A transition towards a sustainable energy system is a challenging process that involves multiple stakeholders with differing viewpoints. Several transition pathways are possible, but the decision regarding which pathway to follow should be based on a justifiable and transparent framework that accounts for the concerns of all relevant stakeholder groups. This study proposes a participatory stakeholder analysis process that includes a two-dimensional power-interest matrix and fuzzy logic to define and classify relevant stakeholder groups. The proposed framework was implemented to recognize the relevant stakeholder groups of the Icelandic energy system and assess their salience. The defined stakeholder groups were then evaluated based on two attributes—power and interest—using data collected from a web-based questionnaire. Considering the wide range of the attributes' values for the many stakeholder groups, fuzzy logic was applied to plot a 3D decision surface, which provided a more accurate assessment of stakeholders' salience. The generated power-interest map visualizes the dynamic influential level of stakeholder groups when it comes to decision-making concerning sustainable energy development. The fuzzy decision surface shows a more accurate image of the difference in the degree of power and interest and saliences of the stakeholder group. Results reveal that Decision-makers, Industrial Users, Professional Interest groups, and Energy Producers have the highest salience and are the most influential stakeholder groups concerning decision-making. Less influential stakeholder group such as Landowners exhibit a high degree of variation in influential level across the sustainable energy themes. The findings suggest that Icelandic decision-makers responsible for energy development face a complex challenge when it comes to designing and implementing a policy that is approved across all stakeholder groups. This study offers new insights to policymakers on the most influential stakeholder groups and the variation of influential level across stakeholders groups in the Icelandic energy system. Understanding the power and interest of different stakeholders can improve the decision- and policy-making process and promote a successful transition to a sustainable energy system.