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

TL;DR

This paper introduces a tensor-based extension of the TOPSIS method for multicriteria decision analysis that incorporates time-series features of criteria, providing a new perspective for ranking alternatives.

Contribution

It proposes a novel tensorial approach to MCDA that considers criteria evolution over time and extends TOPSIS to handle tensor data structures.

Findings

Tensor-based MCDA can effectively incorporate time-series features.

The extended TOPSIS method successfully ranks alternatives considering temporal data.

Computational results demonstrate the method's potential for improved decision-making.

Abstract

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.