Population growth in crowded cities and the resulting increase in vehicle use have led to the problem of insufficient parking. When public parking lots and urban growth are not in coordination, vehicles park on the street and close the crosswalks. In the coming years, this problem will become more complicated with the addition of autonomous vehicles (AVs) to urban traffic. This study addresses the research question of how to effectively select AV parking lots in urban areas experiencing population growth and increased vehicle usage. For this aim, a hybrid Multi-Criteria Decision Making (MCDM) methodology, combining SWARA (Step-wise Weight Assessment Ratio Analysis) and TOPSIS (Technique for Order Preference by Similarity) approaches in a Fermatean Fuzzy (FF) environment is proposed. The decision hierarchy based on the SCOR model has been developed to determine and construct the evaluation criteria. Then, a case study analysis has been applied to selected districts in Istanbul, which is Turkiye's most populous and developing city. Operating expenses, safety and security, and land costs are determined as the most important factors. As a result of the detailed fuzzy analysis, which districts should primarily be chosen for AV parking lots in Istanbul is determined and finally, the robustness and validity of the results obtained by the sensitivity analysis being questioned. The study contributes by providing insights into AV parking lot selection, demonstrating the efficacy of the proposed methodology, and highlighting the importance of addressing this issue in urban planning.