arXiv subjects

Leonardo T. Duarte

Publications and source records attributed to Leonardo T. Duarte.

5 recordsLinked to original sources

arXiv2023

Improving preference disaggregation in multicriteria decision making: incorporating time series analysis and a multi-objective approach

Preference disaggregation analysis (PDA) is a widely used approach in multicriteria decision analysis that aims to extract preferential information from holistic judgments provided by decision makers. This paper presents an original methodological framework for PDA that addresses two significant challenges in this field. Firstly, it considers the multidimensional structure of data to capture decision makers' preferences based on descriptive measures of the criteria time series, such as trend and average. This novel approach enables an understanding of decision makers' preferences in decision-making scenarios involving time series analysis, which is common in medium- to long-term impact decisions. Secondly, the paper addresses the robustness issue commonly encountered in PDA methods by proposing a multi-objective and Monte Carlo simulation approach. This approach enables the consideration of multiple preference models and provides a mechanism to converge towards the most likely preference model. The proposed method is evaluated using real data, demonstrating its effectiveness in capturing preferences based on criteria and time series descriptive measures. The multi-objective analysis highlights the generation of multiple solutions, and, under specific conditions, reveals the possibility of achieving convergence towards a single solution that represents the decision maker's preferences.

math.OC↗

arXiv2022

Analysis of Trade-offs in Fair Principal Component Analysis Based on Multi-objective Optimization

In dimensionality reduction problems, the adopted technique may produce disparities between the representation errors of different groups. For instance, in the projected space, a specific class can be better represented in comparison with another one. In some situations, this unfair result may introduce ethical concerns. Aiming at overcoming this inconvenience, a fairness measure can be considered when performing dimensionality reduction through Principal Component Analysis. However, a solution that increases fairness tends to increase the overall re-construction error. In this context, this paper proposes to address this trade-off by means of a multi-objective-based approach. For this purpose, we adopt a fairness measure associated with the disparity between the representation errors of different groups. Moreover, we investigate if the solution of a classical Principal Component Analysis can be used to find a fair projection. Numerical experiments attest that a fairer result can be achieved with a very small loss in the overall reconstruction error.

cs.LG↗

arXiv2020

An unsupervised capacity identification approach based on Sobol' indices

In many ranking problems, some particular aspects of the addressed situation should be taken into account in the aggregation process. An example is the presence of correlations between criteria, which may introduce bias in the derived ranking. In these cases, aggregation functions based on a capacity may be used to overcome this inconvenience, such as the Choquet integral or the multilinear model. The adoption of such strategies requires a stage to estimate the parameters of these aggregation operators. This task may be difficult in situations in which we do not have either further information about these parameters or preferences given by the decision maker. Therefore, the aim of this paper is to deal with such situations through an unsupervised approach for capacity identification based on the multilinear model. Our goal is to estimate a capacity that can mitigate the bias introduced by correlations in the decision data and, therefore, to provide a fairer result. The viability of our proposal is attested by numerical experiments with synthetic data

eess.SP↗

arXiv2020

Muticriteria decision making based on independent component analysis: A preliminary investigation considering the TOPSIS approach

This work proposes the application of independent component analysis to the problem of ranking different alternatives by considering criteria that are not necessarily statistically independent. In this case, the observed data (the criteria values for all alternatives) can be modeled as mixtures of latent variables. Therefore, in the proposed approach, we perform ranking by means of the TOPSIS approach and based on the independent components extracted from the collected decision data. Numerical experiments attest the usefulness of the proposed approach, as they show that working with latent variables leads to better results compared to already existing methods

eess.SP↗

arXiv2020

A study of the Multicriteria decision analysis based on the time-series features and a TOPSIS method proposal for a tensorial approach

A number of Multiple Criteria Decision Analysis (MCDA) methods have been developed to rank alternatives based on several decision criteria. Usually, MCDA methods deal with the criteria value at the time the decision is made without considering their evolution over time. However, it may be relevant to consider the criteria' time series since providing essential information for decision-making (e.g., an improvement of the criteria). To deal with this issue, we propose a new approach to rank the alternatives based on the criteria time-series features (tendency, variance, etc.). In this novel approach, the data is structured in three dimensions, which require a more complex data structure, as the \textit{tensors}, instead of the classical matrix representation used in MCDA. Consequently, we propose an extension for the TOPSIS method to handle a tensor rather than a matrix. Computational results reveal that it is possible to rank the alternatives from a new perspective by considering meaningful decision-making information.

cs.AI↗