Variations in energy demands require combined heat and power (CHP) systems to be more flexible in adjusting its operations. However, high flexibility is often achieved at the expense of other aspects. In other words, increasing flexibility of a CHP system would require large number of equipment to startup or shutdown. This would lead to potentially high emissions and high start-up/shutdown costs due to sub-optimal fuel choices and poor selection of technologies respectively. In this respect, it would be challenging to determine the optimal CHP operation with high flexibility, low emissions and low start-up/shutdown costs. To address this challenge, operational optimisation must be considered. In this paper, a multi-objective fuzzy optimisation model was developed to optimise system flexibility, fuel emissions, equipment start-up and shutdown costs for a CHP system operation to meet varying energy production requirements. Essentially, fuzzy optimisation is used to maximise the degree of satisfaction among the three mentioned objectives. To demonstrate the proposed approach, a multi-fuel CHP case study consisting of several scenarios was solved. Results from the case study show that a trade-off CHP operation was determined for increased production. The trade-off operation had the degree of satisfaction of 35 % for each objective. The obtained degree of satisfaction indicates that a balance between flexibility, emissions and costs was achieved. In addition, chosen technologies and fuels were analysed and classified under categories such as "must have", "optional" and "must avoid". (C) 2020 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.