International Journal of Neutrosophic Science

In this paper, we study the two-fold algebra based on the n-standard fuzzy number theoretical system as a special type of two-fold fuzzy algebras, where we study the elementary properties of the algebraic operations defined over this system. Also, we prove many results that describe the relations between two-fold substructures and sub-algebras defined by fuzzy number theoretical systems. On the other hand, we provide many different examples to explain our results.

The breakthrough technologies of the Internet of Things (IoT) have modernized classical Consumer Electronics (CE) into next-generation CE with high intelligence and connectivity. This connectivity amongst appliances, actuators, sensors, etc., offers automated control in CE and enables better data availability. However, the data traffic has been exponentially increased owing to its decentralization, diversity, and increasing number of CE devices. Furthermore, the static network-based approaches need exclusive management and manual configuration of CE devices.  The generalization of a Neutrosophic Hypersoft Set (NHSS) is a concept of a soft set. This architecture is a mixture of neutrosophic sets with hypersoft sets. Therefore, the study introduce a Blockchain with Single-Valued Neutrosophic Hypersoft Sets Assisted Threat Detection (BCSVNHS-TD) technique for Secure IoT Assisted CE. The presented BCSVNHS-TD technique applies BC technology for secure communication among CEs. For threat detection, the BCSVNHS-TD method introduces the SVNHS model. Also, the parameter selection of the SVNHS method takes place using the chicken swarm optimization (CSO) technique. An extensive set of tests was involved for exhibiting the better effiency of the BCSVNHS-TD method. The experimental results emphasized that the BCSVNHS-TD method reaches optimal results over other techniques  

Due to the rapid increase in population density, medical sciences now face a major challenge in the automated detection of diseases. Intelligent system assists health personnel in earlier disease diagnosis and provides reliable treatment to reduce the fatality rates. Skin cancer is one of the most severe and deadliest kinds of cancer. A health professional uses dermoscopic images to manually diagnose skin tumors. This technique can be time-consuming and labor-intensive and needs a considerable level of expertise. The automatic recognition method is essential for the earlier diagnosis of skin tumors. In recent times, N-soft Set model has become widespread, which is a generalization of fuzzy set where all the elements have a membership value in the complement (0 to 1) and in the set (0 or 1). This study presents a Skin Cancer Diagnosis using Cubic Pythagorean Fuzzy Hypersoft Set (SCD-CPFHSS) technique. The presented SCD-CPFHSS technique performs identification of skin cancer using the application of NSs and metaheuristic algorithms. In the SCD-CPFHSS technique, neural architectural search network (NASNet) model derives feature extractors from the dermoscopic image. In addition, the efficacy of the NASNet model can be boosted by the design of salp swarm algorithm (SSA). For skin cancer recognition, the SCD-CPFHSS technique applies CPFHSS model. The experimental outcome of the SCD-CPFHSS methodology was validated using medical dataset. The extensive results pointed out that the SCD-CPFHSS technique reaches better results on skin cancer diagnosis  

Beurling (or generalized) prime system has been defined by Arne Beurling in 1937, and several couthers have been working on this during the last century. This work focuses on addressing some concrete examples of an outer generalized prime system involving Beurling zeta function. The core of this work is to create a discrete generalized prime system under a fixed condition to give a new upper bound for Beurling zeta function.

In this paper, we present the topological space of intervals based neutrosophic real numbers , where we clarify how neutrosophic real intervals can be expressed according to the neutrosophic partial order relation, and we use these intervals to build a topological space. On the other hand, we use a similar argument to build a topological space over the intervals of refined neutrosophic numbers, with many illustrated and related examples on open and closed sets.    

Diabetic retinopathy (DR) is an eye disorder triggered by diabetes that might result in loss of sight. Earlier diagnosis of DR is critical since it might cause loss of sight. Manual diagnoses of DR severity by ophthalmologists are time-consuming and challenging. As a result, there has been considerable attention on designing an automatic technique for DR detection using fundus photographs. In medical science, prognosis and diagnosis are the most challenging tasks due to the presence of fuzziness in medical images and the restricted subjectivity of the experts. Neutrosophic Set (NS) in medical image analysis provides an understanding of the NS concepts, together with knowledge of how to collect, handle, interpret, and analyze clinical images using NS techniques. The neutrosophic set (NS), which is a generality of fuzzy set, provides the overcoming prospect of the restriction of fuzzy-based models for the analysis of medical images. This manuscript develops a Robust Diabetic Retinopathy Detection and Grading using Neutrosophic Topological Vector Space (DRDG-NSTVS) technique on fundus images. The DRDG-NSTVS technique begins with Median Filter (MF) noise removal to optimize the clarity of fundus photographs by successfully eliminating noises. Later, the InceptionV3 is used to perform feature extraction for identifying complicated features and patterns related to DR. The parameter tuning is performed by the moth flame optimization (MFO) technique to ensure superior performance of the model. The final diagnoses and classification of DR are accomplished utilizing the NSTVS classifiers that easily perform the uncertainties inherent in medicinal statistics. The simulation was conducted on a benchmark dataset to examine the proposed model performance. This combined method gives a greatly reliable and accurate solution for the earlier diagnosis and detection of DR

Neutrosophic fuzzy logic (NFL) is a prolongation of classical FL that integrates the neutrosophic conception that handles the indeterminacy concept. This method offers a more comprehensive and flexible architecture to handle inconsistent, uncertain, and indeterminate data, which makes it especially helpful in complicated reasoning and decision-making scenarios where classical FL might be defeated. A learning scheme, which is made from the internet and computer as the main components, is called as an e-learning platform. Although the training might happen on or off campuses, utilizing the internet is an integral part of online learning. In the meantime, to significantly augment the education standard, it is essential to forecast the learning style of the user through supervision and feedback. Nonetheless, it averts the intrinsic relationship amongst e-learning behaviors. There might be technological difficulty ranging from network connectivity issue to users memorizing their username and password while executing and developing an educational program. The learning style prediction in e-learning network is complex one and therefore we recommend a new methodology which employs web mining method for the feature extraction and log files of students from the e-learning network. This study develops an Automated Learning Style Prediction using Weighted Neutrosophic Fuzzy Soft Rough Sets (ALST-WNSFSRS) technique in E-learning Platform. The ALST-WNSFSRS technique mainly aims for the prediction of automated learning styles. Initially, the information is gathered from the Kaggle websites and utilizing a web mining method the feature from the web and log files are pre-processed. The preprocessed information is scrutinized to discover the pattern of approach to learning and later investigated the pattern. Then, the feature patterns are clustered by the fuzzy c-means (FCM) clustering technique and later utilizing the WNSFSRS method, the approach to students learning is anticipated. To improve the performance of the WNSFSRS technique, glowworm swarm optimization (GSO) algorithm is used. The performance of the ALST-WNSFSRS technique is compared with existing models and the results reported the supremacy of the ALST-WNSFSRS technique interms of different measures  

In the financial industry, financial fraud is an ever-evolving risk with extreme consequences. Data mining has been instrumental in the recognition of credit card fraud (CCF) during online transactions. CCF recognition, which is a data mining problem, become a challenge owing to its two main reasons - firstly, the profiles of fraudulent and normal behaviors modify continually and then, CCF dataset is extremely lopsided. The implementation of fraud recognition in credit card transactions is tremendously influenced by the sampling methodology on data, detection approach and variable selection utilized. The conception of the neutrosophic hypersoft set (NHSS) is a parameterized family that handles the sub-attributes of the parameter and is an appropriate extension of the NHSS to correctly evaluate the uncertainty, deficiencies, and anxiety in decision-making. In comparison to previous research, NHSS can accommodate additional uncertainty, which is the crucial approach to describe fuzzy datasets in the decision-making algorithm. This study introduces an Automated Credit Card Risk Assessment using Fuzzy Parameterized Neutrosophic Hypersoft Expert Set (ACCRA-FPNHES) technique. In the ACCRA-FPNHES technique, a three-step process is involved. As a primary step, the ACCRA-FPNHES technique designs sparrow search algorithm (SSA) for choosing features. In the second step, the detection of CCF takes place using FPNHES technique. Finally, in the third step, the parameters related to the FPNHES technique can be adjusted by arithmetic optimization algorithm (AOA). The simulation validation of the ACCRA-FPNHES technique can be studied on credit card dataset. The obtained values indicate that the ACCRA-FPNHES technique showcases better performance

In the domain of optimization, linear programming (LP) is recognized as an exceptionally effective method for ensuring the most favorable outcomes. Within the context of LP, the minimum cost flow (MCF) problem is fundamental, with its primary objective being to reduce the transportation costs for a single item moving through a network, under the constraints related to capacity. This network is made up of supply nodes, directed arcs, and demand nodes and each arc has an associated cost and capacity constraint, these factors are certain. However, in practical scenarios, these factors are susceptible to variation due to causal uncertainty. The neutrosophic set theory has surfaced as a challenging approach to tackle the uncertainty that is often encountered in optimization processes. In this manuscript, our primary objective is to address the minimal cost flow (MCF) problem while accounting for the uncertainty inherent in the neutrosophic set. We specifically focus on the cost aspect as SVTN numbers and introduce a new approach based on a customized ranking function handmade for the MCF problem a pioneering endeavor within the field of neutrosophic sets. Additionally, we present numerical example to validate the effectiveness and robustness of our model.  

In the field of survival analysis, the inverse Gompertz distribution is used to mimic human lifetime data patterns. The goal of the neutrosophic inverse Gompertz distribution (NIGD) is to describe a range of indeterminate survival data. The defined distribution is very helpful for modeling somewhat positively skewed unknown data. The main statistical characteristics of the created NIGD, such as the neutrosophic moments, hazard rate, and survival function, are covered in this paper. Additionally, the well-known maximum likelihood estimation method is used to estimate the neutrosophic parameters. A simulation study is conducted to see whether the projected neutrosophic parameters were reached. Not to mention that possible real-world uses of NIGD have been discussed using actual data. To show how well the suggested model performed in comparison to the present distributions, real data were used.  

COVID19 otherwise called Severe Acute Respiratory Syndrome Corona virus-2 is an infectious illness. Another transmittable infection called Pneumonia is mainly attributable to infection because of bacteria in the alveoli of the lungs. Once a diseased lung tissue has infection, it elevates excretion in it. Specialists conduct health examinations and identify the patient through ultrasound, biopsy, or Chest X-ray of lungs to identify whether the patient has these diseases. Incorrect treatment, misdiagnosis, and if the disease was disregarded will result in the fatality. The development of Deep Learning and neutrosophic set (NS) supports the decision-making procedure of professionals to identify patients with this disease. NS is a prolongation of the fuzzy set and classical theories. The NS determines three memberships such as T, I and F. T, I, and F display the degree of truth, the false, and the indeterminacy membership, correspondingly. This enables a more nuanced representation of contradiction, uncertainty, and ambiguity within the dataset, allowing superior handling of imprecise and complex data. This study develops a new Deep learning with Neutrosophic Set-Based k-Nearest Neighbors Classifier for disease detection (DLNSKNN-DD) technique. The major purpose of the DLNSKNN-DD method is to identify the existence of virus pneumonia and COVID-19. In the DLNSKNN-DD technique, the feature extraction from the medical images is carried out by residual network (ResNet50v2). Moreover, the parameter tuning of the ResNetv2 model is done using Adadelta optimizer. The DLNSKNN-DD technique exploits NSKNN model for classification purposes. The performance evaluation of the DLNSKNN-DD algorithm can be assessed on medicinal image dataset. The experimental outcomes underlined the effectual recognition results of the DLNSKNN-DD technique on the identification of diseases  

The swift development in social media through the internet produces vast data in a real-time scenario that has startling effects on large datasets. It generated the high-level use of sentiments and emotions in social networking media. Sentiment analysis (SA) using a neutrosophic set presents a new technique to handle the integral ambiguity and uncertainty in text datasets. Different from classical approaches, which categorize sentiment as positive, negative, or neutral, the neutrosophic set allows for the comparison analysis of truth-, indeterminacy-, and falsie-membership functions for all the sentiments. This allows a more flexible and nuanced representation of sentiments, which accommodates the contradictions and complexities commonly depicted in natural language. SA can accomplish high performance and depth in interpreting and understanding the emotions expressed in uncertain and diverse text datasets by leveraging a neutrosophic set. This manuscript presents a Neutrosophic Vague N-Soft set with a Chimp Optimization Algorithm for Sentiment Analysis (NVNSS-COASA) technique on Social Media. The NVNSS-COASA technique is initiated by the comprehensive preprocessing stage to normalize and clean the text dataset, which ensures superior input for the succeeding stage. Then, the Term Frequency-Inverse Document Frequency (TF-IDF) mechanism is employed to convert the preprocessed text into mathematical features, which capture the word importance in terms of datasets. Subsequently, a strong NVNSS classifier is employed for accurately categorizing the sentiment. We integrate COA for the parameter tuning to further improve the performance of the method. The simulation outcomes emphasized that the NVNSS-COASA method shows superior outcomes over other techniques. The outcomes indicated that the NVNSS-COASA can able to deliver reliable and precise insights from the text dataset.

Network security is any endeavor intended to defend the integrity and usability of the data and network. Fast development in network technology and the scope and amount of information transported on a network is gradually growing. Based on these situations, the complexity and density of cyber-attacks and threats are also increasing. The constantly expanding connectivity makes it more difficult for cyber-security specialists to monitor all the movements on the network. More complex and frequent cyber-attack makes anomaly identification and detection in network events challenging. Machine learning (ML) provides different techniques and tools to automate cyber-attack detection and for prompt prognosis and analysis of attack types. The model of a neutrosophic hypersoft set (NHSS) is a combination of a neutrosophic set with a hypersoft set. It is a useful structure to handle multi-objective problems and multi-attributes with disjoint attributable values. This study derives the Possibility Neutrosophic Hypersoft Set for Cyberattack Detection (pNHSS-CAD) technique to improve network security. The pNHSS-CAD method has its formation in feature selection with the Whale Optimization Algorithm (WOA), which successfully recognizes the important features from the data, thus improving processing speed and reducing dimensionality. Following feature selection, the pNHs-set classifier is employed for the robust detection and identification of cyber-attacks, which leverages the power of the neutrosophic set to deal with ambiguity and uncertainty in the information. The Firefly (FF) technique is applied for hyperparameter fine-tuning, which ensures the model operates at maximum effectiveness to enhance the performance of the classification. This wide-ranging method leads to a very efficient cyberattack recognition method, which can able to accurately mitigate and identify risks in the real world

In this paper, we present the topological space of intervals based symbolic m-plithogenic real numbers of orders between 2 and 5, where we clarify how m-plithogenic real intervals can be expressed according to the symbolic plithogenic partial order relation, and we use these intervals to build a topological space. On the other hand, many illustrated and related examples on open and closed sets will be provided to explain the validity of our approach.    

The Decision-Making Trial and Evaluation Laboratory (DEMATEL) approach is commonly used in examining and illustrating the relationship between different factors in a complex system. This paper proposes a novel approach that integrates the Bipolar neutrosophic Dombi-based IGWHM operator into the DEMATEL method, in which the criteria are analyzed by means of the cause-and-effect relationship diagram. The current studies on the classical DEMATEL approach have some limitations on the aggregation process, particularly in capturing the interrelationship of individual arguments by assessing their impact on each other within a complex system. To enhance the aggregation of complex information in the decision-making framework, the Bipolar neutrosophic Dombi-based Improved Generalized Weighted Heronian mean (IGWHM) operators are employed. The applicability and effectiveness of the proposed approach are demonstrated when solving a selection of transport service providers. The ability of the method to highlight the intricate interdependencies and ranking criteria based on their importance. The sensitivity of the developed approach is observed with variations in the involved parameter. Moreover, a comparative analysis is made with other methods to demonstrate its validity.