positive ideal solution (PIS) and the longest geometric distance from the negative ideal solution (NIS).
The weights of the criteria in TOPSIS method can be calculated using Ordinal Priority Approach, Analytic hierarchy process, etc.
This provides a more realistic form of modelling than non-compensatory methods, which include or exclude alternative solutions based on hard cut-offs.
Vector normalisation was incorporated with the original development of the TOPSIS method,[1] and is calculated using the following formula: In using vector normalisation, the non-linear distances between single dimension scores and ratios should produce smoother trade-offs.