Blasting is widely employed as an accepted mechanism for rock breakage in mining and civil activities. As an environmental side effect of blasting, flyrock should be investigated precisely in open-pit mining operations. This paper proposes a novel integration of artificial neural network and fuzzy cognitive map (FCM) with Z-number reliability information to predict flyrock distance in open-pit mine blasting. The developed model is called the artificial causality-weighted neural networks, based on reliability (ACWNNsR). The reliability information of Z-numbers is used to eliminate uncertainty in expert opinions required for the initial matrix of FCM, which is one of the main advantages of this method. FCM calculates weights of input neurons using the integration of nonlinear Hebbian and differential evolution algorithms. Burden, stemming, spacing, powder factor, and charge per delay are used as the input parameters, and flyrock distance is the output parameter. Four hundred sixteen recorded basting rounds are used from a real large-scale lead–zinc mine to design the architecture of the models. The performance of the proposed ACWNNsR model is compared with the Bayesian regularized neural network and multilayer perceptron neural network and is proven to result in more accurate prediction in estimating blast-induced flyrock distance. In addition, the results of a sensitivity analysis conducted on effective parameters determined the spacing as the most significant parameter in controlling flyrock distance. Based on the type of datasets used in this study, the presented model is recommended for flyrock distance prediction in surface mines where buildings are close to the blasting site.