A comparative study of deep learning models versus ANFIS for multi-modal biometric fusion in authentication systems

Introduction

Biometric authentication has become an essential security measure across industries ranging from finance to defense. Traditional single-modal systems, such as face or fingerprint recognition alone, are vulnerable to spoofing attacks, variations in lighting, sensor errors, and pose inconsistencies. To enhance robustness and reliability, multi-modal biometric systems that combine multiple traits such as face, iris, and palmprint have been widely adopted. One of the critical challenges in these systems lies in the fusion of multi-modal dataeffectively integrating information from various sources to produce a consistent and accurate authentication decision. While deep learning models such as CNNs, DNNs, and Transformerbased architectures have been employed for this purpose, they often come with significant trade-offs: high computational complexity, dependency on large training datasets, limited interpretability, and susceptibility to overfitting [4,14] . In contrast, the Adaptive Neuro-Fuzzy Inference System (ANFIS) offers a promising alternative. ANFIS synergistically combines the learning capabilities of neural networks with the transparency of fuzzy logic, enabling it to handle uncertainties, adapt to dynamic environments, and provide interpretable decisions making it particularly suitable for real-time authentication in resource-constrained settings [1,13,11,16,13,20] . This paper aims to compare ANFIS with other popular deep learning models in the context of multi-modal biometric fusion, analyzing performance metrics such as accuracy, Equal Error Rate (EER), computational cost, scalability, and interpretability. The ultimate goal is to demonstrate that ANFIS, though simpler in structure, delivers competitive or superior results in scenarios demanding real-time, explainable, and secure authentication systems [13,1,13,1,7,15] .

Comparative models for fusion

In multi-modal biometric systems, fusion plays a pivotal role in integrating multiple biometric traits such as face, iris, fingerprint, and palmprint to produce a unified and reliable authentication decision. The effectiveness of such systems depends heavily on the robustness of the fusion strategy employed. This section explores two major categories of fusion models: traditional neuro-fuzzy approaches like the Adaptive Neuro-Fuzzy Inference System (ANFIS) [13] , and modern deep learning architectures including Convolutional Neural Networks (CNNs), Transformer-based models, and hybrid frameworks [3,5,7,10] . Each model is systematically analyzed in terms of its architectural design, fusion level (feature, score, or decision), interpretability, and suitability for real-time biometric authentication under varying constraints [1,13,4,14] . [1,13] ANFIS combines the learning ability of artificial neural networks with the decision-making logic of fuzzy systems. It uses fuzzy if-then rules to map inputs (Features or scores from biometric traits) to an output (Authentication decision) [1,13] .

Adaptive Neuro-Fuzzy Inference System (ANFIS)

Key advantages

 Handles uncertainty and noisy inputs.  Requires less training data.  Provides explainable decision-making.  Adaptable to environmental changes (e.g., lighting, angle).

Mathematical formulation

In inputs are 𝑥 1 , 𝑥 2 , … , 𝑥 𝑛 , and rules are:

Where 𝜇 represents membership functions, and weights 𝑤 𝑖 are learned.

Convolutional Neural Networks (CNNs)

CNNs are excellent at learning spatial hierarchies and extracting local features from biometric images.

Used for

 Feature-level fusion [8] .  Extracting embeddings from face, iris, or palmprint images.

Limitations

 Needs large datasets.  Poor interpretability.  Not ideal for fusing numerical matching scores.

Deep Neural Networks (DNNs)

Fully connected feedforward networks suitable for fusing flattened features or matching scores.

Strengths

 Universal function approximator.  Handles both structured and unstructured inputs.

Weaknesses

 Prone to overfitting.  Black-box behavior.  Computationally heavier than ANFIS [1,13] .

Recurrent Neural Networks (RNNs) / LSTMs

Primarily used for sequential data (e.g., speech, time-series).

They are less common in biometric fusion but may be used if temporal behavior (e.g., pupil movement over time) is modeled [1,7,15] .

Challenges

 Overkill for static biometric data.  Long training times and gradient vanishing issues. [4,14] Transformers leverage attention mechanisms to model longrange dependencies across input features from different modalities.

Transformer-based architectures

Pros

 Excellent for high-dimensional fusion.  Learn inter-modal dependencies effectively.

Cons

 Computationally intensive.  Requires large annotated datasets.  May not be feasible for real-time on-device deployment. Here is a comparative bar chart illustrating how ANFIS and various deep learning models perform across key criteria: [1,13]  Accuracy (% Actual)  Interpretability (1-10 scale, higher is better)  Training Data Need (1-10, lower is better)  Computation (1-10, lower is better)  Real-Time Suitability (1-10, higher is better)

This visual clearly shows that ANFIS achieves a strong balance of high accuracy, interpretability, low data needs, low computation, and high real-time suitability supporting its selection for your biometric fusion model [1,13,1,7,15] .

Research gap and contributions

While existing literature extensively explores deep learning for biometric fusion [1,3,5,7] , three critical gaps remain unaddressed:

 Gap 1: Lack of Systematic ANFIS Benchmarking: No prior work provides rigorous head-to-head comparison of ANFIS against modern Transformer-based architectures under identical experimental conditions with statistical validation [13,14,20] .  Gap 2: Absence of Edge-Deployment Analysis: Existing studies focus on accuracy metrics while ignoring realtime performance, memory footprint, and interpretability essential for mobile and IoT deployments [11,16,18] .  Gap 3: Limited Adaptive Fusion Mechanisms: Current fusion methods use static weights, failing to adapt to varying quality of biometric captures (e.g., poor lighting affecting face but not iris) [1,6,9] . These contributions establish ANFIS as a practical alternative to deep learning for deployment scenarios prioritizing efficiency, interpretability, and real-time performance.

Our novel contributions

Methodology

This section outlines the methodology used to implement and evaluate biometric fusion models using ANFIS, CNN, DNN, RNN/LSTM, and Transformer-based architectures. All models are applied to the fusion of three biometric traits: face, iris, and palmprint. The goal is to integrate features or matching scores from these modalities to determine user authenticity [1,13,2,5,3,4,14,6,1,7,15] .

Data preprocessing and feature extraction

Each modality undergoes preprocessing and feature extraction before fusion:  Face: Histogram equalization + VGGFace CNN feature extractor [2,5] .  Iris: Normalization + Gabor filters for texture encoding.  Palmprint: ROI segmentation + PCA to reduce dimensionality.

Each trait produces a fixed-length feature vector.

Fusion strategies

Three types of fusion are evaluated across all models:

A. Feature-level fusion [8] Feature vectors from all three modalities are concatenated:

Used as input to DNN, CNN, Transformer, and ANFIS [1,13,2,5,3,4,14] .

B. Score-Level Fusion

Each modality produces a matching score 𝑆 ∈ [0,1]. A weighted sum combines them:

Weights 𝑤 𝑖 are optimized using grid search or learning.

C. Hybrid Fusion

Feature-level fusion is followed by score-level refinement: [8] 1. Classify using feature-level model. 2. Fuse decision scores from each model.

Final decision:

𝐷𝑒𝑐𝑖𝑠𝑖𝑜𝑛 = { 𝐴𝑐𝑐𝑒𝑝𝑡 𝑖𝑓 𝑆 𝑓𝑖𝑛𝑎𝑙 ≥ 𝜃 𝑅𝑒𝑗𝑒𝑐𝑡 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

Model-specific processing

Fusion:

Feature-level, score-level, or hybrid. 4. Model Application: ANFIS, CNN, DNN, etc [1,13,2,5,3] . 5. Decision: Final classification accept or reject.

Experimental setup and evaluation

This section outlines the datasets, implementation environment, evaluation criteria, and performance results used to assess the effectiveness of ANFIS and other deep learning models for multi-modal biometric fusion [1,13,1,7,15] .

Datasets 4.1.1 Benchmark datasets

To ensure consistent comparison, standardized public datasets were used: All images were resized and aligned prior to feature extraction. A real-world subset of 20 users was used for realtime testing.

Dataset integration protocol Important note:

The three datasets contain non-overlapping subjects. Therefore, we adopted a virtual multi-modal database approach following established protocols in multimodal biometric research [61,64,72] :

Membership function formula:

The Gaussian membership function used in ANFIS defines how strongly an input 𝑥 𝑖 belongs to a fuzzy set A. It provides a smooth, bell-shaped curve commonly adopted for continuous features because of its differentiability, which aids gradient-based training. The clear and standard mathematical formulation is:

Where:  𝜇𝐴(𝑥 𝑖 ) ∈ is the degree of membership of 𝑥 𝑖 in fuzzy set  𝑐 is the center (mean) of the function, representing the point of maximum membership (𝜇𝐴(𝑐) -1)  𝜎 is the width (standard deviation), determining how spread out the membership curve is  𝑥 𝑖 is the input feature value Sometimes it is represented in compact form as:

𝜇𝐴(𝑥 𝑖 ) = 𝐺𝑎𝑢𝑠𝑠𝑖𝑎𝑛(𝑥 𝑖 ; 𝑐, 𝜎)

The membership function can be tuned during ANFIS training using hybrid learning backpropagation optimizing 𝑐 and 𝜎 yield a sharper peak, emphasizing localized sensitivity, while larger 𝜎 broadens generalization capability.

Deep learning model configurations

Evaluation Metrics

The following metrics were used: 1. Accuracy (%) -Proportion of correct authentication decisions.

Equal Error Rate (EER) -Point where False

Acceptance Rate = False Rejection Rate. 3. F1-Score (%) -Harmonic mean of precision and recall. Below is a bar graph comparing accuracy and EER of each model to visualize performance trade-offs. This chart illustrates that ANFIS outperforms other models in both accuracy and Equal Error Rate (EER) delivering the best balance of precision and reliability with minimal computational cost [1,13] .

Performance comparison

Statistical validation

To ensure the reported performance differences are statistically significant and not due to random variation, we conducted rigorous statistical testing using 10-fold stratified cross-validation [62,68] .

Cross-validation results

Table 5 presents the mean accuracy and standard deviation across 10 folds for each model:

Paired t-test analysis

We performed paired t-tests to compare ANFIS against each competing model using the 10-fold cross-validation scores [65,68,76] . The null hypothesis (H₀) states that there is no significant difference between model performances. Interpretation: All p-values are below the significance threshold (α = 0.05), allowing us to reject the null hypothesis. This confirms that ANFIS performs statistically significantly better than all competing models [24,27,65,68] . We also conducted McNemar's test [68] on the test set predictions to verify consistency: These results provide strong statistical evidence supporting ANFIS superiority across multiple validation frameworks [68,76] .

Discussion and analysis

The experimental results demonstrate that each model exhibits strengths and limitations across various dimensions accuracy, efficiency, interpretability, and resource usage. This section provides an analytical comparison of the findings and discusses why ANFIS emerges as a preferable choice in practical biometric fusion applications [1,13,1,7,15] .

Performance overview

The ANFIS model achieved the highest accuracy (98.1%) and the lowest EER (1.5%), outperforming even transformerbased deep models. Although CNNs and Transformers showed strong performance, their computational overhead and data requirements make them less suitable for deployment on low-power or edge devices [1,13,4,14] .

Interpretability and decision transparency

Interpretability is critical in biometric security, especially in regulated environments like healthcare, law enforcement, or finance. ANFIS, due to its fuzzy rule base, offers transparent decision-making: [1,13]  Users and administrators can trace back decisions to specific rules.  It supports adaptive logic, which adjusts to noise or uncertain conditions (e.g., poor lighting).

By contrast, deep learning models behave as black boxes, offering high accuracy but little explanation of why a classification was made. ANFIS requires far less training time and hardware resources, making it highly suitable for: [1,13]  Embedded systems  Mobile devices  On-device biometric verification (privacy-preserving setup) [1,7,15] Biometric traits often exhibit variability due to environmental conditions (e.g., glare, motion blur). ANFIS can dynamically reweight the importance of each biometric trait during fusion based on their reliability in real time [1,13] . For example:  If the face image is blurry, ANFIS shifts weight to iris and palmprint [1,13] .  Such adaptability is harder to model in CNNs or DNNs without retraining. Although deep models can achieve competitive performance, they are best suited for cloud-based, high-resource deployments not lightweight, secure, and explainable authentication systems.

Computational efficiency

Suitability for real-world biometric fusion

Limitations of deep learning models in this context

Conclusion

This comparative study evaluated the effectiveness of various fusion models including ANFIS, CNNs, DNNs, RNNs, and Transformers in the context of multi-modal biometric authentication using face, iris, and palmprint modalities. Through detailed experimentation on benchmark datasets and real-time user data, the Adaptive Neuro-Fuzzy Inference System (ANFIS) consistently demonstrated superior performance in key areas such as accuracy (98.1%), equal error rate (1.5%), training efficiency, and interpretability [1,13] . While modern deep learning models offer high classification power, they typically require extensive computational resources, large labeled datasets, and are inherently nontransparent. In contrast, ANFIS offers a lightweight, adaptable, and explainable fusion mechanism that is wellsuited for real-time, privacy-preserving, and edge-based biometric systems. Its capability to dynamically adjust to environmental uncertainty and data quality variations further enhances its suitability for practical deployment [1,13] .

Ultimately, this study confirms that ANFIS is not only a technically sound choice but also an ethically and operationally aligned solution for secure multi-modal biometric authentication. Future work will aim to hybridize ANFIS with deep learning components (e.g., fuzzy rule extraction from transformers) and explore edge-based optimization for mobile biometric applications [1,13] .

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