## 1 Introduction
### Fuzzy Logic and Neuro-Fuzzy Systems  
Fuzzy inference systems provide an alternative AI approach that has been applied to handle the uncertainty and nonlinearity in flyrock phenomena. In a pure fuzzy logic model, expert knowledge or data-driven rules map input parameters to flyrock distance using linguistic fuzzy rules. [PERSON] et al. (2017) developed a Mamdani-type fuzzy model for an iron mine in Iran and reported its performance was \"much better\" than a conventional statistical regression on the same 490-blast dataset. The fuzzy model yielded more accurate flyrock predictions and was able to incorporate vague relationships between inputs and outputs that crisp equations could not capture. Similarly, [PERSON] et al. (2017) compared an ANN and a fuzzy inference system for flyrock prediction in the Sungun mine--both models proved useful, but the fuzzy model slightly outperformed the ANN in predictive performance. These outcomes suggest that fuzzy systems, which do not require an explicit functional form, can effectively model the complex interplay of blasting factors. A noted advantage is that fuzzy models provide interpretable if-then rules, which can be meaningful for engineers (e.g., a rule might relate \"high powder factor and short stemming\" to \"long flyrock distance\" in linguistic terms). To leverage the strengths of both neural networks and fuzzy logic, researchers have employed the Adaptive Neuro-Fuzzy Inference System (ANFIS) for flyrock prediction. ANFIS is essentially a neural network that implements fuzzy inference rules and can learn rule parameters from data. [PERSON] and [PERSON] [PERSON] and [PERSON] (2018) applied ANFIS (alongside a standard ANN and Gaussian process regression) to data from a Turkish quarry, using important input features selected via statistical analysis. The ANFIS model proved most accurate, with a mean absolute error (MAE) of only -5.36 m--outperforming the back-propagation ANN in that study. In fact, the intelligent models (ANN, ANFIS, and GPR) all predicted flyrock with \(<\)6 m error (mean percentage errors \(<\) 10%), but ANFIS slightly edged out the others [PERSON] and [PERSON] (2018). In a related study, [PERSON] (2018) demonstrated that simplifying the input set can improve neuro-fuzzy models: using variable selection procedures, he developed two ANFIS models with only 3-4 inputs each, which achieved median errors \(<\) 5 m and MAPE \(<\) 8%. These ANFIS models were not only accurate but also less complex, underlining the benefit of focusing on the most predictive parameters [PERSON] and [PERSON] (2018). Another advantage of neuro-fuzzy approaches is their ability to highlight influential inputs. For instance, [PERSON]'s studies identified the burden-to-hole diameter ratio and specific charge (powder factor) as consistently significant features for flyrock prediction. Recent research has pushed the performance of ANFIS even further by integrating meta-heuristic optimizers (essentially creating hybrid neuro-fuzzy models). [PERSON] et al. [PERSON] et al. (2018) introduced an ANFIS enhanced by a Levy-flight Java algorithm (a modern swarm intelligence optimizer) to predict flyrock. This ANFIS-LJ model achieved R\({}^{2}\)\(\approx\) 0.981 on the test set (with MAE \(\sim\) 1.42 m), and when validated on 13 new production blasts it reached R\({}^{2}\) = 0.988 with only \(\sim\)1.3 m MAE. Such high accuracy (within \(\sim\)1-2 m of observed values) is exemplary for flyrock studies and was obtained using 5-fold cross-validation to ensure the model generalizes well. In a complementary study, another team led by [PERSON] (2018) tested ANFIS models optimized by different algorithms (adaptive differential evolution, genetic algorithm, fireworks, and bee colony). They found the JADE-ANFIS (ANFIS optimized by JADE) to be the best, with an overall prediction accuracy of \(\sim\)97.8% and very low error (MAPE = 1.1%). Competing models in that comparison achieved 89-96% accuracy (MAPE up to 3%), so the JADE-ANFIS was clearly superior [PERSON] et al. (2018); [PERSON] et al. (2018).