Fuel cell-heat engine hybrid system is a relatively new discipline which proposes to utilize the excess high temperature heat of the fuel cell as the heat source for the heat engine. This paper is concerned with a thermodynamic analysis of a molten carbonate fuel cell-SCO2 Brayton hybrid system to optimize its performance based on a list of criteria. Four objective functions are considered, including energy efficiency, power density, exergy destruction rate density and ecological function density, to study the influence of four main parameters, including compressor inlet temperature and turbine inlet temperature of the Brayton cycle, and interconnect plate area and current density of the fuel cell, on the performance of the hybrid cycle. The strong conflict between the objective functions necessitates a multi-objective optimization procedure and, therefore, three scenarios are proposed, each takes into account a combination of three of these objective functions. The multi objective evolutionary method integrated with non-dominated sorting genetic algorithm is used to obtain Pareto optimal frontiers. Finally, three efficient decision-making tools including TOPSIS, LINMAP and Fuzzy are employed by means of which the best answers in each case scenario are selected. Examining the Fuzzy method results for example, in the first scenario, which doesn't consider power density, ecological function density and exergy destruction rate density meet their optimum values, 1.314 and 0.3864 kW/m(2), respectively. However, energy efficiency falls by 10% compared to its maximum, which occurs in the third scenario (0.6676), where ecological function density isn't included, and power density drops by 25% compared to its own in the second scenario (2.2783 kW/m(2)), where energy efficiency is not. This indicates the strong confliction between the objective functions and also the necessity of this kind of analysis. However, the first scenario would roughly provide the best condition for the system if one wanted all the objective functions to be optimum all together.