In recent decades, determining the most appropriate energy producers in the power industry is considered as a strategic factor in moving toward sustainable development. In this paper, energy producers have been assessed by a five-dimensional approach to sustainability as a very strong representation of the energy sustainability. These five comprehensive aspects are environmental, social, economic, technical, and institutional. To rank the energy producers and to overcome the ambiguity of linguistic values of experts' subjective preferences, a revised Grey Relational Analysis (GRA) technique based on the grey numbers is used. To show the performance of the five-dimensional approach, and to verify the developed approach, a case study on Iran's power industry is considered. For this purpose, a number of exploratory interviews were conducted with the experts of the Renewable Energy Organization of Iran (SUNA) and with some academic specialists, and the main factors affecting sustainability assessment of energy producers were identified. To validate the capability of the proposed model, results were compared with the outcome of the GRA method. The results demonstrate the practicality and feasibility of research and indicate that natural gas, solar energy, and wind power are ranked first to third, respectively. (C) 2018 Elsevier Ltd. All rights reserved.