Betania Silva Carneiro Campello

Betania Silva Carneiro Campello, Leonardo Tomazeli Duarte, João Marcos Travassos Romano

Multicriteria decision analysis (MCDA) is a widely used tool to support decisions in which a set of alternatives should be ranked or classified based on multiple criteria. Recent studies in MCDA have shown the relevance of considering not only current evaluations of each criterion but also past data. Past-data-based approaches carry new challenges, especially in time-varying environments. This study deals with this challenge via essential tools of signal processing, such as tensorial representations and adaptive prediction. More specifically, we structure the criteria' past data as a tensor and, by applying adaptive prediction, we compose signals with these prediction values of the criteria. Besides, we transform the prediction in the time domain into a most favorable decision making domain, called the feature domain. We present a novel extension of the MCDA method PROMETHEE II, aimed at addressing the tensor in the feature domain to obtain a ranking of alternatives. Numerical experiments were performed using real-world time series, and our approach is compared with other existing strategies. The results highlight the relevance and efficiency of our proposal, especially for nonstationary time series.

Betania S. C. Campello, Leonardo T. Duarte, João M. T. Romano

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.