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

TL;DR

This work addresses the need for time-aware decision analysis in MCDA by representing past criterion evaluations as a tensor $\mathcal{H} \in \mathbb{R}^{n\times m\times T}$ and predicting future criteria with adaptive filtering to form $\hat{\mathcal{P}} \in \mathbb{R}^{n\times m\times q}$. Predicted signals are converted into a feature tensor $\mathcal{S} \in \mathbb{R}^{n\times m\times w}$ (e.g., mean, slope, coefficient of variation), which feeds a tensor-extension of PROMETHEE II to produce the ranking scores $\hat{\mathbf{f}} \in \mathbb{R}^n$. The methodology combines Recursive Least Squares (RLS) prediction, feature-based tensor representation, and a tensor PROMETHEE II aggregation to yield robust rankings in nonstationary environments, demonstrated on real IMF time-series data. The results show that the predicted-data approach can match benchmark rankings and reveal differences from traditional MCDA, highlighting the value of incorporating temporal features and tensor-based methods in decision support. This framework enables more reliable mid- to long-term decisions when criteria exhibit nonstationary dynamics.

Abstract

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.

Figures (2)

• Figure 1: An example of opening a branch office in which the criteria prediction signals are considered.
• Figure 2: Tensorial proposal in which the features of the prediction signal are obtained from the past data.