In this study, the discharge coefficient of sharp-crested weirs located on circular channels was modeled using the ANFIS and ANFIS-Firefly (ANFIS-FA) algorithm. Also, the Monte Carlo simulations (MCs) were used to enhance the compatibilities of the soft computing models. However, the k-fold cross validation method (k=5) was used to validate the numerical models. According to the input parameters, four models of ANFIS and ANFIS-FA were introduced. Analyzing the numerical results showed that the superior model simulated the discharge coefficient as a function of the Froude number (Fr) and the ratio of flow depth over weir crest to the weir crest height) h/P(. The values of the mean absolute relative error (MARE), root mean square error (RMSE) and correlation coefficient (R) for the superior model were calculated 0.001, 0.002 and 0.999, respectively. However, the maximum error value for this study was less than 2%.