Multicriteria decision support employing adaptive prediction in a tensor-based feature representation

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.

Application of independent component analysis and TOPSIS to deal with dependent criteria in multicriteria decision problems

A vast number of multicriteria decision making methods have been developed to deal with the problem of ranking a set of alternatives evaluated in a multicriteria fashion. Very often, these methods assume that the evaluation among criteria is statistically independent. However, in actual problems, the observed data may comprise dependent criteria, which, among other problems, may result in biased rankings. In order to deal with this issue, we propose a novel approach whose aim is to estimate, from the observed data, a set of independent latent criteria, which can be seen as an alternative representation of the original decision matrix. A central element of our approach is to formulate the decision problem as a blind source separation problem, which allows us to apply independent component analysis techniques to estimate the latent criteria. Moreover, we consider TOPSIS-based approaches to obtain the ranking of alternatives from the latent criteria. Results in both synthetic and actual data attest the relevance of the proposed approach.