Process Integration via the cogeneration energy system is widely utilised for its ability to generate both electricity and usable heat simultaneously. However, the decision to integrate a cogeneration energy system in an energy portfolio requires a synchronous analysis of multiple objectives. Previous work in the field introduced a novel fuzzy P-graph approach for the optimal synthesis of cogeneration and polygeneration systems. In this paper, an integrated evaluation framework using the fuzzy P-graph has been proposed. The conflicting objectives are introduced as indicators in the modelling framework for targeting purposes. The acceptable range of the said objectives is transformed into fuzzy limits. A case study from previous work is adapted to evince the potential of the developed model. The result shows that both demand and cost indicators can be targeted at the same time, allowing the multi-objective decision-making problem in the energy system design to be tackled effectively.