DECISION-MAKING WITH AHP, TOPSIS, SAW, AND WPM: A COMPARATIVE STUDY BASED ON REAL DATA

Decision making is a basic cognitive process that allows choosing the preferred option among alternatives. The alternatives differ in their characteristics and can be considered more or less relevant depending on the combination and importance assigned to evaluation criteria.
Within this context, the value of multi-criteria decision-making techniques is recognized. These methods provide structured and integrated forms for evaluating alternatives and criteria, and provide a collective compromise by aggregating the preferences of multiple decision-makers.
The variety of existing methods and their characteristics are illustrated and systematized, for example, in the work of Wątróbski et al. (2019) and Guarini et al. (2018). Although scientific and applied research in this field has provided a broad framework for the different methods, from an empirical point of view, the selection of multicriteria methods continues to prioritize theoretical and practical simplicity. It has been found that different methods are used for similar decision problems (Wątróbski et al., 2019), and depending on the decision context, the technical assumptions of existing methods are often adjusted (Dias et al., 2018; Marttunen et al., 2017; Wang et al., 2009), leading to difficulties in comparing the results obtained and revealing a mismatch between theory and the underlying needs of real decision contexts. Even if different methods lead to the same classification of alternatives, this does not necessarily determine the merit or robustness of any method (Saaty, 2013).
The selection of multicriteria analysis method is a challenge that has been widely recognized in various decision contexts. In general, the reflection produced in this context focuses on comparing i) the characteristics of the methods (Belton & Stewart, 2002; Wątróbski et al., 2019); ii) the levels of internal consistency enabled by each method (Azhar et al., 2021); iii) different methods, seeking to establish a sense of greater or lesser robustness in the results obtained (Athawale & Chakraborty, 2012).
But more than apprehending the assumptions and technical formalisms associated with each method, it is desirable to complement the body of knowledge in this domain, whose content is fundamentally technical, with other descriptive analytical references with on key decision-making aspects. This framework should support the understanding on how and why different methods produce divergent results for some alternatives and to what extent this information can be useful to determine the suitability of the method in view of the characteristics and objectives of the decision context.
This work analyzes this issue based on data collected in real decision-making contexts, where collective decision-making exercises were carried out to differentiate and establish priorities between alternatives.
The methodological approach followed consisted in comparing four multi-criteria analysis methods, which appear in the literature as the most used (AHP, TOPSIS, SAW and WPM).
The analysis and discussion developed goes beyond the technical aspect associated with other studies. This work enables comparing the final rankings and discuss the consistency of the results, considering: i) the decision matrix, where each alternative is linked to the criteria; and ii) the preference structure based on the weights collectively assigned to the criteria.