Comparative Analysis of the Normalization Techniques in the Context of MCDM Problems

Abstract

NormNormalization 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.

Multi-criteria decision-making for coronavirus disease 2019 applications: a theoretical analysis review

“…Using different normalisation techniques may lead to different rankings. Based on literature, 12 normalisation procedures are used diversely and widely within the MCDM methods (Aytekin 2021 ; Vafaei et al 2018 ). Table 6 lists all employed normalisation techniques for cost and benefit criteria.…”

Fuzzy Ensemble of Multi-Criteria Decision Making Methods for Heating Energy Transition in Danish Households

“…It starts with the selected alternatives and criteria according to the defined problem. Then, the selected alternatives and criteria data, as a format of matrix , are normalized with methods of MinMax, Max, Vector, and Enhanced [24], and weighted with methods of Mean, Standard deviation, Entropy, Angle, Gini, and Criteria importance through inter-criteria (CRITIC) [25]. The generated objective weights and normalized matrix are calculated and combined with the evaluation methods, where Vise Kriterijumska Optimizacija Kompromisno Resenje (VIKOR) and Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) are used to generate ranking data sets × .…”

An Integrated Variance-COPRAS Approach with Nonlinear Fuzzy Data for Ranking Barriers Affecting Sustainable Operations

“…COPRAS [32] is a popular ranking approach that works based on utility functions. It considers the nature of factors and ranks options from different angles by considering complex proportional [52][53][54][55][56][57]. Based on the review presented above and the benefits of COPRAS, it is clear that COPRAS is an attractive approach for decision-making, and a consideration of the personal views of agents is lacking.…”