Exploiting temporal features in multicriteria decision analysis by means of a tensorial formulation of the TOPSIS method

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 it can provide essential information for the 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 (trend, variance, etc.). In this novel approach, the data is structured in three dimensions, which require a more complex data structure, as the tensors, instead of the classical matrix representation used in MCDA. For this, we propose an extension of the TOPSIS method to handle tensors rather than matrices. Computational results confirm that the proposed approach allows to rank the alternatives from a new perspective that can be meaningful to the decision-maker.