Metodologia para análise de compensatoriedade e predefinição de limites entre classes em classificações multicritério

Abstract

In the developments for Multi-Criteria Decision Analysis, two problems stand out that have not yet been clearly resolved in the literature. One deals with defining the compensatory or non-compensatory nature of the criteria and the problem itself to be evaluated. Another problem is the predefinition of limits between classes in compensatory methods or approaches in class alternative allocation problems. For the latter, non-compensatory methods such as the ELECTRE and PROMETHEE families offer an alternative to defining classes through an elicitation process with the decision maker. However, our compensatory methods, due to the very nature of the compensation presented in the evaluation of alternatives, do not present much clarity when making these definitions. Some works suggest the use of statistical techniques, such as quartiles and percentiles, others suggest subjective definitions, but there is still no development that analyzes the information demonstrated in the evaluation matrix and that can suggest an initial definition for class limits in compensatory methods. Thus, the objective defined in this thesis is related to the development of two steps that can assist decision-makers in the analysis of multi-criteria problems: (i) a compensatory index to define the compensatory or non-compensatory nature between the criteria and in a global way, which it will also be useful in choosing the method to be used; and (ii) a methodology based on clustering to define initial limits for classes (groups) in allocation/sorting problems in compensatory methods, initially based on the data presented in the evaluation matrix. To create the methodology covered in the first theme, mathematical and statistical tools will be tested, better covering the relationship between the criteria. The second problem will be solved by comparing cluster analysis methods and compensatory methods for sorting and choosing those that present the best results. The results for the first theme indicated that the standard error, converted into a compensation index, combined with the Pearson and Spearman manifestation tests and their respective demonstration tests can establish possible relationships between the criteria, determining the level of compensation. For the second question, the results showed that clustering and compensatory multi-criteria decision analysis methods may present similarities, with Fuzzy C-means clustering being the one that presented the closest results with TOPSIS-Sort-B, when similarities were observed between the groups and classes and the Silhouette index. Thus, when proposing theme 1, it is in line with the results of theme 2, because before checking the similarity between the techniques, it is possible to check whether the criteria are compensatory to each other. Furthermore, forms of sensitivity analysis were developed for the two themes, in which it is possible to check whether the exclusion of criteria influences the initial ranking (theme 1) and, if the alternatives are allocated to the classes in a coherent way (theme 2), through the limitations of each of them. These results were verified through tests on existing publications and through application to the problem of purchasing electric vehicles (EV) in Brazil.