Enhancing biometric system selection: A hybrid AHP-neutrosophic fuzzy TOPSIS approach

Abstract

A biometric system is essential in improving security and authentication processes across a variety of fields. Due to multiple criteria and alternatives, selecting the most suitable biometric system is a complex decision. We employ a hybrid approach in this study, combining the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) with the Analytic Hierarchical Process (AHP). Biometric technologies are ranked using the TOPSIS method according to the relative weights that AHP determines. By applying the neutrosophic set theory, this approach effectively handles the ambiguity and vagueness inherent in decision-making. Fingerprint, face, Iris, Voice, Hand Veins, Hand geometry and signature are the seven biometric technologies that are incorporated in the framework. Seven essential characteristics are accuracy, security, acceptability, speed and efficiency, ease of collection, universality, distinctiveness used to evaluate these technologies. The model seeks to determine which biometric technology is best suited for a particular application or situation by taking these factors into account. This technique may be applied in other domains in the future.

Introduction

In biometric recognition, identifying people through their physiological and behavioral traits is a complex process, which offers a number of advantages over more conventional identification techniques like ID cards and passwords. Various technologies are used in this process, which makes use of features like signatures, iris patterns, hand vein patterns, facial recognition, fingerprints, hand geometry, and voice recognition [1, 2]. Every biometric characteristic has a unique set of pros and cons. For example, facial recognition is preferred for its speedy processing and non-intrusiveness, while fingerprints are used extensively because they are unique and simple to obtain. However, a biometric system’s suitability is mostly determined by the demands of the particular application and the environment in which it is used.

The fundamental characteristics of the biometric trait itself play a major role in determining how effective a biometric system is. These characteristics include the following: universality (the characteristic must exist in all people), individuality (the characteristic must exist in each person specifically), ease of collection (the characteristic must be simple to quantify), and accuracy (the system must be able to correctly identify individuals). In addition, a biometric system’s overall success is contingent upon a number of factors, including acceptability (the degree to which users are willing to adopt the system), security (the degree to which the system can safeguard sensitive data), and speed and efficiency (the degree to which the system functions and performs) [3, 4].

Choosing the appropriate biometric system for a given application is still a difficult task, even with the advancements in biometric technologies. The wide variety of biometric systems that are currently in use, each with unique performance metrics and operational characteristics, is the source of this complexity. Biometric systems are rapidly taking the place of more outdated technologies in a variety of applications, including time and attendance management, law enforcement, surveillance, and access control [4, 5]. However, a careful assessment and selection procedure is required due to the varying effectiveness of these systems in various contexts.

The chosen human characteristic must satisfy a number of essential requirements in order for a biometric system to be considered effective: accuracy, ease of collection, universality, and individuality. Practical implementation factors like data security, operational efficiency, and user acceptability must also be taken into account. These complex requirements show how important it is to evaluate and choose biometric systems in an organized manner.

Although much research has focused on individual biometric systems, there is a notable lack of frameworks for methodically selecting the best system using multi criteria decision-making (MCDM) techniques. Previous studies often concentrate on specific biometric technologies without providing comprehensive frameworks for evaluating and comparing various systems tailored to specific application needs. This gap limits professionals’ ability to effectively choose suitable biometric systems for diverse applications. Despite extensive research on fingerprint and facial recognition systems, integrated frameworks comparing these to other biometric technologies while considering multiple decision criteria are scarce.

Robust decision support models are crucial for selecting biometric systems in complex environments. Advanced MCDM techniques enhance the precision and relevance of these assessments. Reliable biometric systems are essential in sectors like transportation, banking, and healthcare for preventing unauthorized access and improving security. These models boost performance and reliability, leading to more secure and efficient operations.

This work proposes a decision support model combining Neutrosophic Soft Set (NSS) Fuzzy TOPSIS [6, 7] and Analytic Hierarchy Process (AHP) [8] within an MCDM framework. The model aids in selecting the most suitable biometric system based on specific requirements and preferences. AHP structures and analyzes decisions through hierarchical modeling and pairwise comparisons [8]. NSS Fuzzy TOPSIS addresses ambiguous information by expanding traditional TOPSIS methods [6, 7]. This integrated approach enhances the precision of biometric system evaluations.

The proposed model offers a robust framework for assessing biometric alternatives by integrating advanced MCDM techniques like AHP and NSS Fuzzy TOPSIS [6, 8]. It improves the accuracy and efficiency of biometric system selection by addressing complex decision-making scenarios with rough sets and neutrosophic methods [7, 9]. This novel approach provides a structured evaluation based on various standards and preferences, enhancing informed decision-making [10, 11].

Irvanizam and Zahara improve the RAFSI method with single-valued trapezoidal neutrosophic numbers for better healthcare service quality evaluation [12]. Irvanizam and Zahara extend EDAS for evaluating mathematics teachers using similar neutrosophic numbers for reliable assessments [13]. Irvanizam et al. enhance EDAS and MULTIMOORA methods with bipolar and trapezoidal fuzzy neutrosophic sets, respectively, improving decision-making robustness and objectivity in group contexts [14, 15].

The objective of increasing accuracy and efficiency in biometric system selection techniques has drawn significant attention recently. This review examines integrated methods, focusing on TOPSIS and AHP techniques in decision making. The fundamental idea of the TOPSIS approach [6] is to select the variable nearest to the positive ideal solution, studied extensively by Adeel et al. [16,17,18,19,20,21,22,23,24]. Saqlain et al. [25] used MCDM to predict CWC 2019 results. Knowledge-based systems using AHP, TOPSIS, and Hesitant Fuzzy Sets enhance web app security [26]. The Neutrosophic Hypersoft Set (NHSS) framework addresses uncertainty in decision-making [27]. Combining TOPSIS and GRA in a neutrosophic setting, Green Supplier Selection method aids sustainable supplier evaluation [10]. Integrated approaches using AHP and TOPSIS balance web application usability [11], evaluate IoHT systems [28], and improve smartphone selection [7]. Neutrosophic MCDM for IoT enhances factor estimation [9], while Neutrosophic-TOPSIS for Personnel Selection addresses decision-making complexity [29]. Interval neutrosophic sets are applied in science and engineering [30], and soft sets address hesitancy and uncertainty [22]. Neutrosophic soft sets paired with TOPSIS are explored in various decision-making scenarios [7, 31,32,33,34,35].

Furthermore, the study demonstrates how well neutrosophic methods work in conjunction with AHP and TOPSIS to manage uncertainty and complexity in decision making processes, improving the process’s robustness and reliability [9, 36, 37]. A major improvement in managing uncertainty and complexity is provided by the integration of neutrosophic methods with AHP and TOPSIS in the suggested model. This is important for enhancing the decision-making process when choosing biometric systems [31, 38]. By offering a model that improves the decision-making process’s accuracy, efficiency, and robustness, this study thus makes a contribution to the larger field of decision sciences, especially when it comes to the selection of biometric systems [39,40,41].

The structure of the paper is as follows: Section “Preliminaries” covers the fundamental concepts of neutrosophic theory, such as definitions, operational relations, and accuracy functions. Section “Methodology” outlines an algorithm designed to address MCDM problems in a neutrosophic framework. Section “Numerical analysis” provides a numerical example to illustrate the application of the proposed decision-making method. The paper concludes with Section “Conclusion”, which includes final observations, the implications of the study, and a discussion of its limitations.

Preliminaries

Fuzzy set [42]

If X is a collection of objects denoted generically by x, then a fuzzy set A in X is a set of ordered pairs:

$$\text{A}=\left\{\text{x}, {\upmu }_{\text{A}}\left(\text{x}\right)\right|\text{x }\in \text{ X }\}$$

${\upmu }_{\text{A}}(\text{x})$ is called the membership function (generalized characteristic function) which maps X to the membership space M. Its range is the subset of non-negative real numbers whose supremum is finite. For sup ${\upmu }_{\text{A}}(\text{x})$ = 1: normalized fuzzy set. In Definition 2.1, the membership function of the fuzzy set is a crisp (real-valued) function. Zadeh also defined fuzzy sets in which the membership functions themselves are fuzzy sets.

Neutrosophic set [43]

Let X be a space of points (objects), with a generic element in X denoted by x. A neutrosophic set A in X is characterized by a truth-membership function${\text{T}}_{\text{A}}(\text{x})$, an indeterminacy—membership function ${\text{I}}_{\text{A}}(\text{x})$ and a falsity-membership function${\text{F}}_{\text{A}}(\text{x})$. The functions${\text{T}}_{\text{A}}(\text{x})$, ${\text{I}}_{\text{A}}(\text{x})$ and ${\text{F}}_{\text{A}}(\text{x})$ are real standard or nonstandard subsets of]${0}^{+}$, ${1}^{-}$[, that is ${\text{T}}_{\text{A}}\left(\text{x}\right):\text{ X }\to ]$ ${0}^{+},{0}^{+}[$, ${\text{I}}_{\text{A}}(\text{x}):\text{ X }\to ]$ ${0}^{+},$ ${0}^{+}[$ and ${\text{F}}_{\text{A}}(\text{x}):\text{ X }\to ]$ ${0}^{+},{0}^{+}[$.

There is no restriction on the sum of ${\text{T}}_{\text{A}}(\text{x})$, ${\text{I}}_{\text{A}}(\text{x})$ and ${\text{F}}_{\text{A}}(\text{x})$, so ${0}^{-}\le \text{ sup}$ ${\text{T}}_{\text{A}}\left(\text{x}\right) +\text{ sup}{\text{I}}_{\text{A}}(\text{x})+{\text{supF}}_{\text{A}}\left(\text{x}\right) \le { 3}^{-}.$

Accuracy function [7]

Accuracy function is the method or mathematical form by which neutrosophic numbers.

N are transformed into crisp numbers.

$$\text{A}\left(\text{F}\right) =\text{ x }= \left[\frac{{\text{T}}_{\text{x}}+ {\text{I}}_{\text{x}}+{\text{F}}_{\text{x}}}{3}\right]$$

Operational relations [43]

Let $\text{A}=\langle \text{x}, {\text{T}}_{\text{A}}\left(\text{x}\right), {\text{I}}_{\text{A}}\left(\text{x}\right), {\text{F}}_{\text{A}}\left(\text{x}\right)|\text{ x }\in \text{ X}\rangle$, $B=\langle x, {T}_{B}\left(x\right), {I}_{B}\left(x\right), {F}_{B}\left(x\right)| x \in X \rangle$ are two.

NSs. Operational relations are defined by.

$$\text{A}+\text{B}= \langle {\text{T}}_{\text{A}}\left(\text{x}\right)+ {\text{T}}_{\text{B}}\left(\text{x}\right)- {{\text{T}}_{\text{A}}\left(\text{x}\right)\text{T}}_{\text{B}}\left(\text{x}\right) , {\text{I}}_{\text{A}}\left(\text{x}\right)+ {\text{I}}_{\text{B}}\left(\text{x}\right)- {{\text{I}}_{\text{A}}\left(\text{x}\right)\text{I}}_{\text{B}}\left(\text{x}\right) , {\text{F}}_{\text{A}}\left(\text{x}\right)+ {\text{F}}_{\text{B}}\left(\text{x}\right)- {{\text{F}}_{\text{A}}\left(\text{x}\right)\text{F}}_{\text{B}}\left(\text{x}\right)\rangle ,$$

$${\text{A}}{\text{.B}} = \langle T_{A} \left( x \right)T_{B} \left( x \right),I_{A} \left( x \right)I_{B} \left( x \right),F_{A} \left( x \right)F_{B} \left( x \right)\rangle ,$$

$$\uplambda {\text{A}} = 1 - \left( {1 - {\text{T}}_{{\text{A}}} \left( {\text{x}} \right)} \right)^{\uplambda } , 1 - \left( {1 - {\text{I}}_{{\text{A}}} \left( {\text{x}} \right)} \right)^{\uplambda } , 1 - \left( {1 - {\text{F}}_{{\text{A}}} \left( {\text{x}} \right)} \right)^{\uplambda } , \uplambda > 0$$

$${A}^{\uplambda }= \langle {T}_{A}^{\uplambda }\left(x\right), {I}_{A}^{\uplambda }\left(x\right), {F}_{A}^{\uplambda }\left(x\right) \rangle ,\uplambda >0$$

Methodology

As a new approach to solving the biometric selection problem, our study views the integration of neutrosophic TOPSIS with AHP as a means of selecting best biometric optimally. The TOPSIS method is applied to the problem of biometric selection, as stated in the literature review section. An algorithm for solving the MCDM problem in a neutrosophic environment is proposed in this section.

In the current generation, choosing a biometric system is a difficult problem. Several techniques involving the application of AHP and neutrosophic fuzzy TOPSIS concepts have been put forward to address this complexity. The fuzzy linguistic approach is applied for the few forms of uncertainty present in the selection process. The aim is to examine the level of uncertainty in the biometric selection criteria. Figure 1 specifies the steps of the proposed techniques.

Fig. 1

Steps of the proposed model

There are four phases that comprise the conceptual flow.

Multi-criteria decision making technique

Multi-Criteria Decision Making (MCDM) is a systematic approach that takes into consideration multiple criteria or objectives when evaluating and choosing the best alternative from a set of options. In complex decision-making situations involving multiple factors, it offers a systematic framework that helps decision makers make well-informed decisions. A MCDM problem is typically expressed in matrix form [44]. Figure 2 represents the 3 phases of MCDM technique.

Fig. 2

Procedure of MCDM Technique

MCDM follows the following process:

• a. Formulation of the Problem: Define the decision problem precisely and specify the standards or goals that will be applied in determining the alternatives.

• b. Alternative Identification: List every possibility or course of action that could taken with regard to the decision.

• c. Criteria Definition: Determine the characteristics or criteria that are important in making the decision. These criteria need to be quantifiable and closely related to the decision’s objectives.

AHP approach

Thomas L. Saaty [8] developed the Analytical Hierarchy Process (AHP), a structure method for making decisions. It is a multi-criteria decision-making technique that breaks down complex decisions into smaller, more manageable components in a systematic way that assists in selecting the best option among variety of options. In order to determine priority scales for decision criteria and alternatives, AHP uses mathematical computations and pairwise comparisons. Figure 3 specifies the procedure of the AHP method in conceptual view.

Fig. 3

Steps of AHP Approach in conceptual view

The following procedure below are used to ascertain the relative weights of each criterion.

• 1. Develop a pairwise comparison matrix by using Saaty’s 9-point scale in Table 1 to subjectively evaluate each pair of criteria [8].

• 2. Using the eigenvalue calculation framework specified in [8], normalize the comparison matrix and ascertain the relative weight of each criterion.

• 3. Utilizing the consistency index and consistency ratio concepts as described in reference [8], to evaluate the consistency of subjective perception in pairwise comparisons. Apply the following formula to determine consistency:

  $$\text{CR}= \frac{{\text{CI}}}{{\text{RI}}}$$

  (1)

where RI is a random consistency index, CI is a consistency index, and CR is consistency ratio.

Table 1 Assigning neutrosophic numbers to each linguistic variable

Neutrosophic evaluation

Form a committee of experts in decision-makers to provide their opinions on the suggested criteria and alternatives. Compile the committee’s findings utilizing the neutrosophic scales specified in Table 1.

Once each linguistic variable has been given a neutrosophic number in accordance with the criteria and alternatives, use the accuracy function A(F) to transform the neutrosophic numbers into fuzzy numbers [7].

$$\text{A}\left(\text{F}\right) =\text{ x }= \left[\frac{{\text{T}}_{\text{x}}+ {\text{I}}_{\text{x}}+{\text{F}}_{\text{x}}}{3}\right]$$

(2)

TOPSIS method

A multi-criteria decision-making (MCDM) technique referred to TOPSIS is used to prioritize a set of alternatives according to how similar they are to an ideal solution. It is especially helpful in situations where the decision-making process involves several criteria. As first being developed by Hwang and Yoon in 1981 [6], TOPSIS has gained widespread application in variety of fields, such as environmental studies, engineering, and business. Here is an extensive description of the TOPSIS Method procedure [20, 33], which is shown in Fig. 4.

Fig. 4

Five different phases of TOPSIS method

• a. Normalize the decision matrix: Make a matrix with the criteria represented in columns and the alternatives represented in rows. To make sure that each criteria is unit-free and on the same scale, normalize this matrix. The formula in Eq. (3) yields the normalized value of an element (i, j) in the matrix.

  $${\text{r}}_{{{\text{ij}}}} = \frac{{{\text{x}}_{{{\text{ij}}}} }}{{\sqrt {\mathop \sum \nolimits_{{{\text{n}} = 1}}^{{\text{m}}} {\text{x}}_{{{\text{ij}}}}^{2} } }}$$

  (3)

  where, ${\text{r}}_{\text{ij}}$ is the normalised value of element (i, j), n is the number of the alternatives and ${\text{x}}_{\text{ij}}$ is the initial value of element (i, j).

• b Establish the Weighted Normalized Decision Matrix: To create a weighted normalized decision matrix, multiply each normalized value by the corresponding weight of each criteria determined by the AHP Process. For each element (i, j) in the matrix, the weighted normalized value (V) is:

  $${\text{v}}_{\text{ij}}= {\text{w}}_{\text{j}} \times {\text{r}}_{\text{ij}}$$

  (4)

  where, ${\text{v}}_{\text{ij}}$ is the weighted normalised value of element (i, j) and ${w}_{j}$ is the weight assigned to the criteria j.

• c. Determining the Ideal and Anti-Ideal solutions: Establish the ideal and anti-ideal values for each criteria. The ideal solution $\left({\text{A}}^{+}\right)$ represents the maximal value and the anti-ideal solution $\left({\text{A}}^{-}\right)$ represents the minimal value.

  $${\text{A}}^{+}=(\text{max}\left({\text{v}}_{1\text{j}}\right),\text{ max}\left({\text{v}}_{2\text{j}}\right), \dots ,\text{ max}\left({\text{v}}_{\text{nj}}\right))$$

  (5)
  $${\text{A}}^{-}=(\text{min}\left({\text{v}}_{1\text{j}}\right),\text{ min}\left({\text{v}}_{2\text{j}}\right), \dots ,\text{ min}\left({\text{v}}_{\text{nj}}\right))$$

  (6)

• d. Evaluate the Similarity Points: Using the Euclidean distance, determine how similar each alternative is to the ideal and anti-ideal solutions The formula for the ideal solution [20]is

  $${\text{S}}_{\text{i}}^{+}= \sqrt{\sum_{\text{j}=1}^{\text{n}}{\left({\text{v}}_{\text{ij}}-{\text{A}}_{\text{j}}^{+}\right)}^{2}}$$

  (7)

  and for the anti-ideal solution[20] is

  $${S}_{i}^{-}= \sqrt{\sum_{j=1}^{n}{\left({v}_{ij}-{A}_{j}^{-}\right)}^{2}}$$

  (8)

• e. Determine the Score for TOPSIS: Finally, for each alternative, the TOPSIS score (Relative closeness to Ideal Solution,${\text{R}}_{\text{i}}$) is determined [20] as follows:

  $${\text{R}}_{\text{i}}= \frac{{\text{S}}_{\text{i}}^{-}}{{\text{S}}_{\text{i}}^{+}+{\text{ S}}_{\text{i}}^{-}}$$

  (9)

  where, ${S}_{i}^{+}$ represents the similarity to the ideal solution for alternative i and ${S}_{i}^{-}$represents the similarity to the anti-ideal solution.

Choose the alternatives according to their TOPSIS scores. A solution is considered closer to the ideal one if its TOPSIS score is higher. TOPSIS offers an approach to methodically evaluate and prioritize options according to various factors, considering the separation from the optimal solution as well as the closeness to the anti-optimal solution. It is a systematic process that assists decision-makers in deciding which option, out of several, is best.

Numerical analysis

MCDM approach

Formulation of the problem

The biometric system has been selected as the criterion choosing tool; the public’s choice will then determine the criterion. Based on their criteria, a biometric system has been chosen based on the final result. The market is becoming more competitive due to the advent of new technologies, making it more challenging for users to choose an appropriate biometric. Neutrosophic set was applied to obtain more accuracy in the result as it appears that in the rapidly expanding market, the fuzzy idea result has been improved. Investigating the accuracy of the biometric system’s criterion selection is the study’s target.

Specifications

Criteria and alternatives are crucial in determining a solution to the complicated problem of selection. In this problem formulation, the criteria and alternatives listed as in Table 2 and Table 3 are taken into account.

Table 2 Alternatives under consideration (A)

Table 3 Criteria’s under consideration (C)

Determining the weights of each criteria

• a. Pairwise Comparison Matrix of Criteria is determined by Using Saaty’s 9-point Scales in Table 4.

• b. By dividing each element by its column sum, the normalized pair-wise comparison matrix can be determined, refer Table 5.

• c. Calculating the Consistency.

Table 4 Pairwise comparison matrix of criteria [4]

Table 5 Matrix of normalized pairwise comparison

Using Table 6, we can obtain the Consistency Index. Equation (1) is used to verify the consistency ratio, which comes out to be 0.0625. The criteria weights exhibit a reasonable level of consistency since the value is less than 0.10.

Table 6 Consistency table

Neutrosophic evaluation

• 1. The proposed model has decision makers expert, who assign Linguistic variables with respect to Criteria and Alternatives (see Table 7).

• 2. According to their personal interests, knowledge, and experience, the decision makers will allocate linguistic values from Table 1 to the alternatives and criteria listed above, as indicated in Table 8.

• 3. Conversion of Neutrosophic numbers into fuzzy numbers using accuracy function (see Table 9).

Table 7 Decision matrix with respect to alternatives and criteria’s

Table 8 For every linguistic variable, assign a neutrosophic number

Table 9 Conversion of neutrosophic numbers into fuzzy numbers using A(F)

TOPSIS method

• Step 1: Normalize the Decision Matrix by Eq. (3), refer Table 10.

• Step 2: Compute Weighted Decision Matrix using Eq. (4), refer Table 11.

• Step 3: Determine the ideal (positive and negative) alternatives, refer Table 12.

• Step 4: Eqs. (7 and 8) can be used to determine the separation measure of each alternative, refer Table 13.

• Step 5: Calculate the relative closeness to the ideal solution utilizing Eq. (9), refer Table 14.

Table 10 Standardized decision matrix

Table 11 Weighted decision matrix

Table 12 Positive and negative ideal alternatives

Table 13 Alternatives separation measures

Table 14 TOPSIS score

The Iris alternative is considered to be the most effective for use with the best biometric system. The ${\text{A}}_{3}$ option satisfies the standards for being the best biometric system as well as the decision makers committee’s judgment. Nonetheless, ${\text{A}}_{7}$ is regarded as the worst option since it is unable to satisfy the given assessments and standards in order to achieve its own goals.

Results and discussion

The ranking of biometric systems using the generalized TOPSIS method resulted in the following order [4]: ${\text{A}}_{3}$ (Iris), ${\text{A}}_{1}$ (Fingerprint), ${\text{A}}_{5}$ (Hand veins), ${\text{A}}_{6}$ (Hand geometry), ${\text{A}}_{4}$ (Voice), ${\text{A}}_{2}$ (Face), and ${\text{A}}_{7}$ (Signature). According to this ranking, the Iris-based biometric system emerged as the best option based on the personalized preferences set for decision-making.

In comparison, the following biometric systems were ranked when using the Fuzzy TOPSIS method: ${\text{A}}_{3}$ (Iris), ${\text{A}}_{3}$ (Fingerprint), ${\text{A}}_{4}$ (Voice), ${\text{A}}_{5}$ (Hand veins), ${\text{A}}_{2}$ (Face), ${\text{A}}_{6}$ (Hand geometry), and ${\text{A}}_{7}$ (Signature). Even with varying rankings, the Iris-based biometric system is consistently regarded as one of the best biometric systems to use (Fig. 5).

Fig. 5

Ranking comparison of alternatives

Conclusion

Choosing the best biometric system for security and identity is a difficult choice that is frequently beyond the scope of conventional methods because of uncertain and inconsistent situations. Our study combines the neutrosophic Analytic Hierarchy Process (AHP) and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) to address these problems within the multi-criteria decision-making (MCDM) framework while taking into account different environmental constraints. This work offers a solid framework for assessing biometric systems, enhancing the accuracy and reliability of decision-making.

The implications are significant, improving decision-making with advanced techniques such as TOPSIS and neutrosophic AHP, particularly in cases where the data is ambiguous. The handling of neutrosophic data and the requirement for exact criteria weight determination, require significant computational resources and experience, are important constraints. Incorporate dynamic components, use machine learning for criteria weights, and extend this methodology to new domains in future research. The approach needs to be verified and refined through empirical investigations and practical applications in order to ensure its efficiency in real-world scenarios. By resolving these issues and expanding its use, this methodology can greatly improve the biometric system selection process.