The assessment of criteria weights in multicriteria decision aid methods of value system approaches, often leads to the assessment of preference models with a low degree of robustness due to the assessment of several compatible value functions. This research work presents a methodological frame, which aims to three issues: (a) to explain the nature of low robustness of the estimated preference models, utilising tomographical techniques, visual tools, and specific indices for the robustness measurement, (b) to support the Decision Makers (DMs) towards a deeper understanding of his/her value system, and (c) to acquire additional preference information by the DM estimating a value functions of higher robustness through focused interactive feedbacks. The main scope of this research work is to exploit and enrich the interactive nature of the multicriteria disaggregation–aggregation approach. The proposed methodology is applied on a real world case study along with the utilisation of the RAVI (Robustness Analysis with Visual and Interactive approaches) software developed to support the above mentioned methodological approach.