The multi-criteria decision-making (MCDM) approach involves the collaborative interaction of decision-makers (DMs) to identify one or more optimal solutions near the Pareto frontier, incorporating their preferences. The Pareto-Race method, within the MCDM framework, enables DMs to navigate the Pareto surface by selecting preferred reference directions and speeds, utilizing the Achievement Scalarization Function (ASF) or its augmented version (AASF). While algorithmically feasible, the effectiveness of the Pareto-Race concept relies on effective visualization methods to present past solutions and convey current objective trade-off information to aid DMs in decision-making. Traditional visualization techniques like parallel coordinate plots, radial visualization, and heat maps are often inadequate for this purpose. Hence, we propose integrating the Pareto-Race MCDM approach with an interpretable self-organizing map (iSOM) based visualization method, which maps high-dimensional data into lower-dimensional space for enhanced visual clarity. Our approach involves representing non-dominated solutions near the complete Pareto Front with iSOM plots of objectives and visualizing metrics such as proximity to constraint boundaries, trade-off value, and robustness. This comprehensive visualization assists DMs in effectively selecting new reference directions and step sizes in each iteration, facilitating the identification of the most preferred solution. We demonstrate the effectiveness of our iSOM-enabled Pareto-Race approach on benchmark analytical and real-world engineering examples spanning 3 to 10 objectives.