Topographic friction and spatial equity: a fuzzy RS–GIS accessibility assessment of metropolitan Tehran

Rapid urban growth on steep slopes can intensify accessibility inequalities, yet most studies ignore complex impact of topography, especially in developing-country cities such as Metropolitan Tehran, Iran. To fill this gap, we develop and apply an innovative, friction-aware fuzzy RS–GIS workflow in Tehran, combining OpenStreetMap networks and SRTM90 elevation data, forming 17 thematic layers to generate a continuous 0–1 accessibility surface, overcoming the binary limitations of gravity and cumulative-opportunity models. Facility clusters are first identified using Average Nearest Neighbor and Getis–Ord Gi* statistics, then Euclidean distance is coupled with slope-derived friction in a fuzzy-gamma operator to quantify accessibility to key services across Tehran’s 22 districts. Central districts reach scores up to 0.89—around seven times higher than peripheral districts—and these patterns align with observed trip-attraction peaks and land-use/land-cover data, supporting model validity. The topography-sensitive analysis reveals severe accessibility deficits in Districts 15, 18, 19, 21, and 22 and motivates policies such as new bus corridors and slope-adaptive cable cars. More broadly, by generalizing friction to other impedances, e.g., congestion, the approach offers a transferable tool to advance spatial equity, carbon reduction, and inclusive economic growth in line with SDG-11.