The study utilized a publicly available dataset of 538 labeled histopathological images from TMAs [26]-[28], classified into five tumor types: High-Grade Serous Carcinoma (HGSC), Endometrioid Carcinoma (EC), Clear Cell Carcinoma (CC), Low-Grade Serous Carcinoma (LGSC), and Mucinous Carcinoma (MC). The distribution of samples by tumor type is presented in Fig. 1, where HGSC dominated the set with 222 samples, and LGSC and MC were underrepresented, each with fewer than 50 images. Each image record included contextual metadata such as image width, height, and TMA slide origin. These were leveraged in subsequent modeling to enhance classification logic.

Fig. 2 visualizes the fuzzification process of image width and height, respectively, using triangular membership functions categorized into small, medium, and large sets. Moreover, Fig. 3 shows the confusion matrix of the fuzzy classifier, indicating high classification accuracy for dominant classes like HGSC and EC, and improved recall for sparse classes (LGSC, MC) compared to baseline models.

These visualizations validate the heterogeneity of the dataset and the need for context-aware modeling. Similar research emphasizes these metadata complexities and calls for interpretable, regionalized AI models [29], [30]. The test dataset, consisting of 134 unlabeled samples, served to benchmark model generalizability and simulate deployment scenarios where expert-labeled data is scarce or delayed.

In the fuzzification process, the Input variables—image width, image height, and TMA origin flag—were converted into fuzzy linguistic variables to manage uncertainty and variability across image data. This transformation allows for approximate reasoning in ambiguous classification cases. Membership functions were constructed as follows to define fuzzy categories and thresholds for each variable:

I. Image width: Small (≤35,000 px), medium (35,001–65,000 px), and large (≥65,001 px) II. Image height: Same as width III. TMA status: Binary fuzzy membership (TMA, Non-TMA) Triangular and trapezoidal membership functions were used for computational simplicity and clarity in defining fuzzy boundaries between categories. Triangular functions were applied to the medium range for smooth transition, while trapezoidal shapes captured broader intervals like Small and Large. Fig. 2 illustrates these shapes for image width and height, respectively.

The fuzzy inference system is built on a rule matrix that spans all combinations of the three input variables— image width, image height, and TMA status—each converted into linguistic variables. The 27 rules are summarized in Table 1.

A total of 27 fuzzy if-then rules were constructed to model expert knowledge in relating contextual metadata (e.g., image width, height, TMA status) to tumor type predictions. These rules serve as linguistic approximations to map fuzzy input sets to output decisions. For instance, Eq. (1), one such rule states: IF image width is Small AND image height is Medium AND TMA is True, THEN tumor type is EC with confidence 0.7. IF image width is Medium AND image height is Medium AND TMA is False, THEN tumor type is HGSC with confidence 0.85. IF image width is Large AND image height is Large AND TMA is True, THEN tumor type is MC with confidence (1) 0.9. IF image width is Small AND image height is Small AND TMA is False, THEN tumor type is CC with confidence 0.65. IF image width is Medium AND image height is Large AND TMA is True, THEN tumor type is LGSC with confidence 0.75.

Each rule was developed by analyzing the empirical distribution of metadata combinations and their corresponding tumor class probabilities, informed by the results of the Multinomial Logistic Regression (MLR). The fuzzy rule base can be formally expressed as Eq. (2).

Rᵢ: IF X₁ is A₁ᵢ AND X₂ is A₂ᵢ AND X₃ is A₃ᵢ THEN Y is Bᵢ, (2) where:

X₁ = image width, X₂ = image height, X₃ = TMA flag, Aᵢ =represents fuzzy sets (Small, Medium, Large; True/False), and Bᵢ = corresponds to tumor class labels.

A total of 27 fuzzy if-then rules were constructed to map combinations of input variable states to output tumor classifications. These rules span all logical combinations of three linguistic variables:

− Image width: Small, medium, large − Image height: Small, medium, large − TMA status: True, false

Each combination yields a rule of the form:

IF image width is Medium AND image height is Large AND TMA is False, THEN tumor type is HGSC with confidence 0.82.

The full rule matrix can be visualized as a 3x3x2 decision grid, where each cell corresponds to one rule that connects metadata contexts to a specific tumor type output. This structure provides a comprehensive map of reasoning paths used by the fuzzy inference system and supports both generalization and specificity across tumor classes.

IF image width is Small AND image height is Medium AND TMA is True, THEN tumor type is EC with confidence 0.7.

Rules were derived from empirical data distribution and expert-informed heuristics to capture both quantitative and qualitative decision boundaries. Their development was guided by the statistical significance of contextual features identified in MLR, ensuring each rule had an empirical basis. The rules were encoded using a Mamdani-style inference engine, widely regarded for its interpretability and suitability for systems requiring linguistic inputs and traceable rule evaluation pathways.

Mamdani fuzzy inference was used to evaluate rule outcomes by combining the degrees of truth from multiple fuzzy rules using max–min aggregation. The inference process calculates the firing strength of each rule and applies fuzzy AND/OR operations across antecedents. For example, the aggregation step is computed as:

μoutput = max[min(μwidth(x),μheight(y),μtma(z)) for all rules]. (5) To convert fuzzy outputs to crisp decisions, the centroid defuzzification method was employed, which calculates the center of gravity of the aggregated fuzzy set using the formula:

y ∗ = ∫ y · μ(y) dy / ∫ μ(y) dy. (6) It yields a single tumor label prediction, selected from five classes: HGSC, EC, CC, LGSC, and MC.

As illustrated in Fig. 4, it outlines the entire inference-to-decision pathway, from fuzzification to defuzzified classification. This approach supports interpretable reasoning in uncertain cases and aligns with recent medical AI studies on explainable fuzzy-based clinical decision systems [31], [32].

A MLR model was applied to statistically test the influence of context variables on tumor classification. The following model was fitted:

log(P(Y=i)/P(Y=base)) = β0 + β1imagewidth + β2imageheight + β3*isTMA. (7) Significant predictors (p < 0.05) were retained and interpreted alongside fuzzy rule outcomes to validate the contextual weight of metadata.

To reinforce the contextual validity of our fuzzy inference system, an econometric MLR model was employed. This model quantified the influence of the three key contextual variables—image width, image height, and TMA status—on tumor classification probability.

The estimated MLR equation took the form:

log(P(Y = i)/P(Y = base)) = β₀ + β₁ × imagewidth + β₂ × imageheight + β₃ × isTMA, (8) where:

P(Y = i)= is the probability of predicting a tumor class i, andβ₁–β₃= are regression coefficients representing the influence of each independent variable.

The base category was set to the most frequent tumor class (HGSC) for comparative interpretation. The results showed that both imagewidth and imageheight had statistically significant effects (p < 0.01) on the classification likelihood for multiple tumor types, while isTMA was especially predictive for EC and LGSC. These findings empirically validate the inclusion of metadata in the fuzzy rule architecture.

The coefficient magnitudes and confidence intervals for each predictor across tumor classes are illustrated in

Performance evaluation employed multiple metrics, including overall accuracy, precision, recall, and F1- score—both macro- and micro-averaged—to capture performance across imbalanced tumor categories. The confusion matrix, Fig. 6, provided insight into classifier biases, especially in underrepresented classes like MC and LGSC. Rare class performance was particularly emphasized to ensure diagnostic utility in real-world settings. The fuzzy classifier was benchmarked against Random Forest and MLR using identical features.

The findings reveal stronger recall and precision scores in fuzzy models for EC and LGSC, reflecting the effectiveness of contextual integration. These findings confirm improved interpretability and robustness when fuzzy rules were paired with metadata-rich classifiers [35], [36]. The evaluation underscores that incorporating image metadata through fuzzy logic enhances model sensitivity in underrepresented tumor types.

All classifiers were evaluated on the training dataset using stratified cross-validation and tested on the reserved 134-image test set. The fuzzy classifier consistently outperformed Random Forest and MLR, particularly in its ability to manage class imbalance. The fuzzy system achieved superior recall for low-frequency classes like MC and LGSC while maintaining high precision for dominant types like HGSC and EC. This performance advantage is attributed to the adaptive rule-based structure, which adjusts decision boundaries based on metadata contexts. Such interpretability and flexibility are highly valued in medical AI systems [37].

By integrating image metadata such as width, height, and TMA origin into the rule-based architecture, the framework captured contextual nuances often missed by black-box models. These metadata features were translated into fuzzy sets via membership functions—triangular for transitional regions (e.g., Medium Width) and trapezoidal for terminal categories (Small and Large). For instance, an image with 55,000 pixels in width would belong partially to both Medium and Large categories, enabling nuanced inference.

The membership functions used for fuzzifying image width and height were visualized in Fig. 7, respectively. These plots depict how each data point is assigned degrees of membership across fuzzy sets, facilitating continuous classification rather than hard thresholding.

To operationalize these memberships, the fuzzy inference engine evaluates all activated rules using max–min logic. The outcome of this evaluation is defuzzified using the centroid method, resulting in a crisp tumor prediction. The whole process is mapped visually in Fig. 8, which illustrates how inputs flow through fuzzification, rule evaluation, and defuzzification.

This design enables context-sensitive classification that adapts to image-specific metadata. The structure and function of this fuzzy metadata pipeline are inspired by context-aware fuzzy systems developed for ambient intelligence and applied in medical diagnostics [38], reinforcing its relevance in healthcare environments with limited interpretability support.

The fuzzy inference system effectively modeled ambiguous visual patterns and overlapping class boundaries, particularly in borderline cases like LGSC. Modeling visual patterns was achieved through the use of fuzzy linguistic variables and max–min aggregation during rule evaluation, allowing the model to consider partial memberships rather than force binary classification. For instance, a histopathological image with mixed morphological traits near the LGSC-EC boundary could activate multiple fuzzy rules simultaneously, as evidenced by the highlighted activation paths in Fig. 9.

The resulting output was a composite decision surface that incorporated the strengths of each partial rule activation. This intermediate result was then resolved using the centroid defuzzification method, providing a crisp classification while preserving interpretability. This process allowed the framework to represent ambiguity not as noise but as usable inference information, particularly crucial in pathology, where tissue samples may not conform strictly to a single diagnostic label.

The influence of contextual features was statistically validated through econometric modeling, confirming their significant contribution to tumor classification likelihoods. Using the MLRLR model, represented below as Eq. (9), the study assessed how image width, height, and TMA status affected classification probabilities across tumor types:

log(P(Y = i)/P(Y = base)) = β₀ + β₁ × imagewidth + β₂ × imageheight + β₃ × isTMA. (9)

This formulation enables us to compute the relative log-odds of tumor class membership against a reference category (HGSC in this case). The regression coefficients provide insight into how strongly each contextual variable influences classification decisions. Table 2 summarizes key coefficients, providing a numeric interpretation of the predictors' influence on classification likelihoods. For example, the strong positive coefficient of Image Width for EC and MC highlights its significance in those classifications. Likewise, TMA Status significantly influences EC and LGSC predictions, validating its inclusion in the fuzzy rules and highlighting real-world sampling biases. The horizontal line at zero helps differentiate between statistically significant and non-significant effects. For example, image width showed a strong positive association with EC and MC classification (p < 0.01), suggesting that larger images may encapsulate more informative histopathologic regions for these classes. TMA status, on the other hand, had a marked effect on LGSC and EC predictions, aligning with the intuition that certain tumor types are more frequently sampled via TMAs. These findings confirm our framework’s hypothesis: That contextual metadata is not merely auxiliary but functionally integral to the modeling pipeline. Integrating this statistical insight into fuzzy rule construction enhances model fidelity and avoids arbitrary rule formulation. It also justifies the selection of membership thresholds used during fuzzification. Moreover, the econometric model adds a layer of statistical interpretability, enabling clinical users to understand the rationale behind rule-weighted classifications. The synergy between fuzzy inference and econometric validation creates a robust decision system that addresses both interpretability and data-driven calibration. This methodological fusion has been similarly advocated in recent biomedical studies where hybrid models demonstrate superior diagnostic performance and clinical transparency [39].

The interpretability and low computational complexity of the framework make it well-suited for deployment in low-resource settings. In many ASEAN healthcare environments, computational infrastructure and access to large-scale training datasets are limited, which constrains the adoption of deep learning systems. The proposed fuzzy framework addresses this gap by employing compact rule bases and metadata-aware logic to reduce computational overhead without sacrificing classification quality.

The system's modular pipeline—from metadata fuzzification to decision defuzzification—highlights its transparent, interpretable flow as demonstrated in Fig. 8. The diagram includes labeled stages such as input acquisition, membership function mapping, fuzzy rule activation, aggregation of rule outputs, and final defuzzification using the centroid method. Arrows indicate how contextual metadata traverses through the inference engine, with color-coded blocks denoting each transformation step. This modular breakdown helps clinicians and developers understand not just what decision is made, but how it is derived, supporting explainable AI principles for real-world adoption, especially in clinical and resource-limited environments. Additionally, the fuzzy inference system avoids the complexity of deep CNN architectures by leveraging Mamdani-style rules that are both linguistically interpretable and computationally efficient.

The following operational cost function characterizes the framework’s advantage:

Ctotal = Cfuzz + Ceval + Cdefuzz, where:

(10) Cfuzz = The cost of fuzzification (O(n)), Ceval = The cost of rule evaluation (O(r)), and Cdefuzz= thecost of defuzzification (O(1)).

Compared to CNN-based inference (Typically O(n²) to O(n³)), this model scales linearly with data input size and rule complexity. Together, these results affirm the practical utility of the proposed framework in line with the study’s objectives: To bridge statistical rigor, interpretability, and operational feasibility in medical image classification. The classifier achieved superior macro F1-scores and recall for rare tumor classes like LGSC and MC, validating the fuzzy system's advantage in handling class imbalance. Visualizations of the membership functions and the annotated fuzzy rule pipeline demonstrate how context-aware metadata inputs are transformed into interpretable classification outcomes. Furthermore, econometric validation using MLR confirmed the statistical significance of image width, height, and TMA status in tumor prediction. Overall, the hybrid integration of fuzzy logic, visual context modeling, and statistical inference provides a lightweight, interpretable, and accurate alternative to traditional black-box models, making it particularly well-suited for low-resource clinical settings.