[en] Highlights: • Superiority–inferiority full-infinite mixed-integer method is developed. • The method can tackle uncertainties of fuzzy sets, crisp and functional intervals. • The method is applied to a real case of planning energy system. • Effects of energy-conversion efficiency on energy systems are analyzed. • Results can support policy enactment of conversion efficiency improvement. - Abstract: In this study, a superiority–inferiority full-infinite mixed-integer programming (SFMP) method is developed for analyzing the effect of energy conversion efficiency under uncertainty. SFMP can effectively tackle uncertainties expressed as fuzzy sets, crisp intervals and functional intervals, it also can directly reflect relationships among multiple fuzzy sets through varying superiority and inferiority degrees with a high computational efficiency. Then the developed SFMP is applied to a real case of planning energy system for Bayingolin Mongol Autonomous Prefecture, where multiple scenarios related to different energy-conversion efficiency are concerned. Results for energy processing, energy conversion, capacity expansion, pollutant emission and system cost have been generated. It is proved that SFMP is an effective approach to deal with the uncertainties in energy systems with interactive and uncertain characteristics. A variety of uncertainties existed in energy conversion processes and impact factors could affect the modeling result. Results show that improvement of energy-conversion efficiency can effectively facilitate reducing energy resources consumption, optimizing energy generation pattern, decreasing capacity expansion, as well as mitigating pollutant emissions. Results also reveal that, for the study area, electric power has a highest energy saving potential among heating, oil processing, coal washing and refining. Results can help decision makers to generate desired alternatives that can facilitate policy enactment of conversion efficiency improvement and adjustment of regional energy structure under uncertainty.