Layout design has been supported by some computational tools, where fuzzy systems have been approved as an appropriate method to handle uncertainty in the early design stage. In this paper, a new mathematical model depending on the fuzzy logic and sets theory is proposed to assist in layout design. The model distinctly deals with spatial uncertainty in open planned designs, where there is no clear layout configuration or definite patterns of usage. The model calculates the possibility of occupancy according to space, function and user related parameters and logical rules. It also visualises the architectural plan as being comprised of sub-spaces formed by the distribution of those possibilities. Sub-spaces are characterised as "Fuzzy Architectural Spatial Objects" (FASOs). As a result, layouts are represented as an accumulation of FASOs showing a certain inhabitation pattern. Various layouts can be generated within the identity of FASOs. Architects can evaluate the layouts and propose new ones by organising the FASOs on the plan and considering their relations. After describing the model the paper demonstrates an application which aims to design a proper layout for a major exhibition hall in Istanbul.