Crypto assets have become increasingly popular in recent years due to their many advantages, such as low transaction costs and investment opportunities. The performance of crypto exchanges is an essential factor in developing crypto assets. Therefore, it is necessary to take adequate measures regarding the reliability, speed, user-friendliness, regulation, and supervision of crypto exchanges. However, each measure to be taken creates extra costs for businesses. Studies are needed to determine the factors that most affect the performance of crypto exchanges. This study develops an integrated framework, i.e., fuzzy best–worst method with the Heronian function—the fuzzy measurement of alternatives and ranking according to compromise solution with the Heronian function (FBWM’H–FMARCOS’H), to evaluate cryptocurrency exchanges. In this framework, the fuzzy best–worst method (FBWM) is used to decide the criteria’s importance, fuzzy measurement of alternatives and ranking according to compromise solution (FMARCOS) is used to prioritize the alternatives, and the Heronian function is used to aggregate the results. Integrating a modified FBWM and FMARCOS with Heronian functions is particularly appealing for group decision-making under vagueness. Through case studies, some well-known cryptocurrency exchanges operating in Türkiye are assessed based on seven critical factors in the cryptocurrency exchange evaluation process. The main contribution of this study is generating new priority strategies to increase the performance of crypto exchanges with a novel decision-making methodology. “Perception of security,” “reputation,” and “commission rate” are found as the foremost factors in choosing an appropriate cryptocurrency exchange for investment. Further, the best score is achieved by Coinbase, followed by Binance. The solidity and flexibility of the methodology are also supported by sensitivity and comparative analyses. The findings may pave the way for investors to take appropriate actions without incurring high costs.