Greenhouse gas emissions contribute significantly to the increased intensity of detrimental effects brought forth by climate change. Given that energy systems are major sources of greenhouse gas emissions, efforts are being undertaken to reduce their environmental impact while further improving their economic performance. Among these efforts is the development of polygeneration systems. Based on the principles of process integration, these systems consist of complex networks of integrated process units that yield multiple products for increased economic and environmental sustainability. Optimization techniques such as mathematical programming, provide design solutions to maximize the benefits delivered by these systems. A fuzzy linear programming model for the optimal design of off-shore polygeneration systems was previously developed. However, the design limits of the system performance parameters have yet to be determined. Thus, this study improves upon the model through the generation of its Pareto frontier. The relationship between product demand objectives and the economic objectives of the model are investigated under varying levels of their respective prioritization. The fuzzy optimization of the polygeneration system yields an overall degree of satisfaction of 0.45 with the Sterling engine being excluded. Moreover, the interaction of the product demand and annual net profit objectives is identified to be conflicting in nature. The results of the study allow the decision-makers to easily identify the optimal design of the off-shore polygeneration system based on the respective level of prioritization given to the objectives. In addition, the generated Pareto frontier also visualizes the advantages and tradeoffs between the optimal designs available.