International Journal of Neutrosophic Science

Journal DOI

https://doi.org/10.54216/IJNS

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2690-6805ISSN (Online) 2692-6148ISSN (Print)

Orthogonal distance and similarity for single-valued neutrosophic fuzzy soft expert environment and its application in decision-making

Faisal Al-Sharqi , Ashraf Al-Quran , Hamiden Abd El- Wahed Khalifa , Haifa Alqahtani , Badria A. Ali Yousif , Rawan A. shlaka , Mona Aladil

A soft expert set(SES) is a concept that combines elements of soft sets and expert systems. It aims to incorporate expert knowledge and uncertainty-handling capabilities into the analysis and decision-making processes. On the other hand, the idea of single neutrosophic sets (SVNSs) and fuzzy sets (FSs) are imported models for handling the uncertainty data. In this work, the authors combine the critical features of FSs and SVNSs under expert systems in one model. Accordingly, this model worked to provide decision-makers with more flexibility in the process of interpreting uncertain information. From a scientific point of view, the process of evaluating this high-performance SVNFSES disappears. Therefore, in this paper, we initiated a new approach known as single-valued neutrosophic fuzzy soft expert sets (SVNFSESs) as a new development in a fuzzy soft computing environment. We investigate some fundamental operations on SVNFSESS along with their basic properties. Also, we investigate AND and OR operations between two SVNFSESS as well as several numerical examples to clarify the above fundamental operations. Finally, we have given an Orthogonal Distance and Similarity for SVNFSESs to construct a new algorithm to demonstrate the method’s effectiveness in handling some real-life applications.

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Doi: https://doi.org/10.54216/IJNS.230401

Vol. 23 Issue. 4 PP. 08-22, (2024)

Secondary K-Range Symmetric Neutrosophic Fuzzy Matrices

M. Anandhkumar , H. Prathab , S. M. Chithra , A. S. Prakaash , A. Bobin

This paper introduces and explores the concept of secondary k-Range Symmetric (RS) Neutrosophic Fuzzy Matrices (NFM) and establishes its properties and relationships with other symmetric and secondary symmetric NFMs. The study defines secondary k-RS NFMs and provides insightful numerical examples to illustrate their characteristics. The paper investigates the interconnections among s-k-RS, s-RS, k-RS, and RS NFMs, discuss on their mutual relations. Additionally, the necessary and sufficient conditions for a given NFM to qualify as a s-k-RS NFM are identified. The research demonstrates that k-symmetry implies k-RS, and vice versa, contributing to a comprehensive understanding between different types of symmetries in NFMs. Graphical representations of RS, column symmetric, and kernel symmetric adjacency and incidence NFMs are presented, unveiling intriguing patterns and relationships. While every adjacency NFM is symmetric, range symmetric, column symmetric, and kernel symmetric, the incidence matrix satisfies only kernel symmetric conditions. The study further establishes that every range symmetric adjacency NFM is a kernel symmetric adjacency NFM, though the converse does not hold in general. The existence of multiple generalized inverses of NFMs in Fn is explored, with additional equivalent conditions for certain g-inverses of s-κ-RS NFMs to retain the s-κ-RS property. We conclude by characterizing the generalized inverses belonging to specific sets {1, 2}, {1, 2, 3}, and {1, 2, 4} of s-k-RS NFMs, providing a comprehensive framework for understanding the structure and properties of secondary k-Range Symmetric Neutrosophic Fuzzy Matrices. This research contributes to the mathematical literature by introducing a novel class of NFMs and establishing their fundamental properties and relationships, presenting new perspectives on matrix theory in the context of neutrosophic fuzzy logic.  

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Doi: https://doi.org/10.54216/IJNS.230402

Vol. 23 Issue. 4 PP. 23-28, (2024)

Golden Jackal Optimization with Neutrosophic Rule-Based Classification System for Enhanced Traffic Sign Detection

Mohammed Assiri

Traffic signs detection is a critical function of automatic driving and assisted driving is a significant part of Cooperative Intelligent Transport Systems (CITS). The drivers can obtain the data attained via automated traffic sign detection to improve the comfort and security of motor vehicle driving and regulate the behaviors of drivers.  Recently, deep learning (DL) has been utilized in the fields of traffic sign detection and achieve better results. But there are two major problems in traffic sign recognition to be immediately resolved. Some false sign is always detected due to the interference caused by bad weather, and illumination variation. Some traffic signs of smaller size are increasingly complex to identify than larger size hence the smaller traffic signs go unnoticed. The objective is to achieve the accuracy and robustness of traffic sign detection for detecting smaller traffic signs in a complex environment. Thus, the study presents a Golden Jackal Optimization with Neutrosophic Rule-Based Classification System (GJO-NRCS) technique for Enhanced Traffic Sign Detection. The GJO-NRCS technique aims to detect the presence of distinct types of traffic signs. In the GJO-NRCS technique, DenseNet201 model is exploited for feature extraction process and the GJO algorithm is used for hyperparameter tuning process. For final recognition of traffic signals, the GJO-NRCS technique applies NRCS technique. The simulation values of the GJO-NRCS method can be examined using benchmark dataset. The experimental results inferred that the GJO-NRCS method reaches high efficiency than other techniques.

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Doi: https://doi.org/10.54216/IJNS.230403

Vol. 23 Issue. 4 PP. 29-40, (2024)

A Multi-Criteria Decision-Making Analysis for COVID-19 in Public Health under Neutrosophic Set: Case Study

Heba R. Abdelhady , Shereen Zaki , Mahmoud M. Ismail , Mohamed Emad , Shimaa Said

This paper proposed a framework for assessing the COVID-19 response in Egypt. COVID-19 plays a vital role in public health, and selecting the best response can decrease the impact of the disease. This study used the type 2 neutrosophic set as a framework for dealing with uncertainty. The assessment of the COVID-19 response has various conflicting criteria, so the concept of multi-criteria decision-making (MCDM) is used to deal with COVID-19 criteria. The MCDM methods are adopted with the type-2neutrosophic set—the typ-2 neutrosophic AHP-COPRAS-VIKOR methodology framework. The AHP is used to compute the criteria weights. The COPRAS and VIKOR methods are used to rank the alternatives. The case study in Egypt is conducted to show the best response to COVID-19. Five main criteria and nineteen sub-criteria are used in this paper. The methodologies employed in this paper aid as examples for future research endeavors, inspiring a continued dialogue on refining and advancing MCDM methodologies in public health disasters.

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Doi: https://doi.org/10.54216/IJNS.230404

Vol. 23 Issue. 4 PP. 41-62, (2024)

Enhanced Academic Stress-Coping Skills Assessment in College Students: A Comparative Study of Neutrosophic Distance Measure and Proposed Cubic Pythagorean Fuzzy Hypersoft TOPSIS Method

E. Prabu , M. Gopala Krishnan , A. Bobin

In multi-criteria decision-making scenarios involving real numbers, interval numbers, and a combination of membership and non-membership grades, accurate decision-making is crucial yet challenging. The integration of diverse grade values into a single value poses a significant challenge for decision-makers. To address this issue, this study introduces the concept of a cubic Pythagorean fuzzy hypersoft set, facilitating information aggregation without ambiguity. The characteristics of correlation coefficients and aggregation operators are emphasized, underscoring their importance in decision-making processes. An algorithm based on correlation coefficients (CC) is proposed for the TOPSIS method, which ranks preferences based on their similarity to the ideal solution, applied here to examine how college students cope with academic stress. Furthermore, the efficiency of the proposed method is demonstrated through a comparative study, wherein the correlation coefficient in the TOPSIS method is contrasted with existing distance measures (DMs). Results indicate the superiority of CC in the TOPSIS method over DMs. In addition to comparing the proposed method with existing distance measures, the efficacy of the proposed approach is further demonstrated through a comparative analysis with established neutrosophic distance measures. This comprehensive evaluation highlights the robustness and versatility of the proposed method in addressing the complexities of multi-criteria decision-making scenarios, particularly in assessing stress management strategies among college students, thus providing valuable contributions to decision-making contexts. This study contributes to enhancing decision-making processes, particularly in evaluating stress management strategies among college students, thereby offering valuable insights for academic contexts.

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Doi: https://doi.org/10.54216/IJNS.230405

Vol. 23 Issue. 4 PP. 63-82, (2024)

The Box and Muller Technique for Generating Neutrosophic Random Variables Follow a Normal Distribution

Maissam Jdid , Florentin Smarandache

The focus of operations research is the existence of a problem that requires making an appropriate decision that helps reduce risk and achieves a good level of performance. Operations research methods depend on formulating realistic issues through mathematical models consisting of a goal function and constraints, and the optimal solution is the ideal decision, despite the multiplicity of these methods. However, we encounter many complex issues that cannot be represented mathematically, or many issues that cannot be studied directly. Here comes the importance of the simulation process in all branches of science, as it depends on applying the study to systems similar to real systems and then projecting this. The results if they fit on the real system. So simulation is the process of building, testing, and running models that simulate complex phenomena or systems using specific mathematical models. The simulation process depends on generating a series of random numbers subject to a regular probability distribution in the field [0, 1], and then converting these random numbers into random variables subject to the distribution law. Probability, according to which the system to be simulated operates, using appropriate techniques for both the probability density function and the cumulative distribution function. Classical studies have provided many techniques that are used during the simulation process, and to keep pace with the great scientific development witnessed by our contemporary world, we found that a new vision must be presented for this. Techniques A vision based on the concepts of neutrosophics, the science founded by the American mathematical philosopher Florentin Smarandache. The year 1995, in which new concepts of probabilities and probability distributions are used, as we presented in previous research some techniques from a neutrosophic perspective, and as an extension of what we presented previously, we present in this research a neutrosophic vision of the Box and Muller technique used to generate random variables that follow a normal distribution.

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Doi: https://doi.org/10.54216/IJNS.230406

Vol. 23 Issue. 4 PP. 83-87, (2024)

Group decision-making based on distance measures settings for single-valued neutrosophic fuzzy soft expert environment

Faisal Al-Sharqi , Ashraf Al-Quran , Agaeb Mahal Alanzi , Hamiden Abd El- Wahed Khalifa , Rawan A. shlaka , Ali Mohammad A. Bany Awad , Heba Ghareb Gomaa

A soft expert set is a concept that combines elements of soft sets and expert systems. It aims to incorporate expert knowledge and uncertainty-handling capabilities into the analysis and decision-making processes. On the other hand, the idea of single neutrosophic sets (SVNSs) and fuzzy sets (FSs) are imported models for handling the uncertainty data. In this work, the authors combine the critical features of FSs and SVNSs under expert systems in one model. Accordingly, this model worked to provide decision-makers with more flexibility in the process of interpreting uncertain information. From a scientific point of view, the process of evaluating this high-performance SVNFSES disappears. Therefore, in this paper, we initiated a new approach known as single-valued neutrosophic fuzzy soft expert sets (SVNFSESs) as a new development in a fuzzy soft computing environment. We investigate some fundamental operations on SVNFSESS along with their basic properties. Also, we investigate AND and OR operations between two SVNFSESS as well as several numerical examples to clarify the above fundamental operations. Finally, we have given distance measures (DM) between two SVNFSESs to construct a new algorithm that is used to demonstrate the effectiveness of the method in handling some real-life applications.

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Doi: https://doi.org/10.54216/IJNS.230407

Vol. 23 Issue. 4 PP. 88-103, (2024)

Neutrosophic Logic Empowered Machine Learning Algorithm with Salp Swarm Optimization for Biomedical Image Analysis

Adwan A. Alanazi , Abdelgalal O. I. Abaker , Sayed Abdel-Khalek , Fahad Mohammed Alhomayani , M. Aripov

Leukemia recognition and classification contain the identification of dissimilar kinds of leukemia, a group of blood cancers that affects the bone marrow and blood. A classical model containing microscopic analysis of blood smears to classify abnormal cells analytic of leukemia. Leukemia recognition employing a united technique of neutrosophic logic and deep learning (DL) signifies a new and complete approach to handling uncertainty and difficulty in medical data. Neutrosophic logic permits the representation of unstated or imperfect data, which is general in medical analyses. DL mainly convolutional neural networks (CNN) or recurrent neural networks (RNN), which can mechanically remove difficult patterns from medicinal imageries, improving the accuracy of leukemia recognition. The neutrosophic logic module accommodates the characteristic uncertainty in medicinal data, offering a formalism to manage imperfect or inaccurate data linked with the analysis procedure. The combination of these dual techniques generates a robust structure which capable of leveraging both the control of DL in image analysis and the flexibility of neutrosophic logic in dealing with uncertainties, contributing to more trustworthy and interpretable leukemia recognition methods.  This study develops a new Salp Swarm Algorithm with a Neutrosophic Logic SVM (SSA-NSVM) model for Leukemia Detection and Classification. The SSA-NSVM technique mainly exploits Neutrosophic Logic (NL) concepts with the DL model for the detection of leukemia. To attain this, the SSA-NSVM model uses bilateral filtering (BF) based image pre-processing. In addition, the SSA-NSVM approach applies a modified densely connected networks (DenseNet) technique for learning complex and intrinsic feature patterns. Besides, the hyperparameter range of the modified DenseNet system takes place utilizing a SSA. At last, the NSVM technique is employed for the detection and identification of leukemia. The performance validation of the SSA-NSVM algorithm is verified utilizing a benchmark medicinal image dataset. The simulation values emphasized that the SSA-NSVM model reaches better detection outcomes than other existing approaches.

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Doi: https://doi.org/10.54216/IJNS.230408

Vol. 23 Issue. 4 PP. 104-116, (2024)

Extending the concepts of complex interval valued neutrosophic subbisemiring of bisemiring

M. Palanikumar , Nasreen Kausar , Emre Ozbilge , Ebru Ozbilge

The objective of this paper is to investigate the innovative concept of complex neutrosophic subbisemiring. The novelty of the complex neutrosophic subbisemiring lies in its wide range of truth, indeterminacy, and false function values. It goes beyond the range of [0,1] in the complex plane in contrast to the traditional range [0,1]. Therefore, these three functions can be described mathematically using a complex number in the complex neutrosophic subbisemiring. We develop and analyze the concept of complex interval-valued neutrosophic subbisemiring (CIVNSBS). Moreover, we study homomorphic characteristics and important properties of CIVNSBS. We propose the level sets of CIVNSBS and complex interval valued neutrosophic normal  subbisemiring (CIVNNSBS) of bisemirings. Moreover, we introduce CIVNNSBS of bisemiring. Let ¡ be a complex neutrosophic subset of bisemiring S. Then is a CIVNSBS of S if and only if all non empty level set  is a subbisemiring, where . Let ¡be a CIVNSBS of bisemiring S and V be the strongest complex neutrosophic relation of bisemiring S. Then  ¡ is a CIVNSBS of bisemiring S if and only if V is a CIVNSBS of . We illustrate that homomorphic images of every CIVNSBS is a CIVNSBS and homomorphic pre-images of every CIVNSBS is a CIVNSBS. Examples are provided to illustrate our results.

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Doi: https://doi.org/10.54216/IJNS.230409

Vol. 23 Issue. 4 PP. 117-135, (2024)

Selection process real-life application for new type complex neutrosophic sets using various aggregation operators

Ibraheem Abu Falahah , Abdallah Al-Husban , Lejo J. Manavalan , Jamil J. Jaber , M. Palanikumar , G. Balaji

A new approach to multiple attribute decision-making (MADM) is presented in this article, which is based on (È·1, È·2, È·3) complex neutrosophic sets (CNS). We are extending the CNS in this way. Complex neutrosophic weighted averaging (CNWA), complex neutrosophic weighted geometric (CNWG), complex generalized neutrosophic weighted averaging (CGNWA), and complex generalized neutrosophic weighted geometric (CGNWG). An algorithm utilizing these operators was presented during our discussion. Extensive score and accuracy values are illustrated numerically. We will also discuss idempotency, boundedness, commutativity, and monotonicity of complex neutrosophic sets as part of this communication. You can find the best option faster, easier, and more conveniently with them. Therefore, complex (È·1, È·2, È·3) is more closely associated with more precise conclusions. A fascinating and intriguing finding was also revealed by the study.

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Doi: https://doi.org/10.54216/IJNS.230410

Vol. 23 Issue. 4 PP. 136-153, (2024)

Stable Neutrosophic Crisp Topological Space

Doaa Nihad Tomma , L. A. A. Al-Swidi

The significance and influence of neutrosophic crisp set theory in numerous scientific domains, particularly topology, led us to construct a new definition of topology based on neutrosophic crisp sets, allowing us to regulate its key mathematical ideas. Therefore, we constructed this definition and dubbed it stable neutrosophic crisp topology, where we went over the key idea which is the interior with the vital features.

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Doi: https://doi.org/10.54216/IJNS.230411

Vol. 23 Issue. 4 PP. 154-159, (2024)

Betam-Closed Sets in Fuzzy Neutrosophic Topological Spaces

Nawras N. Sabry , Fatimah M. Mohammed

The current work offers a new concept of sets and called uzzy eutrosophic m-closed sets in fuzzy neutrosophic topology. In fact, the research is an extended form of a research conducted by F. M. Mohammed et.al. [1-7]. It explores a number of noteworthy examples to shed the light on the new characteristics and attributes of these recently formed conceptions, as well as some associated interactions between them.

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Doi: https://doi.org/10.54216/IJNS.230412

Vol. 23 Issue. 4 PP. 160-169, (2024)

Enhancing Digital Social Innovation Ecosystems: A Pythagorean Neutrosophic Bonferroni Mean (PNBM) -DEMATEL Analysis of Barriers Factors for Young Entrepreneurs

Zahari Rodzi , Nur A. Binti Shafie , N. Binti Abdul Razak , Faisal Al-Sharqi , Ashraf Al-Quran , Ali M. A. Bany Awad

This study employs a Pythagorean Neutrosophic Bonferroni Mean (PNBM) - Decision Making Trial and Evaluation Laboratory (DEMATEL) approach to analyze barriers faced by young entrepreneurs in Digital Social Innovation (DSI). Pythagorean Neutrosophic Set (PNS) enriches the analysis, accommodating uncertainties in the complex socio-economic context. Limited Access to Funding emerges as the most influential barrier, showcasing its pivotal role in impacting other DSI challenges. Regulatory and Compliance Challenges are identified as interdependent, emphasizing their interconnected nature with broader barriers. Neutrosophic elements elucidate the uncertainties surrounding financial constraints, regulatory frameworks, and mentorship dynamics. The study contributes to a nuanced understanding of DSI challenges and pioneers the application of neutrosophic logic in socio-economic research. It advocates for a more inclusive decision-making methodology, fostering adaptability in addressing the indeterminate nature of barriers faced by young entrepreneurs navigating the digital social innovation landscape. The findings aim to enhance support systems, fostering a conducive environment for DSI initiatives and encouraging future research in neutrosophic decision-making methodologies.

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Doi: https://doi.org/10.54216/IJNS.230413

Vol. 23 Issue. 4 PP. 170-180, (2024)

Optimization of Neutrosophic Vendor-Buyer Economic Order Quantity Model Using Particle Swarm Optimization

K. Kalaiarasi , N. Anitha , S. Swathi , B. Ranjitha

This research introduces the Neutrosophic Vendor-Buyer Economic Order Quantity (EOQ) model, integrating Neutrosophic Set Theory and Particle Swarm Optimization (PSO) for advanced inventory management. Addressing uncertainties in demand and costs, Neutrosophic Sets quantify truth, indeterminacy, and falsity degrees for key parameters. The model, employing PSO inspired by collective behaviour in nature, aims to minimize the combined total cost (C) encompassing vendor and buyer expenses. A grocery store scenario illustrates the approach, demonstrating substantial total cost reduction through the optimization of decision variables. MATLAB R2015a visualizations include a mesh plot depicting cost changes across varying EOQ and demand variability values, emphasizing optimal solutions. A bar chart compares initial and optimized total costs, showcasing efficiency gains. Cost breakdowns and pie charts detail the impact on vendor and buyer expenses. Sensitivity analysis systematically explores variable influences, aiding decision-makers in understanding trade-offs and optimal ranges by using Python. This comprehensive framework contributes empirical insights for practical implementation, enabling businesses to make informed decisions and enhance adaptive inventory strategies efficiently.

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Doi: https://doi.org/10.54216/IJNS.230414

Vol. 23 Issue. 4 PP. 181-193, (2024)

Single-Valued Pentapartitioned Neutrosophic Bi-Topological Spaces

Suman Das , Prasanna Poojary , Vadiraja Bhatta G. R. , Sunny Kumar Sharma

In this article, we present the notion of Single-Valued Pentapartitioned Neutrosophic Bi-Topological Space (SVPNBTS) as a generalization of Single-Valued Pentapartitioned Neutrosophic Topological Space (SVPNTS) and Neutrosophic Bi-Topological Space (NBTS). Besides, we study the different types of open set and closed set namely single-valued pentapartitioned neutrosophic bi-open set (SVPNBOS), single-valued pentapartitioned neutrosophic bi-closed set (SVPNBCS), single-valued pentapartitioned neutrosophic bi-semi-open set (SVPNBSOS), single-valued pentapartitioned neutrosophic bi-semi-closed set (SVPNBSCS), single-valued pentapartitioned neutrosophic bi-pre-open set (SVPNBPOS), single-valued pentapartitioned neutrosophic bi-pre-closed set (SVPNBPCS), single-valued pentapartitioned neutrosophic bi-b-open set (SVPNBb-OS), single-valued pentapartitioned neutrosophic bi-b-closed set (SVPNBb-CS), etc. via SVPNBTSs. Besides, we introduce the notion of pairwise SVPNOS, pairwise SVPNCS, pairwise SVPNSOS, pairwise SVPNSCS, pairwise SVPNPOS, pairwise SVPNPCS, pairwise SVPNb-OS, pairwise SVPNb-CS, and furnish few illustrative examples on them. Further, we investigate several properties of these classes of sets and prove some interesting results in the form of propositions, theorems, etc. via SVPNBTSs.

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Doi: https://doi.org/10.54216/IJNS.230415

Vol. 23 Issue. 4 PP. 194-205, (2024)

Algebraic properties applied to sin trigonometric complex neutrosophic sets

M. Palanikumar , Omaima alshanqiti

This article presents a new way of analyzing multiple attribute decision-making (MADM) using (â™­1, â™­2, â™­3) sin trigonometric complex neutrosophic sets (ST-CNS). Complex neutrosophic weighted averaging (ST-CNWA), sin trigonometric complex neutrosophic weighted geometric (ST-CNWG), sin trigonometric complex generalized neutrosophic weighted averaging (ST-CGNWA), and sin trigonometric complex generalized neutrosophic weighted geometric (ST-CGNWG). During our discussion, we presented an algorithm that utilized these operators. There are extensive numerical illustrations of score values. Furthermore, we will discuss commutativity, idempotency, and monotonicity of sin trigonometric complex neutrosophic sets as part of our discussion. It is easier, faster, and more convenient to find the best option this way. Consequently, the sin trigonometric complex (â™­1, â™­2, â™­3) is more closely related to precise conclusions. Also revealed by the study was an intriguing and fascinating observation.

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Doi: https://doi.org/10.54216/IJNS.230416

Vol. 23 Issue. 4 PP. 206-223, (2024)

A New Approach to Solve Transportation Problems Under Neutrosophic Environment

Vidhya , Uma Maheswari , Ganesan K.

The transportation problem has received a lot of attention in the field of operations research. In many circumstances, transportation planners may lack clear information on supply, demand, and transportation costs. Fuzzy sets can accept incomplete information by allowing for degrees of membership, which describe the level of certainty or uncertainty associated with each parameter. Three components—truth-membership, indeterminacy-membership, and falsity-membership degrees—are added to fuzzy numbers to create neutrosophic fuzzy numbers, which enables a more complex depiction of uncertainty. In this paper, we discuss the fuzzy transportation problem in a neutrosophic environment. Here the transportation costs, demands, and supplies are represented by neutrosophic trapezoidal fuzzy numbers. The neutrosophic trapezoidal fuzzy numbers are transformed into crisp numbers by using a ranking function and providing numerical examples to show the proposed method's efficiency to get the minimum optimal cost. Finally, we have demonstrated that our proposed method produced a better optimal solution to existing approaches by comparing its results to those of the existing ones.

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Doi: https://doi.org/10.54216/IJNS.230417

Vol. 23 Issue. 4 PP. 224-237, (2024)

On Developing He Method with Mohand Transform to Find Numerical and Exact Solutions of Some Neutrosophic Partial Differential Equations

Nawar Hazim Mohammed

In this paper, we propose a novel combination of the (He) method with (Mohand transform), and this combination is summarized by representing the nonlinear part (or the residue of the operator) with (He) polynomials after applying the Mohand transform. To prove the accuracy of the proposed method, we applied it to several neutrosophic partial differential equations such as neutrosophic version of Helmholtz equation, neutrosophic version of non-linear oscillator, neutrosophic version of Burger's equation, and the neutrosophic version of telegraph equation. The accuracy and effectiveness of the application of the proposed method was verified by comparing the results obtained with other methods using the Maple software package.

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Doi: https://doi.org/10.54216/IJNS.230418

Vol. 23 Issue. 4 PP. 238-243, (2024)

Multipolar neutrosophic subalgebras/ideals of UP-algebras

V. Rajam , N. Rajesh

The notion of neutrosophic m-polar fuzzy sets is much wider than the notion of m-polar fuzzy sets. In this paper, we apply the theory of neutrosophic m-polar fuzzy set on UP-algebras. We introduce the concepts of neutrosophic m-polar fuzzy subalgebras, neutrosophic m-polar fuzzy ideals and neutrosophic m-polar fuzzy strong ideals and some essential properties are discussed. We characterize neutrosophic m-polar fuzzy subalgebras in terms of fuzzy subalgebras and subalgebras of UP-algebras.

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Doi: https://doi.org/10.54216/IJNS.230419

Vol. 23 Issue. 4 PP. 244-257, (2024)

Application of the Neutrosophic TOPSIS for the Analysis of the Violation of Due Process in Ecuadorian Adolescents

Teresa De Jesús M. Guitérrez , Katherine T. Troya Terranova , Erick M. Vásquez Llerena

Due to the increase in violence in Ecuador involving juvenile offenders, an analysis of the situation is proposed from a neutrosophic approach to address the violation of due process in adolescents in Ecuador, highlighting the importance of considering the complexities and ambiguities of the juvenile penal system. Challenges are identified and classified through the PESTEL technique related to legal deficiencies, economic constraints, and socio-environmental factors contributing to juvenile delinquency, which are processed hermeneutically in a TOPSIS that uses single-valued neutrosophic numbers. The processing's main outcome is the influence of legal and economic aspects, thus the need to promote legal reforms, strengthen institutional capacities, invest in preventive programs, and support social reintegration and the responsible use of information technologies. The conclusions emphasize the importance of a comprehensive and coordinated approach to improve juvenile justice in Ecuador, ensuring respect for due process and the rights of adolescents.

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Doi: https://doi.org/10.54216/IJNS.230420

Vol. 23 Issue. 4 PP. 258-271, (2024)

New algebraic approach towards interval-valued neutrosophic cubic vague set based on subbisemiring over bisemiring

S. Selvaraj , Gharib Gharib , Abdallah Al-Husban , Maha Al Soudi , K. Lenin Muthu K. , Murugan Palanikumar , K. Sundareswari

We introduce the concept of an interval-valued neutrosophic cubic vague subbisemiring (IVNCVSBS), level sets of IVNCVSBS of a bisemiring. IVNCVSBSs are the new extension of neutrosophic subbisemirings and SBS over bisemirings. Let ℵ be a neutrosophic vague subset in $X$, we show that ℶ is a IVNCVSBS of X if and only if all non-empty level set is a SBS of X. Let ℵ be a IVNCVSBS of a bisemiring X and strongest cubic neutrosophic vague relation of X, we prove that ℵ is a IVNCVSBS of X × X. Let ℵ be any IVNCVSBS of X, prove that pseudo cubic neutrosophic vague coset is a IVNCVSBS of X. Let ℵ1, ℵ2,..., ℵn be the family of IVNCVSBS of X1, X2,..., Xn respectively. The homomorphic image of every IVNCVSBS is an IVNCVSBS. The homomorphic pre-image of every IVNCVSBS is an IVNCVSBS. Examples are provided to strengthen our results.

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Doi: https://doi.org/10.54216/IJNS.230421

Vol. 23 Issue. 4 PP. 272-292, (2024)

On Some Symbolic 2-Plithogenic and 3-Plithogenic Real Series

Oliver Von Shtawzen , Bahadir Tantay , Foziljonov Ibrohimjon

The objective of this paper is to study the expansion of symbolic 2-plithogenic and symbolic 3-plithogenic real functions in one variable with real series, where many famous expansions will be presented according to the Taylor series applied for symbolic plithogenic functions defined over symbolic plithogenic rings. Also, we provide many related examples to clarify and to explain the expansion method and properties.

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Doi: https://doi.org/10.54216/IJNS.230422

Vol. 23 Issue. 4 PP. 292-301, (2024)

Fusion of Expert Judgment using the Neutrosophic Delphi Method to Evaluate Tax Behavior

Ingrid Joselyne D. Basurto , Carmen Marina M. Cabrita , Pico P. Ermerly Espinosa , Tonguc Cagin

The tax behavior of taxpayers has gained increasing relevance in the economic and legal context of Ecuador. The tax system plays a fundamental role in the generation of income for the State and the financing of public policies. In this sense, understanding and evaluating how taxpayers comply with their tax obligations becomes crucial to guarantee equity and efficiency in tax collection. In this regard, the objective is to examine the various legal aspects that affect the compliance of tax obligations by taxpayers in the Babahoyo canton. The Neutrosophic Delphi method was used to model the study. As a result, it is seen that the tax authorities should promote educational campaigns in the canton for the knowledge and understanding of their citizens about the current regulations and thus strengthen the tax system for the benefit of the economic and social development of the country.

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Doi: https://doi.org/10.54216/IJNS.230423

Vol. 23 Issue. 4 PP. 302-307, (2024)

Fuzzy Parameterized Single-Valued Neutrosophic Subset based Artificial Intelligence for Sustainable Financial Crisis Prediction and Green Finance

Adam Mohamed Omer , Fadoua Kouki , Adeeb Alhebri , Radwan Hussien Alkebssi , Ebrahim Mohammed Al-Matari

Predicting sustainable financial crises and promoting green finance are paramount in fast developing economic landscape. Leveraging advanced AI-driven technologies, such as Neutrosophic logic, enables a nuanced understanding of complex sustainability factors influencing financial markets. By incorporating these advanced technologies, organizations can proactively mitigate and identify risks related to unsustainable practices while fostering investment aligned with environmental, social, and governance (ESG) principles. This proactive stance improves financial resilience and contributes to the transition towards a resilient and more sustainable financial ecosystem. We can navigate future challenges with foresight and responsibility through the synergy of sustainable financial crisis prediction and green finance initiatives, which ensures a prosperous and environmentally conscious financial future for the generation to come. This study develops a new optimal Fuzzy Parameterized Single-Valued Neutrosophic Subset for financial crisis prediction and green finance (OFPSVNS-FCPGF) technique. The OFPSVNS-FCPGF technique intends to recognize the presence of the financial disaster in the sustainable and green finance sector. In the OFPSVNS-FCPGF technique, Z-score normalization is primarily used to measure the economic data into a beneficial layout. For the procedure of prediction, the OFPSVNS-FCPGF approach designs the FPSVNS approach which detects the occurrence of financial crises or not. Furthermore, the parameter tuning of the FPSVNS technique takes place utilizing the grasshopper optimization algorithm (GOA). To illustrate the improved FCP outcomes of the OFPSVNS-FCPGF model, a series of simulations were involved. An wide comparison study specified that the OFPSVNS-FCPGF method gains significant outcomes in the green finance sector.

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Doi: https://doi.org/10.54216/IJNS.230424

Vol. 23 Issue. 4 PP. 308-322, (2024)

Neutrosophic Fuzzy Simple Additive Weighting with Artificial Intelligence for Sustainable Heart Disease Recognition and Classification

Ahmedia Musa M. Ibrahim , Mohammed M. A. Almazah , Badr Eldeen A. A. Abouzeed , Murtada K. Abdalla Abdelmahmod

Heart disease (HD) is considered the main cause of death rate around the world. Multiple systems and biomedical instruments in hospitals take large amounts of medical data. Thus, understanding the data linked with HD is vital to enhance the prediction performance. The timely intervention of HD is the most important factor in preventing patients from additional damage. In recent times, non-invasive medical procedures, including artificial intelligence-based approaches have been used in the healthcare sector. Particularly machine learning (ML) applies various techniques and algorithms that are extensively applied and are especially effective in accurately detecting HDs within short period. However, HD prediction is a challenging task. The largest size of medicinal database has made it a challenge for clinicians to understand the complicated feature relations and make disease predictions. Therefore, this study presents a Neutrosophic Fuzzy SAW with Artificial Intelligence for Sustainable Heart Disease Recognition and Classification (NFSAW-AISHDC) technique in Healthcare Sector. The NFSAW-AISHDC technique mainly focuses on the adoption of neutrosophic fuzzy simple additive weighting (NFSAW) with feature selection process for HD detection. The NFSAW-AISHDC method exploits min-max scalar to scale the input medical data. For feature selection, the NFSAW-AISHDC method uses beluga whale optimization (BWO) algorithm to choose feature subsets. Moreover, the NFSAW-AISHDC technique applies NFSAW approach to the identification of HDs. The performance values of the NFSAW-AISHDC methodology undergoes using benchmark database. The experimental outcome underlined the promising results of the NFSAW-AISHDC method with other models.

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Doi: https://doi.org/10.54216/IJNS.230425

Vol. 23 Issue. 4 PP. 323-336, (2024)

Safeguarding Financial Integrity with Interval-Valued Neutrosophic Analytic Hierarchy Process for Sustainable Accounting Systems

Adeeb Alhebri

Nowadays, financial integrity within sustainable accounting systems is critical endeavor in ensuring intricate landscape of sustainable finance. Detection of financial fraud within sustainable accounting systems is crucial for upholding environmental, social, and governance (ESG) standards and sustaining the integrity of financial practices. Leveraging advanced AI-driven technologies, these systems can effectively analyze abundance of financial data to detect suspicious patterns and anomalies indicative of fraudulent activities. Incorporating Neutrosophic logic into sustainable accounting systems improves the efficiency of financial fraud detection by accommodating inherent uncertainty in complex financial data. By leveraging this ground-breaking technology, organizations can effectively navigate the complex financial landscape while ensuring the integrity of their accounting practices. Neutrosophic logic facilitates the modelling of contradictory and ambiguous information, enabling more nuanced detection and analysis of fraudulent activities that may remain unnoticed. This study develops an automated financial fraud detection using improved sparrow search algorithm with Interval-Valued Neutrosophic Analytic Hierarchy Process (ISSA-IVNAHP) technique. The ISSA-IVNAHP technique aims to protect financial integrity via the identification of financial frauds in Sustainable Accounting Systems. The ISSA-IVNAHP technique incorporates a two-stage process. Initially, the ISSA-IVNAHP method designs ISSA-based feature subset selection approach for the optimal feature selection. Next, in the second stage, the ISSA-IVNAHP technique uses IVNAHP technique for decision-making process that enables to detection of the presence and absence of financial fraud. The simulation results of the ISSA-IVNAHP technique can be examined on financial fraud database. The experimental values reported that the ISSA-IVNAHP methodology attains maximum effeciency over other models

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Doi: https://doi.org/10.54216/IJNS.230426

Vol. 23 Issue. 4 PP. 337-349, (2024)

On Certain Algebraic Properties of Symbolic 3-Plithogenic Real Square Matrices

P. Prabakaran , Bilal Abdallah , Turayeva Dinara Tulkunovna

The main objective of this article is to study the inverse of invertible symbolic 3-plithogenic real square matrices using the concept of adjoints and characteristic polynomials. Also, the symbolic 3-plithogenic version of Cayley-Hamilton theorem was proved and provided enough examples to enhance understanding.

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Doi: https://doi.org/10.54216/IJNS.230427

Vol. 23 Issue. 4 PP. 350-357, (2024)

On neutrosophic N-deductive systems of Hilbert algebras

Aiyared Iampan , N. Rajesh

The notion of neutrosophic N-deductive systems of Hilbert algebras is introduced, and several properties are investigated. Conditions for neutrosophic N-structures to be neutrosophic N-deductive systems of Hilbert algebras are provided. Relations between neutrosophic N-deductive systems and their level subsets are considered. The Cartesian product of neutrosophic N-structures is also supplied. Finally, we also find the property of the homomorphic pre-image of neutrosophic N-deductive systems.

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Doi: https://doi.org/10.54216/IJNS.230429

Vol. 23 Issue. 4 PP. 358-368, (2024)

On the Geometry of Weak Fuzzy Complex Numbers and Applications to the Classification of Some A-Curves

Abdallah Shihadeh , Wael Mahmoud M. Salameh , Malik Bataineh , Hassan Al-Tarawneh , Ayman Alahmade , Abdallah Al-Husban

The concept of A-curves is considered as a novel application of real field extensions in solving some algebraic vectorial equations defined by Euclidean norms. In this paper, we present a novel insight through the classification of A-curves by illustrating many new semi-module isomorphisms between the direct product of weak fuzzy complex numbers with itself and the direct product of classical Euclidean vector spaces multiplied by itself. These isomorphisms will give us a full classification of A-curves that are related to weak fuzzy complex ring. Also, we provide many examples to explain the contribution of our work.

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Doi: https://doi.org/10.54216/IJNS.230428

Vol. 23 Issue. 4 PP. 369-375, (2024)

An Algebraic Approach to the Symbolic 5-Plithogenic Vector Spaces

Sara Sawalmeh , Cuauhtemoc Samaniego , Khakimova Khulkar Khamitovna

The objective of this paper is to study for the first time the concept of symbolic 5-plithogenic vector space defined over symbolic 5-plithogenic field. Many results about the algebraic properties of this class of spaces will be obtained, where we define AH-subspaces, AH-linear transformations, and kernels. Also, we study the inner products defined over symbolic 5-plithogenic vector spaces and determine the conditions of orthogonality in these spaces with many interesting examples.

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Doi: https://doi.org/10.54216/IJNS.230430

Vol. 23 Issue. 4 PP. 376-385, (2024)

An Effective Algorithm for Solving Weak Fuzzy Complex Diophantine Equations in Two Variables

Mayada Abualhomos , Wael Mahmoud M. Salameh , Malik Bataineh , Mowafaq Omar Al-Qadri , Ayman Alahmade , Abdallah Al-Husban

Weak fuzzy complex numbers are defined as , with  as an extension of real numbers with . This paper is dedicated to studying weak fuzzy complex linear Diophantine equations in two weak fuzzy complex variables, by transforming the weak fuzzy complex Diophantine equation to a classical equivalent Diophantine system and going directly from the solutions of classical system into the desired equation. Algorithms for generating solutions of the previous equation will be presented in terms of theorems with many related examples that clarify the validity of our work.

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Doi: https://doi.org/10.54216/IJNS.230431

Vol. 23 Issue. 4 PP. 386-394, (2024)

Fuzzy Metric Space of Weak Fuzzy Complex Numbers and Plithogenic Metric Spaces

Hazim M. Wali Al-Tameemi

The main goal of this work is to define for the first time the concept of the metric space of weak fuzzy complex numbers, where we present a suitable metric defined over the ring of weak fuzzy complex numbers, and we study the open balls, closed balls, and torus generated from its structure. On the other hand, we study the symbolic 2-plithogenic and 3-plithogenic/4-plithogenic metric space and its ability to be generated from classical metrics, with many interesting properties related to its analytical structure. Also, many examples will be illustrated to clarify and explain the novelty of this work.

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Doi: https://doi.org/10.54216/IJNS.230432

Vol. 23 Issue. 4 PP. 395-404, (2024)

Information Fusion for the Training of Public Administrators: Design of a Composite Indicator through the Integration of AHP and TOPSIS Methods

Noel Batista Hernández , Katherine E. Prieto Izquierdo , Denisse M. Valle Rodríguez , Adam Marks

The article addresses the importance of capacity development among public administrators to ensure the efficient functioning of the state and the provision of quality services to the citizenry. This entails acquiring legal knowledge, ethical principles, and technical skills in areas such as strategic planning, financial management, and policy evaluation. In addressing the evaluation of public administrators' training programs, the Analytic Hierarchy Process (AHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) methods are employed. The methodology delineates the fundamental concepts and key equations to understand the application of these methods in evaluating public administrators' training programs. The findings underscore the significance of specific competencies in public administrators' training. These competencies, combined with comprehensive training encompassing cognitive, attitudinal, and instrumental dimensions, can equip professionals to confront current governmental challenges effectively. The article emphasizes the relevance of capacity development among public administrators and introduces methods such as AHP and TOPSIS to assess and enhance training programs in this field, aiming to bolster the state's capacity to respond efficiently to societal needs.

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Doi: https://doi.org/10.54216/IJNS.230433

Vol. 23 Issue. 4 PP. 405-414, (2024)

Optimal Single-Valued Neutrosophic Sine Trigonometric Aggregation Operators for Accurate Financial Fraud Detection Model

Fadoua Kouki

Financial fraud may be regarded as any fraud targeting financial organisations including crypto exchanges, banks, fintech, and lending organizations, or any criminal activity associated with the payment process. Financial fraud detection cites protocol set prepared to circumvent the destruction produced by fraudulent activities happening in financial service suppliers. Ecological financial fraud detection (FD) includes the usage of ethical and sustainable performs within fraud actions recognition from the financial area. In recent times, DL and ML techniques have been used in CCF recognition owing to their ability to construct a robust mechanism to discover fraud businesses. Therefore, this study develops an Optimal Single Valued Neutrosophic Sine Trigonometric Aggregation Operator (O-SVNSTAO) for Accurate Financial Fraud Detection Model. The genetic-inspired particle swarm optimization (GIPSO) feature selection model efficiently discerns the relevant attribute from sophisticated financial databases, improving the model's discriminative power while alleviating dimensionality problems. Consequently, the SVNSTAO classifier leverages the features selected to discern complicated features inherent in fraudulent actions, which facilitates accurate diagnosis. Moreover, the COA parameter tuning mechanism enhances the SVNSTAO model's parameter, which ensures adaptability and optimum performance to varied fraud settings. Empirical analysis of real-time financial datasets demonstrates the superiority of O-SVNSTAO technique over classical methods, underlining its effectiveness in discovering financial fraud with exceptional efficiency and reliability

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Doi: https://doi.org/10.54216/IJNS.230434

Vol. 23 Issue. 4 PP. 415-425, (2024)

Arithmetic Optimization Algorithm with Adaptive Neuro-Fuzzy Interference System for Predicting Financial Crisis

Fadoua Kouki

Financial technology (Fintech) is paramount in driving advanced technologies, economies, society, and several other sectors. Smart Fintech is the new-generation Fintech, primarily stimulated and endowed by compuational technology. Smart Fintech syndicates DSAI and renovates economies and finance for dynamic, smart, customized, automated services and systems, economies and financial companies, and the industry. The strength and development of the country’s economies are assessed by the correct forecasting. Financial crisis prediction (FCP) has the substantial consequence on the economies. Previous studies mainly emphasise statistical, DL, and ML methodologies for predicting the financial well-being of the business. Therefore, this article develops a new Arithmetic Optimization Algorithm with Adaptive Neuro-Fuzzy Interference System (AOA-ANFIS) technique for Predicting Financial Crisis. The presented AOA-ANFIS technique aims to predict the presence of financial crises or not. The model incorporates three major elements: Arithmetic Optimization Algorithm (AOA) for feature selection, Adaptive Neuro-Fuzzy Inference System (ANFIS) as the classification algorithm, and Bat Optimization Algorithm (BOA) for parameter tuning. The AOA feature selection model effectively detects the important attributes from a large proportion of financial indicators, augmenting the model's prediction capability while decreasing computational difficulty. Subsequently, the ANFIS classifier exploits the features selected for capturing the intricate non-linear relations intrinsic in financial data, permitting accurate crisis calculation. Additionally, the BOA parameter tuning model augments the ANFIS model's parameters, ensuring robustness and optimum performance. Experimental outcomes on varied financial databases validate the higher efficiency of the AOA-ANFIS technique over underlying processes, demonstrating its effectiveness in forecasting financial crises with great reliability and precision.

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Doi: https://doi.org/10.54216/IJNS.230435

Vol. 23 Issue. 4 PP. 426-438, (2024)