Identity verification using authenticity evaluation of handwritten signatures is an important issue. There have been several approaches for the verification of signatures using dynamics of the signing process. Most of these approaches extract only global characteristics. With the aim of capturing both dynamic global and local features, this paper introduces a novel model for verifying handwritten dynamic signatures using neutrosophic rule-based verification system (NRVS) and Genetic NRVS (GNRVS) models. The neutrosophic Logic is structured to reflect multiple types of knowledge and relations among all features using three values: truth, indeterminacy, and falsity. These three values are determined by neutrosophic membership functions. The proposed model also is able to deal with all features without the need to select from them. In the GNRVS model, the neutrosophic rules are automatically chosen by Genetic Algorithms. The performance of the proposed system is tested on the MCYT-Signature-100 dataset. In terms of the accuracy, average error rate, false acceptance rate, and false rejection rate, the experimental results indicate that the proposed model has a significant advantage compared to different well-known models.

Biometrics is a wide research field that addresses distinguishing people according to recognizing some measurable anatomical or behavioral characteristics. Biometrics have been gradually replacing traditional methods that recognize people according to what they own, such as cards or keys, or what they know, such as passwords [

Signature verification is the process where the biometric algorithm aims to validate a person’s stated identity by matching the signature sample submitted to one or more reference signatures previously entered [

In signature verification, rule-based verification/classification approaches are widely used. Any classification system that uses the IF-THEN rules for verification/classification purposes can be referred to as a rule-based verification/classification system. Typically, any IF-THEN rule is a term on the left-hand side (LHS) and right-hand side (RHS) where LHS is a series of satisfying conditions to derive RHS-represented conclusion. For rule-based verification/classification, the LHS of the rule predominantly consists of a conjunction of attribute checks, while its RHS is a class label (Genuine or forgery). Fuzzy sets and fuzzy logic are used in the Fuzzy Rule-based Classification system (FRBCs) to represent and model various types of information about the problem at hand, which is online signature verification in our case. FRBCs have received significant attention among biometric researchers due to the good behavior in the real-time datasets and have been applied effectively to a wide variety of problems in multiple domains [

This paper presents Neutrosophic rule-based verification/classification system (NRVS) to verify online-signature.

NRVS extends the fuzzy rule-based verification/classification by defining each logical variable using its degrees of truth, indeterminacy, and falsity. Instead of fuzzy Logic, the antecedents and descendants of the rules are composed of neutrosophical logic arguments. To the best of our knowledge, Neutrosophic logic was never used in the identity verification of online signatures. Further, for improving our NRVS model’s verification performance, the genetic algorithm is employed for refining and optimizing the neutrosophic “IF-THEN” rules. Further, the proposed model is capable to treat global and regional features as well as vague features that cannot be categorized as global or regional features. The strength in the NRVS is due to usage of the indeterminacy term introduced by the neutrosophic logic.

The rest of the paper is structured as follows: A summary of the previous work is introduced in Section 2. In Section 3, theoretical background about Neutrosophic Logic and Neutrosophic Set is introduced. Further, the proposed NRVS model and its hybridization with Genetic Algorithms, GNRVS are introduced in Section 4. In Section 5, the experimental results and discussions are introduced. Finally, some concluding remarks and future directions are given in Section 6.

In studying online signature, one has to address the following concepts: registration and acquisition of data, preprocessing, feature selection and extraction, classification, and verification [

There are three strategies in the extraction of features: extraction based on features that rely on global features as in [

In classification and verification phase, researchers proposed strategies that calculate a signature similarity score. They match the score with a global or user-dependent tolerance to achieve the verification outcome. There exist three matching perspectives here: global [

In the literature, several strategies were proposed to choose the best features combination to mitigate the error in verification [

Experimentally, in [

Many approaches have been suggested in the literature for approximating the time functions accompanying the signing procedure. The Fourier Transform was applied in [

Fuzzy logic approaches are used in online signature verification. For example, in [

Neutrosophy has emerged strongly in the scientific world in the last few years. In [

The fuzzy set (FS) theory was developed by Zadeh in mid-1960s, to manage fuzzy, and vague data. It is defined by _{A}(

For example, the FS theory mismanages incompleteness and contradiction in the information. Therefore, the neutrosophic set theory was designed to manage incomplete and also incompatible data. Besides, the neutrosophic set theory is a massive framework that aims to generalize all sets’ principles, it is a generalization of the classic set theory, FS theory, FS with interval values, intuitionist FS, and intuitionist FS with interval values [

Smarandache introduced neutrosophy in 1995, which deals with the origin, scope, and nature of neutralities, as well as their experiences with specific mental visions [

Both

Smarandache proposed basic principles for the neutrosophic system in [

Mathematically, let the

For a space of objects, _{A}), a falsity _{A}(_{A}). _{A}(_{A}(_{A}(^{−}0, 1^{+}[ (i.e., _{A}, _{A}, _{A}(^{−}0, 1^{+}[). There is no limitation on the sum of _{A}(_{A}(_{A}(^{−}0 ≤ _{A}(_{A}(_{A}(^{+}.

Neutrosophic set operators can be created by more than one way [

Complement: The complement

for

Union: The union

for

Intersection: The intersection

for

Containment:

for

• Difference: The difference of two neutrosophic sets

for

Neutrosophic logic has been constructed to serve mathematically building models containing uncertainty of many different types ambiguity or vagueness, inconsistency or contradiction, redundancy or incompleteness, and incompleteness [^{−}0, 1^{+}[, where

^{−}0, 1^{+}[ [

Number of attributes used.

The maximum and minimum value of each attribute.

The number and names of classes.

Our proposed Neutrosophic Rule-based Verification System (NRVS) utilizes the Neutrosophic Logic to generalize the Fuzzy Rule-based Verification scheme. In NRVS, the origins and consequences of the “IF-THEN” principles are all neutrosophic logic statements. There are three phases on the NRVS:

Neutrosophication: Implementation of the knowledge base (KB) in neutrosophic logic by translating raw data using the three neutrosophic features: truthmembering, falsity-membering, and indeterminacy membering.

Inference Engine: To achieve a neutrosophic output, KB and the neutrosophic “IF-THEN” implication rules are implemented, and

Deneutrosophication: Use three functions similar to those used by neutrosophisation, transforms the neutrosophic output of the second phase to a crisp value.

The KB used above contains the available neutrosophic “IF-THEN” rules mode. After that, the knowledge base uses neutrosophic sets to collect the neutrosophic rule semantics.

The following membership functions are specified:

Truth membership function.

Falsity membership function.

Indeterminacy membership function.

Such membership functions will be drawn using the function of the Fuzzy Trapezoidal membership. In the neutrosophic type, three neutrosophic components are required to reflect each value for each feature. We applied three membership functions to each value in each attribute of the dataset in order to get those three components.

The aim, here, is to develop rules to be used predominantly during the verification phase. Suppose that the data is in the form _{1}, _{2},_{n}, since _{i} is the _{i} ∈ 1, 2,_{training}) which has labelled instances and testing data (_{testing}) that have unlabelled instances. During this phase, the training and testing data produce exact neutrosophic rules. In NRVS, in each neutrosophic rule, each attribute has three components that define the three degrees of truth, indeterminacy, and falsehood.

The matrix of testing is built in this phase without class labelling. For each testing rule (_{t} ∈ _{testing}), the percentage of intersections between the test rule and other training rules should be determined (_{training}) (see _{1}, _{2},_{q}, where _{i} is the matching percentage between _{t} and the training rule _{i}. The testing rule is assigned the training rule-class label, which has a maximum intersected percentage. When there is no overlap of at least 50% between the training rules and the existing testing rules (_{i}

(_{training} = _{training} ∪ _{t}). Finally, the test matrix that projected class labels is contrasted with the same matrix that currently carries class labels. To evaluate our model, the confusion matrix is computed. Different terms, such as True Positive (TP), True Negative (TN), False Positive (FP), and False Negative (FN), can be computed from the confusion matrix.

An example of comparison with neutrosophic and fuzzy classifiers is given by

_{1} and C_{2}), each one has five instances, and each instance is represented by only two features f_{1} and f_{2} (see

All values in the dataset are converted into a neutrosophical space in the neutrosophication phase. Therefore, each value is expressed by three values (_{low}, _{Medium}, _{High}_{Low}, _{Medium}_{Low}, _{Medium}, _{High}

Class label ( |
||
---|---|---|

10.0 | 10.0 | _{1} |

14.0 | 6.0 | _{1} |

16.0 | 16.0 | _{1} |

12.0 | 14.0 | _{1} |

20.0 | 6.0 | _{1} |

21.0 | 12.0 | _{2} |

22.0 | 16.0 | _{2} |

24.0 | 4.0 | _{2} |

25.0 | 7.0 | _{2} |

26.0 | 14.0 | _{2} |

Value | _{Low} |
t_{Medium} |
_{High} |
_{LowMedium} |
_{MediumHigh} |
_{Low} |
_{Medium} |
_{High} |
---|---|---|---|---|---|---|---|---|

7.0 | 0.666 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 1.0 | 1.0 |

10.0 | 1.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 1.0 | 1.0 |

16.0 | 0.0 | 0.500 | 0.0 | 0.0 | 0.0 | 0.750 | 0.249 | 1.0 |

21.0 | 0.0 | 0.0 | 0.249 | 0.0 | 0.250 | 1.0 | 0.874 | 0.125 |

12.0 | 0.0 | 0.0 | 0.111 | 0.0 | 0.666 | 1.0 | 0.666 | 0.333 |

The rules of training and test data are obtained in the neutrosophic space in the 3rd phase (

Samples of the training rules are as follows:

where the rule [3, 5, 8][3, 5, 8] → class _{2} means: if _{1} is [_{2} is [_{2}. The testing rules are as follows:

Lastly, in the verification/classification phase of the NRVS model, all training rules will be applied to match each rule in the test data. (see _{1}, and as shown, four instances are correctly classified, and only the first testing instance is misclassified.

The proposed GNRVS combines the Genetic Algorithm (GA) and NRVS model. The GA is used in the NRVS model to refine the neutrosophic “IF-THEN” rules [

The proposed GNRVS model has the same steps as the NRVS model, but a new phase is called the Genetic-based machine learning phase. In this phase, GA is used for refining linguistic rules in the KB. Algorithm 1 summarizes the steps of the GNRVS model.

Three experiments have been carried out in this paper. In the first (in Section 5.1), the proposed NRVS model is compared with conventional classifiers [

Experiments are carried out using

In our experiments, we used the MCYT-Signature-100 dataset. This dataset includes ten-print fingerprint and online signature modes for each person registered in the dataset (330 persons). It contains many samples of each modality under various control levels to deal with the inevitable variability of each function during the registration process, as outlined below. The signatures were acquired using Device: WACOM Intuos (Inking pen)

The results of a 10 × 10-fold cross-validation were obtained in all experiments. The dataset samples were divided, in a random manner, into

In this experiment, the proposed NRVS model is evaluated by comparing the results of it with (i) six well-known learning algorithms, namely, Multilayer Perceptron (MLP) [

In terms of the accuracy, all models obtained high accuracy, and the proposed NRVS obtained the second-best accuracy, while SVM and NB achieved the worst accuracies.

In terms of specificity, the NRVS, k-NN, and SVM obtained the best specificity. Moreover, NRVS obtained competitive sensitivity results compared to the other models.

The NRVS, k-NN, and SVM models outperform the other models in terms of the precision results.

In terms of F1-Score, NRVS obtained competitive results compared to the other models.

To conclude, the proposed NRVS model achieved promising results compared to the mentioned conventional classifiers.

Metrics | SVM | NB | RF | DT | MLP | LDA | K-NN | NRVS |
---|---|---|---|---|---|---|---|---|

Accuracy | 0.953 | 0.958 | 0.992 | 0.992 | 0.992 | 0.987 | 0.962 | 0.989 |

Precision | 1.0 | 0.958 | 0.992 | 0.989 | 0.987 | 0.975 | 1.0 | 1.0 |

Sensitivity | 0.905 | 0.953 | 0.993 | 0.996 | 0.998 | 0.999 | 0.925 | 0.979 |

Specificity | 1.0 | 0.962 | 0.991 | 0.989 | 0.987 | 0.975 | 1.0 | 1.0 |

F_{1}-Score |
0.950 | 0.955 | 0.993 | 0.993 | 0.992 | 0.987 | 0.961 | 0.989 |

This experiment aims to compare the proposed NRVS model with one of the rulebased systems, such as the Fuzzy Rule-based Verification System (FRVS), which is one of the most well-known rule-based systems. This comparison aims to show that NRVS generalizes and outperforms the FRVS model. Many research proposed methods based on a fuzzy rule-based verification system such as [

The general structure of the fuzzy rule-based system [

Knowledge Base: this contains two parts: database and rule base. The dataBase part contains the dataset and the fuzzy membership functions used in the rulesbased system and will be used in the inference engine. The rule base part contains fuzzy rules in the form of “IF-THEN” rules.

Fuzzifier: this component converts the crisp input to fuzzy input which input to the inference engine.

Inference Engine: this component produces the results as the fuzzy output by using the fuzzy input and knowledge base.

Defuzzifier: this converts the fuzzy output into the crisp output.

In this sub-experiment, we use the membership function proposed in Mahmood et al. (2013). The results of this experiment, according to different evaluation metrics are summarized in

Metrics | FRVS | Fuzzy approach [ |
NRVS |
---|---|---|---|

Accuracy | 0.788 | 0.964 | 0.989 |

Precision | 0.960 | 0.966 | 1.0 |

Sensitivity | 0.596 | 0.961 | 0.979 |

Specificity | 0.976 | 0.967 | 1.0 |

F_{1}-Score |
0.735 | 0.964 | 0.989 |

Metrics | Fuzzy approach [ |
NRVS |
---|---|---|

FAR | 3.29 | 0 |

FRR | 3.82 | 2.1 |

From

This experiment is conducted to compare the proposed GNRVS verification system with the NRVS. In this experiment, as in the previous two experiments, we used all attributes,

Metrics | Fuzzy-genetic approach [ |
NRVS | GNRVS |
---|---|---|---|

Accuracy | 0.976 | 0.985 | 0.992 |

Precision | 0.975 | 1.0 | 1.0 |

Sensitivity | 0.976 | 0.979 | 0.984 |

Specificity | 0.975 | 1.0 | 1.0 |

F_{1}-Score |
0.976 | 0.989 | 0.991 |

Metrics | Fuzzy-genetic approach [ |
NRVS | GNRVS |
---|---|---|---|

FAR | 2.32 | 0 | 0 |

FRR | 2.48 | 2.1 | 1.59 |

From the results in

GNRVS improves NRVS in terms of all measures.

GNRVS achieves better accuracy as RF, DT, and MLP.

GNRVS as NRVS is better than the RF, DT, and MLP classifiers in terms of precision and Specificity measures.

GNRVS improves the proposed NRVS model in terms of F1-Score to achieve the second-best results.

Additionally, from

This paper proposes a novel model to verify online-signatures based on their dynamic characteristics using neutrosophic rule-based verification system (NRVS) that generalizes the fuzzy rule-based verification system. The proposed system has three primary stages: Firstly, stable features are derived from online signature data in the feature extraction process. Secondly, the proposed NRVS is used to classify signatures into authentic signatures and forgeries by generating neutrosophic “IF-THEN” rules. Thirdly, a hybridization of NRVS and Genertic Algorithms (GNRVS) is used to refine the neutrosophic “IF-THEN” rules generated in the previous stage. The MCYT-Signature-100 dataset, which has 8250 genuine signatures and 8250 forgery signatures, is used to test the proposed system. To evaluate the proposed model, various experiments were carried out and we obtained promising results. Overall, the observations of the proposed model show that it could be applied for handwritten signature verification. We plan to develop a hybrid framework between a neutrosophic, a rule-based system, and deep learning in future work.