The mean error estimation of TOPSIS method using a fuzzy reference models

The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is a commonly used multi-criteria decision-making method. A number of authors have proposed improvements, known as extensions, of the TOPSIS method, but these extensions have not been examined with respect to accuracy. Accuracy estimation is very difficult because reference values for the obtained results are not known, therefore, the results of each extension are compared to one another. In this paper, the author propose a new method to estimate the mean error of TOPSIS with the use of a fuzzy reference model (FRM). This method provides reference values. In experiments involving 1,000 models, 28 million cases are simulated to estimate the mean error. Results of four commonly used normalization procedures were compared. Additionally, the author demonstrated the relationship between the value of the mean error and the nonlinearity of models and a number of alternatives.