Article Preview
TopIntroduction
In most cases, choosing between multiple alternatives and criteria is a difficult task for the decision-makers. In such cases, MCDM techniques provide a convenient way for decision-makers to reach a solution. In MCDM models, each alternative has a performance rating for each attribute, and performance ratings for different attributes are usually measured by different units. Therefore, normalization procedures are used to transform different units of measure into comparable units in MCDM models (Celen, 2014, p. 186).
The first step in most MCDM methods is the normalization procedure. Different normalization techniques can have different effects on the ranking results. This causes deviation from the optimal ranking. Therefore, the selection of suitable normalization techniques plays an significant role on the final results of the decision problems (Vafaei et al., 2020, p. 43).
The effects of different normalization techniques on MCDM methods have been investigated in various studies in the literature. Gardziejczyk & Zabicki (2017) dealt with the selection of road alignment variant problem and compared the results obtained using eleven different normalization techniques. They concluded that Van Delft & Nijkamp, linear and pattern normalization techniques generated the most consistent results. Migilinskas & Ustinovichius (2007) examined the effects of eight popular normalization procedures in their studies. It was concluded that proximity to ideal point and sum normalization techniques gave healthy results in the presence of five or fewer alternatives. Chakraborty & Yeh (2009) tested the effect of normalization techniques for the Simple Additive Weighting (SAW) method. It was shown that vector normalization was more appropriate than other procedures. Vafaei et al. (2020) tested the suitability of four different normalization techniques for the Analytical Hierarchy Process (AHP) method. It was determined that the best normalization technique for the AHP method is the max-min. Jafaryeganeh et al. (2020) measured the effect of four different normalization techniques for Weighted Sum Method (WSM), Weighted Product Method (WPM), Technique for Order Preferences by Similarity to an Ideal Solution (TOPSIS) and Elimination et Choice Translating Reality (ELECTRE) methods. It was found that normalization techniques that can preserve the dominance order of the alternatives result in a similar final design choice. Aytekin (2021) used fourteen sets representing different decision problem scenarios to compare different normalization techniques. It was concluded that the decision-maker chooses the alternative with the highest value in the criteria or, on the contrary, optimization-based normalization techniques should be preferred. Reference-based normalization techniques are considered suitable for situations where ideal values determined by the decision maker for each criterion. Brauers & Zavadskas (2006) proved the appropriateness of five normalization procedures for the Multi-objective Optimization By Ratio Analysis (MOORA) method. It was determined that the vector normalization technique produced the most consistent results. Milani et al. (2005) used different normalization procedures for the TOPSIS method. The results showed that linear normalization techniques did not significantly affect the variant ranking. Yazdani et al. (2017) measured the effects of different normalization techniques for the COmplex PRoportional ASsessment (COPRAS)-G model. It was determined that the number of criteria and alternatives affected the ranking results. Peldschus (2007) compared different normalization procedures and determined that normalization procedures had an effect on the MCDM results. It was also concluded that a linear normalization cannot be used to solve maximization or minimization problems. Kosareva et al. (2018) used the various normalization techniques to test the SAW method. They found that of all five techniques, none were the best or worst in all cases and the logarithmic normalization technique was the worst in some cases. Vafaei et al. (2016) examined the effects of the most suitable techniques for the Analytical Hierarchy Process (AHP) method. It was revealed that the logarithmic normalization technique could not be used in the AHP method, asit leads to zero or infinite values in normalized data. Celen (2014) tested the various normalization procedures for the FAHP and TOPSIS. It was determined that the most coherent results were obtained by vector normalization. Ersoy (2021) tested the suitability of eight normalization techniques for the ROV method. It was determined that non-linear normalization was the most suitable technique for ROV method.