The multi-level cards method: Weights elicitation, consistency checking and restoration for hierarchical criteria

The Simos method is an intuitive and interactive technique in Multiple Criteria Decision Aiding (MCDA) for determining the weights of the evaluation criteria, based on the Decision Maker’s preferences. While the original method offers simplicity, it has several limitations, such as rigidity in weight calculation, insufficient flexibility in accurately capturing the true preferences of the Decision Maker (DM), and issues with the robustness of the results. Extensions, such as the Simos-Roy-Figueira (SRF) method, also known as the ‘‘Revised Simos method’’, have introduced greater control over weight distribution. However, when criteria are organized in a hierarchical structure, additional information is necessary, while grouping of the criteria can lead to inconsistencies. Furthermore, as the complexity of a decision problem grows, along with the number and intricacy of the criteria, it becomes increasingly challenging for DMs to provide accurate and consistent input. This paper proposes a new SRF extension called the Multi-Level Cards (MLC) method to accommodate hierarchical criteria. The Deck-of-Cards game is designed to compare criteria within and across groups in a structured manner. A consistency checking and restoration process is also developed using an iterative model to ensure reliable and coherent weight elicitation. The proposed MLC method enhances flexibility and precision by enabling cross-group comparisons and addressing inconsistencies. A didactic example involving multi-dimensional criteria illustrates the method’s effectiveness in complex decision-making contexts.