Brunno e Souza Rodrigues, Carla Martins Floriano, Valdecy Pereira and Marcos Costa Roboredo
This paper presents an algorithm that can elicitate all or any combination of parameters for the ELECTRE II, III or IV, methods. The algorithm takes some steps of a machine…
Abstract
Purpose
This paper presents an algorithm that can elicitate all or any combination of parameters for the ELECTRE II, III or IV, methods. The algorithm takes some steps of a machine learning ensemble technique, the random forest, and for that, the authors named the approach as Ranking Trees Algorithm.
Design/methodology/approach
First, for a given method, the authors generate a set of ELECTRE models, where each model solves a random sample of criteria and actions (alternatives). Second, for each generated model, all actions are projected in a 1D space; in general, the best actions have higher values in a 1D space than the worst ones; therefore, they can be used to guide the genetic algorithm in the final step, the optimization phase. Finally, in the optimization phase, each model has its parameters optimized.
Findings
The results can be used in two different ways; the authors can merge all models, to find the elicitated parameters in this way, or the authors can ensemble the models, and the median of all ranks represents the final rank. The numerical examples achieved a Kendall Tau correlation rank over 0.85, and these results could perform as well as the results obtained by a group of specialists.
Originality/value
For the first time, the elicitation of ELECTRE parameters is made by an ensemble technique composed of a set of uncorrelated multicriteria models that can generate robust solutions.
Details
Keywords
Carla Martins Floriano, Valdecy Pereira and Brunno e Souza Rodrigues
Although the multi-criteria technique analytic hierarchy process (AHP) has successfully been applied in many areas, either selecting or ranking alternatives or to derive priority…
Abstract
Purpose
Although the multi-criteria technique analytic hierarchy process (AHP) has successfully been applied in many areas, either selecting or ranking alternatives or to derive priority vector (weights) for a set of criteria, there is a significant drawback in using this technique if the pairwise comparison matrix (PCM) has inconsistent comparisons, in other words, a consistency ratio (CR) above the value of 0.1, the final solution cannot be validated. Many studies have been developed to treat the inconsistency problem, but few of them tried to satisfy different quality measures, which are minimum inconsistency (
Design/methodology/approach
The approach is defined in four steps: first, the decision-maker should choose which quality measures she/he wishes to use, ranging from one to all quality measures. In the second step, the authors encode the PCM to be used in a many-objective optimization algorithm (MOOA), and each pairwise comparison can be adjusted individually. The authors generate consistent solutions from the obtained Pareto optimal front that carry the desired quality measures in the third step. Lastly, the decision-maker selects the most suitable solution for her/his problem. Remarkably, as the decision-maker can choose one (mono-objective), two (multi-objective), three or more (many-objectives) quality measures, not all MOOAs can handle or perform well in mono- or multi-objective problems. The unified non-sorting algorithm III (U-NSGA III) is the most appropriate MOOA for this type of scenario because it was specially designed to handle mono-, multi- and many-objective problems.
Findings
The use of two quality measures should not guarantee that the adjusted PCM is similar to the original PCM; hence, the decision-maker should consider using more quality measures if the objective is to preserve the original PCM characteristics.
Originality/value
For the first time, a many-objective approach reduces the CR to consistent levels with the ability to consider one or more quality measures and allows the decision-maker to adjust each pairwise comparison individually.