Influence of data transformation on multicriteria evaluation result

Abstract

The main idea of quantitative multiple criteria decision-making methods (MCDM) is comprising values of a chosen set of criteria into a single cumulative criterion of evaluation. Units of measurement can be different: per cent, ranks, grades, money units, physical units, etc. Consequently, their incorporation into a single evaluation criterion is possible if values of criteria are independent of units of measurement. Such dimensionless values are obtained by normalizing the values. Criteria can be both minimizing and maximizing. Some MCDA methods imply transformation of minimizing criteria into maximizing ones. Moreover, values of criteria can me negative (profit, growth rate, etc.), but some MCDA methods can use only positive criteria. Therefore, majority of MCDA methods use both normalization and transformation of criteria with negative values. There are different formulae available. Even in the same method different transformation and normalization formulae can be used. Nevertheless, using different transformation and normalization formulae can lead to differences in results of evaluation. In this paper it is shown that different types of transformation and normalization of data applied to popular MCDA methods, such as SAW or TOPSIS may produce considerable differences in evaluation. Consequently, attention has to be paid to making a choice of the type of normalization, which reveals preferences of decision-maker. Dependence of evaluation results on the chosen type of transformation or normalization is demonstrated. A case-study is provided.