Fig 1.
Structure of Fuzzy MOGWO algorithm in Process Mining, considering six metrics.
Table 1.
Professional academic comparison between the related studies and the current study. This comparative mapping also directly supports the identification of research gaps addressed in the present study.
Table 2.
Differences between classical Fuzzy Miner and proposed Fuzzy Causal Matrix.
Fig 2.
Comparative representations of fuzzy process models Left: Classical Fuzzy Miner shown as a weighted fuzzy graph, where node‑ and edge‑level simplification guides qualitative interpretation.
Right: The proposed Fuzzy Causal Matrix (FCM), which encodes all pairwise causal relations as numerical membership values. This matrix‑based representation not only improves scalability but also enables direct integration into multi‑objective optimization since each candidate model can be evaluated numerically without graph reconstruction and supports precise computation of interpretability metrics such as density, cyclomatic complexity, directness, and fuzzy‑rule complexity.
Table 3.
Model Type, analyzability and flexibility of related studies compared to the current study. This comparative classification highlights the strengths and limitations of existing models and informs the design objectives of the current stud.
Table 4.
Maps existing process discovery algorithms to different event log structures.
Table 5.
An illustrative example of an event log.
Table 6.
Example of a Fuzzy Causal Matrix. This high membership degree indicates that activity A has a strong causal influence on the execution of activity C.
Fig 3.
Flowchart of Fuzzy MOGWO algorithm.
Table 7.
Example mapping of numerical RFG/DI values to fuzzy linguistic terms using triangular membership functions.
Table 8.
Mamdani Fuzzy Rule Base for Leader Influence Adjustment (LIA).
Fig 4.
Sigmoid transfer function applied in Fuzzy MOGWO parameter updates.
The function regulates the wolves’ positional adjustments, progressively reducing exploration and enhancing exploitation as the optimization advances [27].
Fig 5.
Flower Model representation of a discovered process model with high Consistency but low Precision.
Although the model aligns well with many observed behaviors in the event Log, it also allows numerous traces absent from the log, leading to reduced Precision despite an organized, “flower-like” structure [15].
Fig 6.
Spaghetti Model representation of a discovered process model with low Simplicity and interpretability.
The highly entangled flow reflects poor structural clarity and makes expert interpretation difficult, emphasizing the trade-off between model coverage and understandability.
Fig 7.
Illustrative comparison of high- and low-Explainability process models.
Table 9.
Noise-Free event logs [30].
Fig 8.
Detail of six criteria’s Scores for Noise-Free event log.
Fig 9.
Norm Score of Noise-Free event logs by Four Different Methods.
Fig 10.
Radar chart comparison of Fuzzy MOGWO and competing algorithms across six evaluation criteria.
Each axis represents one dimension: Precision, Generalization, Consistency, Simplicity, Robustness, and Explainability. Higher values indicate better performance. The plotted values correspond to the average normalized scores obtained from noisy event logs (n = 10 synthetic logs). Fuzzy MOGWO shows a balanced overall profile, with notable strengths in Robustness and Consistency, while Inductive Miner exhibits competitive performance in Simplicity and Precision. Alpha Miner and Fuzzy Miner demonstrate lower Generalization and Explainability scores. Scores were normalized to [0, 1] for comparability. This chart visually complements the quantitative analyses presented in Tables X and Y.
Table 10.
Average metric differences between Fuzzy MOGWO and best competitor (noise-free logs).
Table 11.
p-values from paired t-tests comparing Fuzzy MOGWO and best competitor across six evaluation metrics (noise-free logs).
Fig 11.
Details score of noisy event logs by four different methods.
Fig 12.
Norm Score of Noisy event logs by Three Different Methods.
Fig 13.
Radar Chart of db1 noisy to db10 noisy.
Table 12.
Average metric differences between FUZZY MOGWO and best competitor (noisy logs).
Table 13.
p-values from paired t-tests comparing Fuzzy MOGWO and best competitor across six evaluation metrics (noisy logs).
Table 14.
Average Performance of Fuzzy MOGWO on Real event logs Across Six Quality Metrics.
Table 15.
Reported Performance of PSO Miner on Real event logs [14].
Table 16.
Dominance-Based Quality Comparison between Fuzzy MOGWO and PSO Miner on Real evenst logs.
Table 17.
p-values from paired t-tests comparing Fuzzy MOGWO and best competitor across two evaluation metrics (Real-World event logs).
Table 18.
Runtime comparison (in seconds) of Alpha, Inductive Miner, Fuzzy Miner, and the proposed Fuzzy MOGWO across real-life and synthetic event logs.
Table 19.
Stability of normalized performance scores of Fuzzy MOGWO across 30 independent random seeds under different noise levels.
Fig 14.
Box plots of normalized scores across 30 random seeds at four noise levels (0%, 5%, 10%, and 20%).
Table 20.
Runtime stability of Fuzzy MOGWO across 30 independent executions under different noise levels.
Table 21.
Conformance and expert evaluation results for FUZZY MOGWO and PSO Miner on real-world event logs BPIC2015−1, BPIC2017, and Sepsis).
Table 22.
Mean normalized scores under different metric weighting scenarios in noise-free and noisy (20%) settings.
Fig 15.
Sensitivity analysis results showing mean normalized scores for different metric weighting scenarios across noise-free and noisy (20%) settings.