A comparison between TOPSIS and SAW methods

The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and Simple Additive Weighting (SAW) are among the most employed approaches for aggregating performances in Multi-Criteria Decision-Making (MCDM). TOPSIS and SAW are two MCDM methods based on the value function approach and are often used in combination with other MCDM methods in order to produce rankings of alternatives. In this paper, first, we analyse some common features of these two MCDM methods with a specific reference to the additive properties of the value function and to the sensitivity of the value function to trade-off weights. Based on such methodological insights, an experimental comparison of the results provided by these two aggregation methods across a computational test is performed. Specifically, similarities in rankings of alternatives produced by TOPSIS and SAW are evaluated under three different Minkowski distances (namely, the Euclidean, Manhattan and Tchebichev ones). Similarities are measured trough a set of statistical indices. Results show that TOPSIS, when used in combination with a Manhattan distance, produces rankings which are extremely similar to the ones resulting from SAW. Similarities are also Experimental results confirm that rankings produced by TOPSIS methods are closer to SAW ones when similar formal properties are satisfied.