There are numerous cases in real life when we come across problems involving the optimization of multiple objectives simultaneously. One of the complexities of solving such problems is that often one or more objectives are usually conflicting under given conditions. In this study, the benefits of relying on a deployed Clinical Decision Support System (CDSS) concerning the overall reputation of a health facility has been studied. The analysis is performed in terms of a cooperative Bayesian game-theoretic model. The game is played between two players of which the first player is a patient who needs quick and accurate medical attention and the second player is the hospital administration that relies on medical experts as well as integrated multi-objective clinical data classification systems for decision-making. The proposed model ''MEAF''-Multi-objective Evolutionary Algorithm using Fuzzy Genetics attempts to address accuracy and interpretability simultaneously using Evolutionary Algorithms (EAs). This model enables a H CDSS to detect a disease accurately by using the available resources efficiently. The results of our simulation show that H CDSS produces better and accurate results in detecting disease with efficient resource utilization along with the reduced computational cost. This approach has also produced a better response for both players based on Bayesian Nash Equilibrium. Finally, the proposed model has been tested for accuracy, efficient resource utilization, and computationally cost-effective solution.