Influence of a normalization method on ranking accuracy in multi-criteria decisions

Abstract

The paper analyses the problem of ranking accuracy in multiple criteria decision-making (MCDM) methods. The result of a multi-criteria analysis is a function of the initial criteria values. Usually, in the process of measurement some errors occur in the criteria values of the initial MCDM matrix. Assuming that errors of determining the initial criteria values are stochastic, the methods of the theory of probability and mathematical statistics can be applied for evaluating the accuracy of the results of a multi-criteria analysis [1]. Moreover, the choice of criteria or weight transformation theory may affect the solution [2, etc.]. Accordingly, the aim of the research is to evaluate the influence of an initial criteria values’ normalization method on the ranking accuracy. An algorithm of the Technique for the Order Preference by Similarity to Ideal Solution (TOPSIS) that applies criteria values’ transformation through a normalization of vectors is analyzed and the linear transformation is also considered. The methodology for measuring the accuracy of determining the relative significance of alternatives as a function of the criteria values is developed. A computational experiment is presented, to compare the results of a multiple criteria analysis that uses both transformation methods in a particular situation, and conclusions are made.