Polygeneration systems have been utilized to simultaneously generate a number of energy and utility products such as heat, power, cooling and treated water. Its implementation has proven to increase fuel efficiency and to reduce the associated carbon footprint in products in comparison to stand-alone production systems. The polygeneration system consists of interdependent process units whose design capacities will depend on the expected product demands. Because of the multiple product streams generated and the associated demands, it is necessary to design a system which aims to simultaneously meet potentially conflicting product demand targets. Fuzzy optimization has initially been used to identify the optimal solution which simultaneously satisfices multiple product demand targets. However, real life decision-making may require an evaluation of alternative solutions. This aspect can be addressed by the P-graph methodology which is able to provide both optimal and sub-optimal network designs. This work thus proposes the development of a fuzzy P-graph model for the design of a polygeneration system. The capabilities of the model are demonstrated in a case study. The model results identify both optimal and sub-optimal design options which generate products within the defined demand targets and which can be further evaluated for other parameters such as robustness for final decision-making.