Comparative analysis of normalization techniques in the context of MCDM problems

Abstract

Normalization is an essential step in data analysis and for MCDM methods. This study aims to outline the positive and negative features of the normalization techniques that can be used in MCDM problems. In order to compare the different normalization techniques, fourteen sets representing different scenarios of decision problems were used. According to the results, if the decision-maker chooses to take the alternative with the highest value in the criteria and avoid the one with the lowest value, or vice versa, optimization-based normalization techniques should be preferred, whereas the reference-based normalization techniques are considered appropriate for situations where there are ideal values determined by the decision-maker for each criterion. However, if the decision-maker believes that the values in the criteria do not represent the monotonous increasing or decreasing benefit/cost, then non-linear normalization techniques should be used. Also, in the event of a change in the conditions mentioned above, the decision maker may opt for mixed normalization techniques. However, some data structures, such as the presence of zero, and negative values in the decision matrix, can prevent the use of some normalization techniques. The choice of the normalization technique may also be affected by the problem of rank reversal, the range of normalized values, obtaining the same optimization aspect for all criteria, and the validity of results.