Thermodynamic, exergy, economic and environmental analysis of a solid oxide fuel cell and gas turbine hybrid cycle have been done in this paper. Also, multi-objective optimization of this cycle has been done by NSGA-II algorithm. In order to defining of the optimum design point, interactive fuzzy multi-objective method has been used. At optimum point, the cost function value, 0.0435 (U.S$/s) and exergy efficiency approximately 57.7% have been obtained. As well, sensitivity analysis of fuel cost per energy unit into objective functions has been done. In addition, rising inlet temperature of gas turbine from 900 up to 1600 (K), has caused an increase in output power up to 8.5% and entropy generation about 30% and a reduction in exergy efficiency from 61.9% to 51.7%. By evaluation of entropy generation rate, it has been concluded that most of enthalpy generation rate (32%) is related to combustion chamber. Increasing of fuel cell stack temperature causes an increase in exergy efficiency from 56.6% up to 60.2% and about 34.8% in output power of the cycle and a reduction in exergy efficiency from 62.8% to 59.1% and 8.4% in fuel cell power. Also, payback time of this cycle is about 3.12 years. (C) 2017 Elsevier Ltd. All rights reserved.