A map is important for autonomous mobile robots to traverse an environment safely and efficiently through highly competent abilities in path planning, navigation and localization. Maps are generated from sensors data. However, sensor uncertainties affect the mapping process and thus influence the performance of path planning, navigation and localization capabilities. This thesis proposes to incorporate sensor uncertainty information in robot environmental map using Fuzzy Boundary Representation (B-rep). Fuzzy B-rep map is generated by first converting measured range data into scan polygons, then combining scan polygons into resultant robot B-rep map by union operation and finally fuzzifying the B-rep map by sweeping sensor uncertainty membership function along generated B-rep map. A map of the fifth floor of E1 building is generated using the proposed method to demonstrate the alleviation in computational and memory load for robot environment mapping using Fuzzy B-rep, in contrast to the conventional grid based mapping methods.