Throughout the recent decade, numerous investigations were done on Braysson cycles that were yielded in various output power and thermal efficiency analyses. Throughout the current research, the dimensionless power density and thermal efficiency are optimized using NSGA algorithm and finite time thermodynamic analysis. Compares optimum outcomes gained in this paper by executing LINMAP, TOPSIS and Fuzzy Bellman-Zadeh decision makers with relevant outcomes gained in previous works. Furthermore, it was shown that the FUZZY decision-maker provides better solutions in comparison with other implemented decision makers. Finally, analysis of deviation was carried out on the basis of the MAPE technique and it was obtained that the average deviation of results generated by the aforementioned decision maker were 0.015% and 0.03% for the dimensionless power density and thermal efficiency, respectively. The highest deviations of outcomes gained by used decision makers are 0.12% and 0.04% for the thermal efficiency and dimensionless power density, correspondingly. Outcomes of this study may be useful for any further design of Braysson engines. Moreover, optimized results of this research are the basis of further research for comparison and validation. (C) 2015 Elsevier Ltd. All rights reserved.